Probable Justice: Risk, Insurance, and the Welfare State 9780226731094

Citation preview

Probable Justice

Probable Justice Risk, Insurance, and the Welfare State

RACHEL Z. FRIEDMAN

The University of Chicago Press Chicago and London

The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2020 by The University of Chicago All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations in critical articles and reviews. For more information, contact the University of Chicago Press, 1427 E. 60th St., Chicago, IL 60637. Published 2020 Printed in the United States of America 29 28 27 26 25 24 23 22 21 20

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ISBN-13: 978-0-226-73076-9 (cloth) ISBN-13: 978-0-226-73093-6 (paper) ISBN-13: 978-0-226-73109-4 (e-book) DOI: https://doi.org/10.7208/chicago/9780226731094.001.0001 Library of Congress Cataloging-in-Publication Data Names: Friedman, Rachel Z., author. Title: Probable justice : risk, insurance, and the welfare state / Rachel Z. Friedman. Description: Chicago : University of Chicago Press, 2020. | Includes bibliographical references and index. Identifiers: LCCN 2020005335 | ISBN 9780226730769 (cloth) | ISBN 9780226730936 (paperback) | ISBN 9780226731094 (ebook) Subjects: LCSH: Social security—United States. | Welfare state—United States. | Risk—United States. | Probabilities. Classification: LCC HD7125 .F754 2020 | DDC 361.973—dc23 LC record available at https://lccn.loc.gov/2020005335 This paper meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).

CONTENTS

Preface / ix INTRODUCTION

/1

Out of Many, One / 2 Justice and Chance / 4 The Character of Probability / 6 The Context of This Work / 7 The Approach of the Project / 10 Overview of the Argument / 12 A Qualified Defense / 15 ONE

/ The Origins of Risk and the Growth of Insurance / 17 Insurance: A Brief Primer / 18 The Early History of Modern Insurance / 21 Pre-insurance Practices / 21 The Emergence of Premium Insurance / 22 The Theory and Practice of Early Marine Insurance / 24

Probability Theory and the Doctrine of Aleatory Contracts / 25 The Legal Background of Early Probability Theory / 25 Probabilistic Justice / 27 Equipossibility and the Distributive Turn / 29

Life Insurance and Probabilistic Justice / 33 Equity in Empirical Probability Theory / 34 The Birth of Statistical Life Insurance / 39 Mutualism with and without Risk / 42 T WO

/ Probabilistic Justice and the Beginnings of Social Insurance / 45 Precursors to Social Insurance / 48 Social Insurance and the Liberal Idea / 48

vi / Contents Richard Price: Property and Political Arithmetic / 51 Friendly Society Reform: Social Insurance Writ Small / 57

The First Social Insurance Plans: Mutual Insurance Writ Large / 61 Early Proposals / 61 Condorcet: Probability and Perfectibility / 63 Thomas Paine: Welfare without Insurance / 65 THREE

/ The Promise of Probability / 69

The Practical Aims of Late-Classical Probability / 71 Inverse Probability / 71 Epistemic Equiprobability / 75

Between Individual Choice and Social Responsibility / 77 A New Rationale and Its Challenges / 78 Mathematical and Moral Expectation / 83 A Social Duty to Insure? / 86

Social Insurance in Theory and in Practice / 89 Mutualism with and without Risk, Revisited / 91 Causal Laws and Rational Planners / 94 A Social Insurance Moment / 98 FOUR

/ The Collectivization of Risk and the Early Welfare States / 105 The Rise of the Collective View of Chance / 106 A New Interpretation of Probability / 106 A Modified Case for Insurance / 110 The Ethical Character of Frequentist Probability / 114 Frequentist Social Welfare / 119

Risk in the Early Welfare States / 121 The Question of Responsibility / 123 The Subjects and Targets of Social Policy / 127 The Flexible Actuarialism of Early Social Insurance / 130 FIVE

/ The Egalitarian Welfare State and the Ambiguities of Insurance / 138 The Egalitarian Welfare State Emerges / 140

The Centrality of Insurance to Postwar Egalitarian Welfare / 140 The Amorphous Appeal of Insurance / 142 The Limits of Universal Social Insurance / 145

Subjective Probability and the Personalization of Chance / 148 Keynes’s Transitional Account / 148 The Rise of the Subjectivist View / 153 The Moral Character of Subjective Probability / 155

Contents / vii The Egalitarian Welfare State without Probability / 159 Probability versus Justice / 159 Rawls and Social Insurance without Risk / 161 The Persistence of Probability / 163 Insurance and Distributive Theory after Rawls / 165

The Fate of Social Insurance in the Twentieth Century and Beyond / 168 The Problem of Polarization / 168 The Impact of Information / 169 CONCLUSION

/ 173

The Long-Standing Appeal of Insurance / 173 Explaining the Welfare State / 175 The Limits of Social Insurance / 177 A Contemporary Example / 179

Acknowledgments / 183 Notes / 185 Index / 245

P R E FAC E

As this book went to press, the global crisis caused by the COVID-19 virus was unfolding around the world. Many economies had come to a near halt, as businesses, schools, and universities closed their doors to reduce the spread of the disease. Public health systems faced unprecedented demands, as many hospitals found themselves overwhelmed with patients and undersupplied with equipment and staff. The crisis is likely to have a serious impact on welfare states and on their social insurance programs in particular. While it is still far too early to meaningfully predict these longterm effects, two observations stand out as relevant to the historical and theoretical study that follows. First, the speed with which many states turned to their social insurance systems to alleviate some of the economic burdens of the pandemic confirms how central these institutions are and how, at least in a state of emergency, they are able to generate consensus even in politically polarized environments. Within weeks of the outbreak, numerous governments had resolved to use their unemployment insurance schemes to help the rapidly rising number of those out of work. Some also adjusted sickness- and parental-leave benefits to enable workers to stay home without losing their livelihoods. Whether all these policies were wisely formulated, and will be judiciously financed, remains to be seen. Yet the fact that so many governments immediately turned to social insurance speaks to its salience and relative adaptability to the economic consequences of new hazards. Second, this crisis has illustrated some of the persistent challenges of probabilistic reasoning in public life. The pandemic took most governments, healthcare providers, and individuals by surprise, unprepared for the far-reaching toll it would take. Even as the crisis reached global proportions, it took time for leaders and citizens to react, due to the inevitable difficulties of anticipating its progression and to individuals’ reluctance

x / Preface

to change their behavior. It appears that two developments have in turn helped governments begin to manage the spread of the disease. The first is their ability to collect and analyze information about how and to whom it is likely to spread. The second is the perception of uncertainty among individuals, and especially the recognition that we still know relatively little about how the virus affects different groups or categories of people. Having set in, this recognition thrust people around the world into a rare experience of shared vulnerability, as the illness took its toll with little apparent regard for the distinctions that usually set us apart. In such moments, we are more inclined to look to governments to guide our choices and facilitate collective action for the safety and well-being of all. We are also more inclined to perceive what makes us alike, above all the fragility and neediness of our bodies, and to countenance a sharing of burdens that transcends individual distinctions. In the wake of the crisis, these perceptions may lead to greater public demand for social safety nets and even generate far-reaching changes to welfare programs. Yet it is also inevitable that after some time has passed, in a state of greater calm and armed with greater knowledge, we will each turn back to our own habits of judgment, attendant to our own particular needs, circumstances, fears, and goals. We may be less aware of what makes us alike and more driven by the desire for personal independence and distinction. The concept of probability, with which we quantify and manage uncertainty, points in both directions—that is, to drawing conclusions from large-scale observations and to the guidance of individual prudential judgments. Not only may these diverge from one another, but both are also subject to continual change in light of new information. The challenge for public policy, and social insurance specifically, is to somehow bridge or combine the two. These observations lend support to one of the central claims of this book: namely, that a distinctive set of concepts and tools lies at the heart of the liberal democratic political order, promising us both personal protection against misfortune and a mechanism to fairly apportion its burdens. The concept of risk and the practice of insurance are not simply technical or morally neutral in nature but rather mirrors of our principled commitments and tools for their realization. Understanding their character and evolution can shed light on long-standing tensions in our politics. It can also help us appreciate the ways in which our institutions address or manage those tensions, as well as their inability to fully resolve them. As a result, while the analysis that follows does not offer solutions to our current crisis, it may help to clarify enduring questions and prompt a rethinking of their answers.

Introduction

This book offers an account of how and why social insurance became one of the central distributive mechanisms in the arsenal of liberal democracies. As used here, social insurance refers to a publicly orchestrated system of contributions and distributions that provides event-conditioned benefits to its members. First proposed around the time of the French Revolution, such policies began to spread throughout Western Europe toward the end of the nineteenth century. Within the next hundred years, they had become a hallmark of industrialized states, and today they constitute one of the largest budgetary items in most wealthy democracies.1 From pensions and unemployment support to healthcare and parental-leave policies, social insurance permeates the daily lives of modern citizens, promising protection against many fortuities that could affect their livelihoods and well-being. Despite its prominence, however, social insurance evokes confusion and disagreement among the public and experts alike. Consider, briefly, the American Social Security system. Created in 1935, this program provides benefits to retired and disabled workers, as well as family members of the retired, disabled, and deceased. Nearly all of the system’s revenue comes from payroll taxes, levied up to a given level of earnings, which are split evenly between employers and employees and used to fund the claims of current beneficiaries.2 Since the inception of the program, the total number of beneficiaries has steadily climbed, reaching nearly 63 million Americans in 2018.3 Among the elderly, who constitute more than two-thirds of those receiving benefits, Social Security is often a life-sustaining resource, providing the majority or even the entirety of income for a significant portion of beneficiaries.4 While Social Security has enjoyed remarkable popularity since its founding, in recent decades concerns about the program’s financial sustainability

2 / Introduction

have tempered public enthusiasm. Although some point out that Social Security technically does not contribute to the federal government deficit because it pays benefits only from designated trust funds, these funds are currently slated to decrease over time as fertility rates decline and fewer workers are left to fund the benefits of longer-living retirees. In 2019, the Social Security Board of Trustees stated that combined trust fund reserves will run out by 2035.5 Politicians and policy analysts have responded to these concerns by proposing a variety of plans to strengthen the program. Voices from the political left have advocated increasing the rate of contributions, raising or removing the earnings ceiling for payroll taxes, and directing additional tax revenues on high earners and investments into Social Security. Meanwhile, voices on the right have proposed lowering benefits, raising the retirement age, and replacing or supplementing the program with a system of individually owned accounts, into which each worker’s payroll taxes would go.6 Among the questions raised by both sets of proposals is whether the program is, as one commentator puts it, “just another government benefit, with higher earners subsidizing lower earners,” or a more traditional insurance program, in which “you earn your benefits and receive your fair share.”7 The purpose of this book is not to defend any particular policy stance in the ongoing debates over Social Security or any other social insurance program. Rather, it aims to shed light on such debates by uncovering their philosophical origins and history. As we will see, social insurance has always appealed both to a kind of individual liberty or self-sufficiency and to a sense of mutuality or shared fate, and it has proposed to reconcile these commitments in different ways over time. Without minimizing the differences between partisan aims, considering these aims in the context of the political tradition that I trace here underscores the common framework in which both sides operate, along with the promise and limitations of insurance as a policy device.

Out of Many, One Debates over Social Security attest to widespread confusion about the workings and purpose of social insurance. Most people know that they or their employers pay taxes or contributions into designated funds, some of which may be returned to them in the event that they retire, become unemployed or disabled, or have a child. Public health insurance, while organized separately and often more complex, entails a similar logic. Yet most citizens have little understanding of the relationship between what they

Introduction / 3

pay into the system and what they get out of it. Is social insurance like an annuity or accrued property right, for which the individual’s contributions guarantee a certain return, or is it more like a tax, an amount paid into a general fund with no promise of a corresponding benefit?8 Is it a form of self-protection, in the way that commercial insurance is thought to be, or is it a contribution to the common good, even at personal expense? Examining actual social insurance programs does not provide definitive answers. States have adopted a myriad of financing and benefit arrangements, many of which appear intractably—even deliberately—vague about the terms of the agreement they purport to offer. During the early years of Social Security, for example, it was a common mistake to regard the program as an annuity scheme in which contributors were entitled to receive benefits at a certain age based on their prior contributions. As a result, many participants were surprised to find that they had to retire to receive payments, even after reaching the age of eligibility.9 It was only in 1960, in the case of Flemming v. Nestor, that the United States Supreme Court held that a Social Security beneficiary is not quite like an annuity holder because her eligibility and the amount she receives are not simply a function of contractually determined payments. “The ‘right’ to Social Security benefits is in one sense ‘earned,’” the Court noted, since it rests on the judgment that those who have contributed deserve to receive support later in life. Yet the “practical effectuation of that judgment” depends on a host of prudential considerations, making the idea of an accrued property right inapt.10 On this view, then, social insurance is at once an entitlement and a tax—and, as such, perhaps it is something else altogether. Turning from the realm of policy to that of scholarship, one finds an equally bewildering variety of explanations for social insurance. Some have theorized it as a tool of economic self-interest, satisfying individual preferences for security where private provision fails to do so.11 Others have seen it as an instantiation—successful or merely attempted—of noneconomic values such as social equality and solidarity or mutual aid.12 Some have understood it as a means by which oppressed or vulnerable groups extract resources from the state on their own behalf.13 Still others have seen it as a grudging compromise with socialism or a reactionary attempt to save capitalism by blunting its harder edges.14 Clearly, insurance-type welfare programs have served very different ends in different times and places. Yet the fact remains that in its broad outlines, something called social insurance has long been a fixture of political life, both as a mechanism for financing distributive policies and as a justification for those programs. Our language and our political reality

4 / Introduction

thus encourage us to regard it as a single phenomenon, and to that end we must continue searching for a more unified account. I propose that we will achieve greater clarity by narrowing our focus and considering social insurance as an evolving distributive arrangement or regime, in which material resources are divided based on a certain view of citizens’ equality or desert.15 On this view, social insurance represents an account of fair or equitable distribution, granting to those who have contributed their fair share the protection to which they are entitled.16 Of course, even this seemingly simple formulation remains ambiguous: What is each person’s fair share, and to how much is each entitled? Is fair recompense defined by how much one has contributed, and thus by a kind of merit, or by the extent of one’s misfortune, and therefore by a kind of need? Yet, I will argue, it is precisely by looking at social insurance in this light that we can perceive its distinctive and unifying characteristic. A central claim of this book is that social insurance is a distributive arrangement that by its very nature combines distinct principles, blurring the line between them in a way that has allowed for its plasticity and political resilience. The defining source of its character, I maintain, is the concept of risk. Risk plays a central role in insurance as the quantified expression of an uncertainty or a possible harm. In the popular imagination, risk is often regarded as a purely technical concept: exact, impartial, and disconnected from moral questions. My argument challenges this view. It focuses on probability theory, the discipline most directly responsible for interpreting and calculating risk.17 As will soon be explained in greater detail, the concept of probability has always had a dual character: It is both an aid to individual reason under conditions of uncertainty and a measurement of chance events in the world. In both of these aspects, probability theory rests on and furthers normative claims—claims about individual rationality, about the nature of equality, and about the relationship between the two. A central contention of this book is therefore that the quantification of uncertainty via mathematical probability is often a moral and political effort embedded in what appears to be a technical one.

Justice and Chance Social insurance responds to a fundamental political problem: the vulnerability of justice to chance. Consideration of this problem dates to the birth of political philosophy: In Plato’s Republic, for example, the just regime de-

Introduction / 5

pends on an unlikely coincidence of philosophy and political power; in Aristotle’s Politics, even the best-possible regime requires near-impossible gifts of fortune.18 Modern political thought has attempted to formulate more attainable visions of political justice, ones less subject to the vicissitudes of chance.19 Nevertheless, the challenges posed by uncertain and uncontrollable forces persist on these accounts as well. Looking from the vantage of contemporary political thought, we find that this problem has two salient interpretations. The first, now prominent in moral and political philosophy, considers how resources ought to be distributed given the many circumstances over which individuals have no control. If it is true that a just distribution tracks personal effort or responsibility, then material benefits or disadvantages resulting from strokes of fortune are very likely to be unjust. On this view, justice requires correcting for the effects of chance in initial endowments and in outcomes that the individual could not have foreseen or prevented.20 The second interpretation focuses on the challenge of making decisions in the face of uncertainty about empirical events. Policymakers are likely to be uncertain about the causes of social problems, the consequences of policy choices, and even the possibility of adequately implementing their own decisions. Citizens also disagree about such questions, basing their judgments on different information, habits of reasoning, and understandings of what will promote their own good. Such uncertainty poses a problem for justice because it threatens the possibility of collective agreement and because misguided or ineffective policies may have unfair consequences. Some philosophers have sought refuge from this problem in the logic of rights, with its guarantee, at least in matters of critical importance, that individual decision making will remain free from hapless incursions by the state.21 The social contract tradition, as originally articulated in the seventeenth century, offered a version of this solution that remains central to our politics today. By positing a fundamental equality among human beings, and with it a natural right to pursue self-preservation, early liberal thinkers attempted to fashion a system of government that would serve the interests of each and secure the agreement of all. Yet even this solution does not eliminate the need for instrumental reasoning on the part of governments, with all its attendant uncertainty, or resolve the difficulties of collective action given citizens’ conflicting estimates of chancy phenomena. As it turns out, these two facets of the problem—the distributive and the decision-theoretic, respectively—both received seminal treatment in the theory of probability.22 This discipline, which emerged around the same

6 / Introduction

time as the first social contract theories, set out to estimate uncertainty in rigorous, universal, and authoritative ways appropriate for all rational people. In so doing, it spoke simultaneously to the demand for a compelling account of practical reason under uncertainty and to the call for a fair distribution of resources. In the best case, these two facets of the calculus would align, just like the individual rationale and the collective advantages of the social contract itself. That the concept of probability is dualistic has been well noted both within the discipline and among recent commentators.23 Less remarked upon, however, is the continued relevance of this dichotomy for insurance, which was the first practice to invoke risk and then successfully utilize mathematical probabilities. Throughout this book, I argue that probability bequeathed to insurance its central ambiguity, along with the ongoing (but not entirely successful) effort to resolve it.

The Character of Probability The concept of probability has a rich and contested past. The term itself refers to a measured likelihood or to an individual’s belief that an uncertain eventuality will come to pass.24 In modern times, it has become associated with quantification and calculation. Probability theory, often in conjunction with statistics, is responsible for generating those numbers. It also interprets what these numbers mean and thereby lends them practical import. What does, or could, a probability value mean? As Ian Hacking has influentially argued, the concept of probability is Janus-faced in that it has two enduring aspects.25 One, which Hacking calls the epistemic, concerns the degree of belief warranted by a given body of evidence. An example of this sort of probability might be my belief, based on the weather report or simply opening my window, that there is a 25 percent chance of rain today. The other aspect, which Hacking calls the aleatory, concerns the laws of chance processes, or the tendency of some events to produce stable relative frequencies when a number of trials are conducted. An example of this sort is the observed mortality of members of a statistical class. The first aspect thus governs rational credence in the face of uncertainty, or the logical process of making sound inferences on the basis of given information; the second makes statements about facts or observations in the physical world. As Hacking shows, these two aspects of probability both date to the seventeenth-century emergence of the concept. Despite efforts to distinguish them or to purge one or the other, philosophers have been unable to

Introduction / 7

decisively establish the priority of either, while practitioners have continued to employ both. For the purposes of my analysis, the significance of this duality is that probability correspondingly offers two kinds of practical counsel. One aims to show individuals how to assign probabilities to uncertain propositions, often to help them choose the actions most likely to promote their goals. The other provides a measurement of equality among parties who wish to apportion the consequences of an uncertain event. Probability thus guides both individual choice and the fair distribution of resources in the face of chance. I contend that both forms of counsel find expression in insurance. Social insurance differs from the commercial variety most obviously in that the state has the power to compel participation. This allows the state to evade to some degree the demand for an individualized accounting of expected losses and for premiums that reflect those values. Social insurance is also distinct in the risks that it covers, which historically have been confined to a certain kind of economic hazard. The question of why social insurance has been concerned primarily with such risks is one I will take up shortly, and I will also have more to say about why the distinction between social and commercial insurance is not as significant as is often supposed.26 For now, I wish to emphasize that insurance, broadly understood, reflects the same fundamental duality of probability: On one hand, it represents a form of sound personal judgment; on the other, it secures a just or fair distribution of resources.27 Questions about whether, and if so how, these two faces or interpretations align lie at the heart of many contemporary debates about the welfare state.

The Context of This Work The past few decades have witnessed growing interest in the history and social significance of risk. Historians and sociologists of science have unearthed the assumptions and traced the evolution of mathematical probability and statistics.28 Sociologists and historians have explored the social contexts and moral significance of insurance.29 Finally, political scientists, legal scholars, and political economists have explained the insurance rationale for social policies, making a powerful case that individual perceptions of risk, and the concomitant desire for insurance-type protection, have long been key determinants of national welfare schemes.30 These ideas, however, have not received comparable attention within political theory.31 This is especially striking given that major strands in con-

8 / Introduction

temporary distributive philosophy rely heavily on this family of concepts. Social insurance is therefore due for a sustained historical and theoretical analysis of the type that I perform here, one that accounts for its varied interpretations and its remarkable persistence as a political phenomenon.32 A number of important works have lately demonstrated the value of a genealogical approach to the concepts of probability and risk.33 My study is similar in that it unearths the latent assumptions of and mutations in the idea of social insurance, thereby showing that an element of the political landscape that we often take for granted is far from inevitable, particularly in its current form. Yet my aim is not solely or primarily critical. As will be explained further, I offer a qualified defense of social insurance, one that emphasizes its tendency to channel political debate within a single practice or set of institutions. It would be a mistake to rule out the liberating potential of such an analysis, and as we will see, the rubric of insurance does indeed constrain distributive politics in significant ways.34 I hope first, however, to help readers appreciate that social insurance also solves an important problem—that of conflicting distributive claims, resulting from a plurality of judgments and ends—by accommodating the very unresolved duality from which a more directly liberationist approach would have us freed. This work further departs from its predecessors in connecting the evolution of risk to the history of political thought. For example, drawing on what I understand as the foundational aims of the social contract tradition, I contend that social insurance is closely tied to the logic of modern liberalism. Once the purpose of politics is understood as the protection of individuals’ lives and property, and once prudence is defined as the deferral of short-term gratification for the sake of long-term security, it is not a stretch to regard civil society as one great mutual insurer.35 That the political thought of early modern liberalism also hinges on the mechanism of contract only heightens this resemblance.36 While the first social insurance proposals differed from early social contract theories in their explicitly distributive focus, they were animated by the same fundamental question: how to generate an agreement among diverse individuals that is at once choice-worthy for each and fair to all. In addition, I refer here to social insurance as a regime, specifically one with a mixed distributive character. The notion of a regime in this sense comes originally from Aristotle, as does the understanding that different regimes reflect the distributive claims of their most authoritative constituents.37 Social insurance is not a politeia in the sense of an all-encompassing

Introduction / 9

political order. It is, however, a major part of the liberal democratic order and of the way citizens understand that order. Even more, like Aristotle’s conception of a regime, social insurance is explicitly distributive, reflecting some of our strongest, if not always harmonious, convictions about desert, equality, and fairness. In a sense, this book is situated at the intersection of two recent bodies of scholarship, one focusing on the epistemology or mathematics of risk and the other on its sociology and politics. Works in the latter group have highlighted various ways in which determinations of risk reflect moral and political commitments.38 These works and mine share an understanding that accounts of risk are intertwined with politics and with competing interests or claims about the ends of the political community. Where my analysis differs most perceptibly from these predecessors is in focusing on the hazards associated with social insurance, which have a number of distinguishing characteristics. First, unlike ecological and technological risks, the risks associated with the welfare state relate directly to the distribution of wealth—in particular to the loss of earnings or earning potential.39 This is a major reason why these risks have proven amenable in principle to insurance—which, after all, is a financial device that emerged to limit the downsides of commercial activity for those who would be devastated by such loss. Second, although the risks covered by social insurance tend to be regarded as social or systemic, caused by forces beyond the individual’s control, they are also perceived as manageable in the aggregate, thanks to large-scale statistical regularities and, where necessary, the coercive powers of the state. On one hand, then, social insurance can be seen as consistent with successful participation in a market economy, a judicious means of self-protection that any reasonable person would undertake. On the other hand, it reflects a powerful intuition that market participation is not simply a choice and that many of its outcomes do not reflect individual prudence or merit of any kind. The type of risk associated with social insurance is hardly the only risk relevant to political life: The dangers of war, revolution, natural disaster, and other environmental harms are just as much political problems as are economic insecurity and inequality. Yet the question of how to cope with economic risk does lie at the heart of the liberal project, with its commitments to individual liberty—especially in the form of enterprise and acquisitiveness, which invite risk—and to equality, which is often threatened by risk. Social insurance, as the mirror of probability’s two faces, is central to the ongoing effort to reconcile the two.

10 / Introduction

The Approach of the Project The argument of this book frequently refers to and relies on scholarship from disciplines beyond my own. I therefore gratefully acknowledge my debt to those whose insights have paved the way and benefited my thinking. First, the following analysis draws on much of the excellent work done over the past few decades on the history of probability and statistics. The claim of this book to originality, however, lies not in explicating the intricate development of probabilistic and statistical thinking but in noting connections between some of these developments and contemporaneous social and political thought. I have also benefited from important work on the history and sociology of risk and insurance. My contribution as a political theorist, however, lies primarily in telling an overarching story of evolution and thereby drawing lessons for the self-understanding of liberal democracies. The latter task has not been endeavored before, at least not with the focus or on the scale that is attempted here. I therefore hope that the relative breadth of my analysis, and the corresponding lack of indepth treatment of particular historical topics, will be understood as it is intended: as an effort not to cover all ground but to chart a path that future researchers may fill in and modify as appropriate.40 Finally, while frequently referring to empirical work on the history and political economy of welfare, this book does not definitively explain the development of social policy over the past 250 years. Rather, in unearthing affinities between certain philosophical developments and public policy, its aim is considerably more modest: to point out that the concept of risk and how we define it has implications for the justification and design of public policy, and to show that history furnishes several examples of this often-overlooked relationship. In tracing this relationship, it is not always possible to claim a direct historical connection between probability theory and welfare policy. In some instances, a particular thinker provides the link: The Marquis de Condorcet, Francis Ysidro Edgeworth, and John Maynard Keynes are examples of philosophers whose interests spanned both fields. But elsewhere the argument focuses more on the resonance of ideas across the two domains. Given that probability plays a central role in theories of both rationality and fairness, and given the ongoing prominence of insurance practices in modern states, it is not surprising that the former found expression in public life, even if at times indirectly or implicitly rather than through the conscious embrace of political actors. Although this book does not set out to rigorously explain the adoption

Introduction / 11

of particular policies, I contend that the notion of a policy paradigm, as influentially expounded by political scientist Peter Hall, helps to illuminate how ideas about probability and insurance have influenced the development of welfare states.41 As Hall explains, policymakers “work within a framework of ideas and standards that specifies not only the goals of policy and the kind of instruments that can be used to attain them, but also the very nature of the problems they are meant to be addressing.”42 These ideas, which have a status somewhat independent of institutions, are part of the arsenal used by interest groups, parties, and experts to influence political discourse and acquire power. The accounts of social insurance considered in this book constitute an evolving policy paradigm in this sense. They possess a number of attributes that scholars have found central to the definition of such paradigms, including an understanding of justice and the role of the state, a conception of a problem requiring public intervention, and a choice of the means best suited to achieve the aims of public policy.43 At the same time, I will argue, this paradigm is ambiguous and flexible enough to accommodate various interpretations, which has helped it to remain in force over such a long period of time.44 Social insurance as conceived in the light of mathematical probability thus facilitates both the “puzzling” aspect of policymaking, in which political actors collectively solve social problems, and the “powering” aspect, in which they vie with one another for dominance.45 That is, social insurance is both an answer to problems of economic insecurity and a tool by which politicians, bureaucrats, and organizations have secured or entrenched their political fortunes.46 Before proceeding further, it will be helpful to say a few words about what I mean when I refer to a “welfare state.” This is a state that, in a substantial portion of its policies and social spending, acts on the premise that government should provide citizens with the basic conditions necessary for a successful life, including protection against various forms of misfortune that could seriously impede that life. More specifically, the protection offered by a welfare state is often seen as an entailment of political membership rather than a matter of charity, and it has the aim of promoting some understanding of equality among citizens. This intentionally encompassing definition has the advantage of distinguishing welfare policy from many earlier forms of social provision, while also allowing for a range of practical expressions. For example, a welfare state could offer a basic floor below which no one is allowed to fall, or it could provide an optimal rather than minimal level of resources and services.47 Although many of the proposals and policies that I will discuss here predate the term “welfare state,”

12 / Introduction

which came into usage in Britain after the Second World War, I believe that understanding the concept in this expansive light will allow us to perceive normative continuities that might otherwise be obscured. It also gives a clue as to why insurance principles have been so central to the welfare project, even if the insurance mechanism does not exhaust the purposes or workings of welfare states.

Overview of the Argument The argument of this book proceeds in five chronologically arranged chapters, each of which covers a period in the history of probability theory and corresponding developments in welfare thought and practice. Geographically, it focuses primarily on Western Europe, particularly France and Great Britain, and on the United States, since many of the intellectual developments that drive our story took place in these countries. The first chapter catalogs the origins of risk, the birth of mathematical probability, and the early development of insurance. Risk emerged in maritime contracts as a commodity exchanged between two parties, one of whom sought to reduce exposure to losses and the other of whom sought to profit from the uncertainty of the first. Under canon law, such contracts raised the legal and theoretical challenge of how to translate uncertain future profits into fair present prices. Although the rules for doing so were primarily qualitative, they were guided by the well-established principle that each party’s gain should be proportional to his investment. Probability theory was born in the mid-seventeenth century out of an attempt to quantify this rule in the context of an interrupted game of chance. Although recent decades have seen a surge of historical interest in this development, little attention has been given to the fact that early philosophers of probability introduced the language of distributive justice into their analyses.48 They did so by explicitly defining mathematical expectation as a party’s fair share of a common pool or, in other words, as a kind of distributive entitlement determined by one’s potential to win or lose the total pot. I refer to this principle as probabilistic justice, and I argue that it significantly influenced the history of annuities and insurance.49 Among other things, it helped to legitimize life insurance in England in the mid-1700s, the success of which was seen as proof of the reliability and usefulness of statistical probabilities. Thenceforth, the understanding of insurance as an equitable distributive arrangement would provide a key moral justification for the practice. This vision coexisted somewhat uneasily, however, with

Introduction / 13

the origins of insurance as a commercial exchange—at times an obviously speculative one, at that—and the more prudential, instrumental logic entailed therein. This is the central tension animating the ideas of risk and insurance, which has been present from their inception but which received confirmation and formalization thanks to developments in mathematical probability. Chapter 2, which focuses primarily on the second half of the eighteenth century, argues that the same account of probabilistic justice that had helped to legitimize life insurance also inspired both the friendly society reform movement and the first social insurance proposals in England and France. Mutual and social insurance assume that if enough individuals combine together, paying into the common pool an amount determined by their risks, they can equitably share the burdens of a misfortune that happens to strike any one of them. The fairness of this agreement hinges on the parties’ mathematical equality: Assuming their odds of encountering misfortune are equal, each should pay the same amount to receive the same benefit. The introduction of statistics into probability calculations created a problem, however: While statistical averages are useful to an insurance company or a state acting on behalf of the aggregate good, they do not capture all of the information that an individual considers when acting on behalf of her own good. The result may be a discrepancy between the premium calculated for a statistical group and one that an individual considers reasonable or fair. This problem is the main subject of chapter 3, which brings our story through to the mid-nineteenth century. Thinkers of the period addressed this problem with the concept of utility or moral expectation. By touting the advantages of personal security or the utility derived from being insured, they justified group insurance as beneficial even when the individual’s premiums do not strictly match her mathematical expectation. In retrospect, these accounts appear marred by a number of unsubstantiated assumptions. Yet many of their flaws are better understood in light of the theorists’ practical aims, in particular their desire to preserve the personal relevance of probability values despite the increasingly statistical, aggregative tendencies of the calculus. By contrast, as I argue in chapter 4, the account of probability that became influential in the mid-nineteenth century defined mathematical likelihoods as relevant exclusively to statistical groups, not individuals. This view, known as frequentism, offered a novel account of the relationship between individual judgment and empirical frequencies, according to which the former is derivative of the latter. The frequentist view had close

14 / Introduction

affinities and historical ties with utilitarianism. It also, I argue, accords with the shape and justification of many of the earliest welfare programs instantiated in Western Europe around the turn of the twentieth century. Finally, in chapter 5, which covers the period from the end of World War II through the late twentieth century, I argue that advanced liberal welfare states built on the frequentist idea of social insurance while unsuccessfully attempting to move beyond it. By this time, the more limited risk pooling of the earlier vision no longer seemed adequate to the tasks of welfare, which sought to guarantee self-respect among all citizens regardless of class or status. Yet as long as social policies were still considered “insurance,” they continued to appeal to the idea of probabilistic justice and its (at least partial) basis in empirical likelihoods. As a result of this disconnect between the aims of welfare and the workings of insurance, many incisive critics came to think that the insurance rubric was unduly constraining or confusing and should be abandoned altogether. The account of probability that became dominant during this period also called into question the virtues of social insurance, but for entirely different reasons. The theory of subjective probability differed from nearly every previous account in allowing for the specific numerical quantification of all types of uncertainty, regardless of the amount of empirical evidence available. It did this by understanding all reasoning as a kind of wager on what an event’s outcome was likely to be. As a result, subjective accounts effectively collapsed the moral distinction between insurance and gambling, calling earlier theories of social insurance into question at about the same time that the practice of welfare did the same. Despite (or perhaps because of) these developments, the most prominent work of late twentieth-century political philosophy was a defense of social insurance, or so I argue toward the end of chapter 5. John Rawls’s remarkably influential theory of justice can be read as an effort to preserve key elements of this distributive regime after both social and economic theory had called it into question. By excluding mathematical likelihoods from his account of the social decision procedure, Rawls effectively sidestepped the problem of probability’s duality: Because there is no empirical knowledge on which participants can distinguish themselves or identify with a class, there also is no perspectival dichotomy between the individual, with his own judgments and aspirations, and the state or burdensharing collective. Rawls’s argument thus seems to affirm that the only incontestable account of equality for insurance purposes is one that is not probabilistic at all.

Introduction / 15

A Qualified Defense In one sense, then, Rawls’s social contract is the culmination of the social insurance tradition that I recount, and in another sense it amounts to a decisive break from that tradition. As an effort to reconcile or sublimate probability’s two sides, social insurance as I understand it amounts to a kind of mixed regime, one that recognizes both individual distinction and an equality rooted in shared needs. Its determinations are at any given moment contestable and remain subject to ongoing adjustment in light of competing claims. Yet it manages to channel such claims rather successfully because, like probability itself, it appeals simultaneously to two sets of concerns. In imagining insurance without numerical likelihoods, I argue, Rawls does away with this dual-faceted appeal, underestimating the psychological sources of the welfare state and the lasting political implications of probabilistic reasoning. In addition, one of the indirect consequences of Rawls’s thought has been to encourage a gap between the normative political theory of distributive justice and the empirical political science of the welfare state. While Rawls intentionally discarded probabilities in the name of an abstract and universal equality, many political scientists have emphasized the importance of risk-based solidarities in driving welfare policy.50 The latter trend has been fruitful and promises to yield further insights into the electoral politics of welfare. Yet such explanations remain largely disconnected from normative debates about justice. The analysis that follows is intended to help bridge this gap, positioning political theorists to engage more directly with political scientists regarding the character and purposes of social insurance. Ultimately, my argument amounts to a qualified defense of probabilistic social insurance (meaning social insurance that employs probabilities of some kind). It is one thing to point out the dualistic character of a practice and another to defend such dualism as a necessary or desirable feature of public policy.51 Moreover, the success of any particular social insurance program will depend crucially on its context and design. Nevertheless, I wish to call attention to what I regard as a virtue of the paradigm as a whole: its appeal both to the prudential judgment of individuals and to norms of reciprocity or mutual support among citizens who relate to one another as equals. Social insurance cannot do away with probability without altering this basic character. One could regard this as a constraint, relegating policy to some liminal space between possessive individualism and a more egalitarian or solidaristic distribution. Today, however, at a time of

16 / Introduction

great polarization in many democracies around the world, it may be better to view it as an opportunity. Social insurance has the capacity to accommodate more than one principle at once and, in so doing, to channel political disagreement. My aim is to explain its ongoing appeal and situate it in its rightful place as a tool for promoting other moral and political ends. This book is therefore a call for a kind of political moderation—for the recognition that existing institutions serve an important purpose, even if they do not satisfy purist impulses. At the same time, it is a call for a kind of political imagination, a willingness to reexamine and rethink the relationship between risk and distributive justice. Only by thinking seriously about probability will we be in a position to understand what policies based on insurance principles can, and cannot, achieve.

ONE

The Origins of Risk and the Growth of Insurance

This chapter traces the early history of insurance and mathematical probability. In so doing, it lays the foundations for my argument that social insurance inherited a duality from the concept of risk, one that was already present in the earliest accounts of premium insurance yet found confirmation and formal expression in probability theory. This duality was first manifest in the fact that insurance, as originally understood, expressed both the logic of commercial self-interest and that of equitable partnership; it was simultaneously a tool for personal gain and one for mitigating and sharing loss. In identifying this tension at the root of the practice, and then showing how the discipline of mathematical probability reflected it, I argue that these essential modern tools for coping with uncertainty were ambiguous from their inception. In addition, this chapter offers an explanation as to how it is that insurance, despite its frequent association with gambling, also took on for many advocates the image of a just arrangement for mutually sharing burdens. This explanation is certainly not intended to be exhaustive. Others have skillfully traced the historical and ideological changes thanks to which life insurance in particular came to appear opposed to speculation rather than of a piece with it. Yet my account, by highlighting the distributive focus of several early accounts of probability, helps to explain the enduring strength of the equitable, mutualistic image of the practice alongside its more speculative one. Both, I maintain, are key constituents of our understanding of insurance. Before delving into this historical study, however, I briefly introduce the concept of insurance from a more contemporary point of view.

18 / Chapter One

Insurance: A Brief Primer Insurance is an agreement to transfer costs associated with an uncertain event. Its modern form is distinguished by the appearance of risk, an entity that represents the possible loss or uncertainty and that is exchanged or shifted between the insurer and the insured. In return for shouldering this burden, the insurer receives a premium that reflects both the likelihood of the event and the amount of the loss. In principle, insurers play no role in the actual affairs of those they insure, and their financial interest is limited to ensuring that the premium they receive is fair or otherwise adequate. Today, commentators often refer to two models of insurance: risk exchange and risk pooling.1 In the first model, two parties who differ in their willingness or ability to absorb a possible loss trade the risk between them, protecting the insured from devastation should the event come to pass, and giving the insurer a chance to gain if it does not. This model thus assumes some discrepancy between the parties, whether in their capacity to shoulder loss, in their desire for an uncertain gain, or in their estimations of the probability of the event in question. It also allows that at least one party, the insurer, is motivated by the pursuit of gain and regards the agreement primarily as a means to commercial advantage. In the second model, groups of people who face the same risk and have roughly the same willingness or ability to absorb it contribute to a common fund that compensates participants who encounter the event. Thanks to the regularity of statistical frequencies—that is, the fact that rates of mortality, some diseases, and other hazards are relatively constant over large numbers of similar people—the insurance company or association can estimate how many members of the risk pool will require compensation and determine their premiums accordingly. This model therefore emphasizes the similarity of the insured, both in their probabilities of incurring loss and in their desire to avoid it. It also suggests that they are driven primarily by the need to reduce their exposure to events that could undermine their long-term welfare or that of their loved ones. While this distinction is often a helpful one, the two categories are not airtight. Risk pooling does entail a transfer of the aggregated risks of all participants from the insured to the insurance company or association. Risk exchange, meanwhile, also off-loads risk for the purpose of minimizing loss.2 In principle, perhaps the most important feature distinguishing the two models is that risk pooling reduces the variance in outcomes for the insured. The reason for this is that, assuming they are similarly situated, the observed losses for the group will continuously approach their

The Origins of Risk and the Growth of Insurance / 19

projected losses as the number of participants increases. Insurers benefit from this phenomenon whenever they spread their own risks over a large pool of similar policyholders. Yet risk pooling also uses it to benefit the insured, allowing them to collectively reduce the uncertainty facing each one individually. Early thinking about insurance did not distinguish between exchanging and pooling risks, most obviously because the latter, which relies on statistical probabilities, had not been explicitly recognized as such when the first insurance contracts were made. Even after this development, however, both risk pooling and risk spreading were frequently theorized as species of exchange. Many of the arguments we will encounter in the coming chapters incorporated elements or justifications from both models. I submit that the reason for this is not simply that thinkers were confused about a question that contemporary observers have managed to clarify. Rather, I suggest that it is part of the character of insurance to elide any clear separation between the logic of commercial exchange and that of cooperative mutual aid. This was true at its inception and was reinforced as soon as risk became the province of mathematical probability.3 Indeed, an advantage of studying the history of thinking about insurance is that it unsettles assumptions and reveals long-standing problems that contemporary analyses may ignore. To take another example, it is now common to invoke the idea of risk aversion to explain why individuals purchase insurance. Often risk aversion is understood as a consequence of the diminishing marginal utility of money, an idea famously proposed by Swiss mathematician Daniel Bernoulli in 1738.4 Bernoulli argued that the pain that one feels on losing a given sum depends on the amount of wealth with which one begins: Someone with fewer initial assets will suffer more from a given loss than someone who starts out with a greater fortune. Moreover, for any one individual the pain of losing a sum of money will exceed the pleasure of winning it, meaning that even mathematically fair wagers can result in a loss of utility for the players. The declining marginal utility of money may help to explain why people choose to insure rather than live with uncertainty, as many economists have supposed.5 Yet the idea of risk aversion introduces a separate psychological element that can vary from individual to individual, even at the same initial level of wealth.6 Indeed, it appears that risk aversion and diminishing marginal utility are analytically distinct, and that the choice to insure could be motivated by a fearful disposition regardless of one’s initial level of wealth.7 The fact that earlier theorists did not explicitly countenance such dispositional preferences partly reflects their moral assump-

20 / Chapter One

tions and aims, including their effort to justify insurance as choice-worthy and gambling as condemnable for all responsible people.8 It also suggests that the introduction of this idea into the analysis of insurance has important consequences, for example, necessitating a different justification for risk-pooling arrangements than many of those employed in the past.9 A third common notion that becomes unsettled in light of the analysis that follows is that of actuarial fairness. This is the idea that insurance premiums should reflect the individual’s own risk, in particular her expected losses as determined by the amount at stake and her probability of losing it. The argument supporting this idea is that by calibrating each person’s payments with expected withdrawals, it is possible to ensure that everyone will contribute an amount proportional to what she receives, and that the scheme as a whole will remain financially viable, collecting enough in premiums to cover what it ultimately pays out in benefits. While this claim has long been central to the theory of probability and insurance, it entails a number of unresolved difficulties. One is that of determining empirical or objective probabilities for each participant, a problem not only for unpredictable and systemic risks—those with very low probabilities or which result from some underlying interdependence—but for any statistical risk that depends on classification, a practice that is inevitably variable and somewhat imprecise.10 Another difficulty concerns the fact that, even if we assume objective risks are determinable, they may not be identical with individuals’ personal or subjective risk evaluations. This means that if actuarial fairness is a function not of objective risk but of what individuals agree to accept, and in particular their acceptance of premiums that they believe reflect their expected losses, then those premiums may vary widely even between individuals who share the same empirical risk profile.11 Partly as a result of these difficulties, and to avoid anachronism, I refer to the idea of equity found in early thinking about probability and insurance as “probabilistic justice” rather than actuarial fairness. The term “probabilistic justice,” in my view, better reflects the ambiguity in the concept of probability itself, specifically that it can refer both to objective and subjective evaluations of risk. The idea is consequently broader than actuarial fairness: It refers to an agreement in which participants understand themselves as equals in the face of chance, based on an abstract, quantitative identity between them. This idea, I maintain, has guided thinking about the welfare state, with and without regard to actuarial fairness more strictly construed.

The Origins of Risk and the Growth of Insurance / 21

The Early History of Modern Insurance Pre-insurance Practices Our focus here is modern insurance, meaning insurance as a practice that explicitly invokes risk. To be sure, what we think of today as risk-shifting and risk-spreading arrangements were known long before the advent of modern premium insurance. For example, Karl Van D’Elden reports that Greek slave owners could purchase protection against financial losses resulting from the escape of their slaves. Roman soldiers had a part of their pay withheld to provide relief to their families if they died in battle, and Roman citizens could join clubs that provided a burial allowance in exchange for a regular fee that was paid in advance. On at least two occasions, the Roman government tried to ensure adequate supplies by indemnifying traders for losses they incurred at sea or due to war. And by the early Middle Ages, cooperative guilds across Europe provided assistance to members in the event of various contingencies, taken from a common fund to which all members contributed.12 All of these proto-insurance arrangements reflected the idea of shifting or spreading potential losses to protect participants from catastrophic outcomes. All specified the relevant dangers and promised payment should an unfortunate event come to pass. Yet none shared the most important distinguishing features of modern insurance. First, none explicitly tied the insured party’s payment to an ex ante quantitative assessment of the danger or loss being insured against. Instead, either they operated on an ex post basis, soliciting contributions or devising compensation after the loss had already occurred, or they linked contributions to compensation but not to the likelihood of the loss.13 Second, and as a result, none involved the explicit quantification and transfer of the commodity known as risk to a party whose only role was to carry that burden. Although, as we will see, Roman and late-medieval maritime loans did anticipate insurance in imagining the projected loss as a tradable entity, none involved a party whose involvement was limited to shouldering that loss. As a result, such arrangements did not entail the specific aims and challenges of insurance as it subsequently emerged in its modern form. It may seem needlessly restrictive to define insurance in this way.14 After all, various forms of cooperative scheme have existed for millennia, both before and after the emergence of premium insurance, and they were born out of the same impetus that gave rise to the latter. Yet, I will argue, it was

22 / Chapter One

probabilistic life insurance in particular that most directly influenced the future not only of the insurance industry but also of numerous proposals for social welfare on a much broader scale. As a result, it is fair to say that both the presuppositions and the limitations of social insurance as it subsequently developed should be traced to modern statistical insurance, not to its preprobabilistic cousins. The Emergence of Premium Insurance Although scholars do not all agree about when exactly modern maritime insurance emerged in Europe, there is little question that it arose directly out of late thirteenth-century commercial developments.15 Prior to this period, merchants shipping their goods by sea had used various partnership arrangements and loans to reduce their financial exposure in the event of a shipwreck.16 Early variations on the sea loan conditioned repayment with interest on the safe arrival of the ship, thereby offering the merchant some protection in the event of loss. Such arrangements trace back to Roman law, where provision was made for transactions that shifted potential losses between parties for a specified price. Roman maritime loans in particular entailed set rates of interest paid to the lender in exchange for his agreement to forfeit his loan should the voyage fail.17 Lenders thus acted like insurers in guaranteeing the ship for a price, but because their rates were fixed by statute rather than linked to the particular enterprise, their loans lacked the most significant feature of modern insurance, namely an assessment of the anticipated loss, or risk, to which the guarantee’s price is tied. With the revival of Roman law in the twelfth century and the subsequent rise of the sedentary merchant, new uncertainty-shifting arrangements began to evolve. In particular, a novel form of sea loan emerged in which shipowners lent money to merchants on the condition that the loan would be repaid on safe arrival of the latter’s goods, but forgiven if the goods did not reach their destination. This arrangement not only offered a financial cushion to merchants in the event of a loss, but may also have increased the likelihood of a successful voyage by giving the shipowner a financial interest in protecting the cargo.18 These loans apparently entailed varying rates of interest that depended on the particular voyage, an anticipation of later risk assessments.19 Yet they too differed from modern insurance in that they were essentially partnerships between the merchant and the shipowner, each of whom had a direct financial stake in the voyage.20 The earliest insurance contracts outwardly resembled sea loans but in fact modified the underlying arrangement significantly. Rather than loan-

The Origins of Risk and the Growth of Insurance / 23

ing the money first and forfeiting it in the event of nonarrival, here the insurer promised to pay a sum of money in the event that a shipment did not arrive safely.21 In exchange for this promise to shoulder the merchant’s loss, the insurer received a premium determined specifically for that voyage and paid by the merchant in advance. The premium, which varied according to the length of the voyage and a number of other factors that might affect its success, was commonly referred to as rischio, the linguistic predecessor of risk.22 Insurance thus differed from its predecessors in two key respects: First, it involved the explicit exchange of an uncertainty, independent of the underlying property being insured; and second, it involved a party, the insurer, whose role in the transaction was limited to its assumption of that risk. The first of these two distinguishing features is reflected in the introduction of the premium. The premium rested on the assumption that the likely downside of a business venture could be alienated from the underlying property and, its value having been assessed, traded between two parties. The idea that a probable loss could be alienated and transferred was not the sudden innovation of maritime insurance.23 Yet the insurance premium is the most direct progenitor of the concept of risk as we know it: namely, a measurement of a potential loss made before the relevant contingency occurs and exchanged independently of the good to which it refers. Not only do we owe the term “risk” directly to maritime insurance’s rischio, but maritime insurance also appears to have been the first widespread practice to involve the explicit exchange of this commodity.24 The understanding of risk as an independently tradable good relates closely to the second feature distinguishing maritime insurance from its predecessors: the introduction of a party not directly involved in the primary venture. While sea loans typically involved partners to the enterprise, insurance agreements were made between merchants and underwriters who had no connection to the business beyond their assumption of the risk.25 Like the premium, then, this arrangement reflects important assumptions about the independence and fungibility of risk.26 The emergence of risk as an independently tradable good may have been, at least in part, a response to canon law prohibitions on usury.27 Maritime loans were clearly problematic because of their use of interest as compensation for the lender.28 Insurance, however, bypassed the loan in favor of a lease or sale, in which the insurer assumes the risk and is compensated accordingly.29 Although canon law had long regarded the bearing of risk as a marker of ownership and denied that one could profit simply from its assumption, by the late fifteenth century most commentators were appar-

24 / Chapter One

ently willing to overlook this doctrine and accept the exchange of risk independent of title.30 Insurance was subsequently accepted in fifteenth- and sixteenth-century juristic writings as being in principle a fair exchange.31 The Theory and Practice of Early Marine Insurance Analytically and legally, one of the central challenges in the early practice of insurance was how to fairly price the risk.32 Canon law norms of contractual equity—that is, the equality between two parties that renders their transaction fair—required that the financial exposure of each side be proportional to his total share of the profits.33 In general, the question of how to understand and measure equality in economic exchange was a subject of ongoing discussion among jurists and theologians throughout the medieval period. Insurance contracts, the outcome of which hinges on a contingency, added another dimension to the challenge. Because the actual profits to each party from such arrangements were uncertain, the fair price had to incorporate not only the final amount at stake but also the likelihood that those profits would be obtained.34 In practice, early insurance premiums were based more on guesswork and negotiation than rigorous calculation. The first underwriters were not specialists but merchants, shipowners, bankers, and others who underwrote as a sideline to their principal businesses.35 Some modern commentators have interpreted early maritime insurance as a kind of club good or service, exchanged among members of a merchant community to enhance the commercial outcomes of all.36 On this view, the first insurance markets constituted a mutually beneficial system of finance or “network of reciprocal guarantees,” which redistributed losses and thereby enabled members to continue trading despite what would otherwise be fatal blows to their business.37 Even if risk pooling of this (nonactuarial) kind played an important role in the first insurance markets, it is also the case that many early agreements looked more like wagers than forms of mutual aid.38 Betting was prominent in the development of maritime insurance, particularly as the commercial center of Europe shifted to Antwerp in the sixteenth century. While merchants may have insured to reduce their risks, insurers were attracted to the speculative side of the practice.39 Historian Andrea Addobbati suggests that premiums initially responded to the need for a speculative element in the arrangement, even in its mutualistic form: Because variable, they could stimulate the supply of insurance from outside the narrow merchant community wherever the need for coverage was not equally distributed within

The Origins of Risk and the Growth of Insurance / 25

it.40 Over time, as insurance spread from its maritime context onto dry land, it became common for policyholders to take out insurance even on cargo, lives, or events in which they had no underlying interest at all.41 The line between risk reduction and speculation in insurance has thus always been a murky one. On one hand, insurance seems to be of a piece with the risk-reducing partnerships out of which it grew, a tool for minimizing the possibility of harm by foreseeing, calculating, and transferring it. The concept of risk itself, according to historian Sylvain Piron, “implicates a particular manner of relating to a future contingent event, according to an active mode of anticipation.” What most distinguishes this mode from others is “the fact that the anticipation leads one to think in advance about eventual consequences,” specifically the possible damage, and to perform various “mental operations concerning the limitation, evaluation, or distribution of this damage.”42 On the other hand, however, insurance is also a bet on the outcome of an event between two parties whose interests are not necessarily aligned. Even if one side insures to minimize a possible loss, the other could be taking his chances to secure a gain. The coexistence of mutual protection and speculation, or risk pooling and risk exchange, in early insurance markets speaks to the dualistic character of the practice. Throughout its history, insurance has been seen both as an equitable partnership designed to minimize losses and as a means of commercial gain. If in practice early insurance often took the latter form, theoretical defenses have tended to emphasize the former. As we will now see, such defenses found important echoes in the theory of mathematical probability, which articulated a vision of aleatory contracts as ideal equitable partnerships. The standard of equity applied to such contracts, first by scholastic jurists and then by probability theorists, combined an appreciation of their uncertain character with an attempt to render their initial conditions fair. The early probabilists thereby suggested, in effect, that wagering of a sort could be not only prudent but also just, and that justice of this kind could be attained despite the apparently arbitrary effects of chance.43

Probability Theory and the Doctrine of Aleatory Contracts The Legal Background of Early Probability Theory Mathematical probability owes both its inspiration and much of its conceptual apparatus to late sixteenth- and early seventeenth-century discussions regarding the legality of aleatory contracts.44 These are contracts that involve an element of chance, including annuities, insurance, games,

26 / Chapter One

inheritances, and futures contracts. Under canon law, such contracts raised the question of whether the transaction ran afoul of church prohibitions on usury and gambling. Like all contracts, their legality in this respect hinged on whether the exchange was reciprocal or equitable, meaning that one side was not benefiting unfairly at the other’s expense. From this perspective, the challenge for aleatory contracts in particular was to equalize the two sides at the moment of their agreement despite the uncertainty of the final outcome. This in turn required some method of translating uncertain future profits into fair present prices. Until the advent of mathematical probability, the rules for doing so were primarily qualitative and were guided by the Rule of Fellowship, which held that each party’s gain should be proportional to his investment.45 Where the outcome of an agreement was uncertain, some estimation of the likely or probable gain had to be made. Out of this necessity, a qualitative account of what we now know as mathematical expectation, or the product of likelihood and outcome value, emerged. In principle, by equalizing this entity the parties could come to a fair agreement, ensuring that neither side exposed itself to a greater extent than was justified by its likely reward.46 The authors of the Port-Royal Logic, writing in 1662, thus explained that “to judge what one must do to obtain a benefit, or avoid a harm, it is necessary to consider not only the benefit or the harm in itself, but also the probability that it will arrive or not arrive, and to regard geometrically the proportion of all of these things together.” They then clarified what it is that makes a wager or aleatory contract fair: Games in which all of the parties face exactly the same expectation are equitable, “as much as games can be,” while “those which deviate from this proportion are manifestly unjust.”47 Lotteries are an obvious example of an unjust game since those who purchase tickets pay more than their expected benefit, and part of the excess goes to the lottery master in the form of profits. The French jurist Jean Domat, writing toward the end of the seventeenth century, summarized the dominant approach to aleatory contracts at the time. “In contracts in which one trades a right,” he explained, or something else that depends on an uncertain event, and from which one can arrive either at a profit or at a loss, depending on the difference of events, he is free to treat it as the sort in which one, for example, renounces all profit and discharges all loss, or  .  .  . takes a sum for everything he can expect to gain.  .  .  . In this way a party who wishes to retire from the agreement can determine with the others what is his present and certain profit, or what he

The Origins of Risk and the Growth of Insurance / 27 stands to lose, whatever events may arrive. . . . Thus they arrive between them at a kind of equality in their lots, which makes their agreement just.48

Domat’s account described what the early probabilists tried to render mathematically exact—that is, the expectations of parties to a contract in which final profits depend on the unknown outcome. It also articulated the rationale for doing so, namely to arrive at a kind of equality between the two sides and thereby render the contract fair. The fair price of each party’s lot is the present equivalent of his uncertain future winnings. If one party then wishes to “retire from the agreement,” preferring the security of a known sum to the possibility of a loss, he can calculate his “present and certain profit” as a function of the amount at stake and his odds of obtaining it, and justly leave the arrangement with that amount in hand.49 Requiring that parties pay the just price, or expectation value, for their respective lots is meant to ensure that, proportionally speaking, no one stands to gain or lose more than anyone else. The earliest theorists of mathematical probability operated within this legal and moral framework, which left an indelible impression on the apparatus of insurance as well.50 Probabilistic Justice The 1654 correspondence between Blaise Pascal and Pierre de Fermat, published in 1679 and frequently cited as the birth of mathematical probability, quantified what the Logic and Domat described.51 In it, the two authors attempted to calculate the amount due to a player in an interrupted game of chance—someone who, as in Domat’s account, prefers to take the fair price rather than test luck by following through with the wager. Pascal, although he did not use the term “expectation,” attempted to find the amount to which the player is entitled by dividing the amount at stake by the player’s relative chances of winning it.52 As in the contemporaneous legal analyses, the working assumption was that by paying the expectation value, the departing player occupies a position equivalent to that of a player who continues, and the game is consequently fair. Subsequent probabilists readily took on the same challenge—to, as the Dutch natural philosopher Christiaan Huygens put it, “determine how much greater a share of the stakes I should get than my opponent if we agree to quit with the game unfinished.” They were even more explicit in defining the player’s expectation as the wager’s fair price. An early use of the term “expectation” came from Huygens, who published his On Reck-

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oning in Games of Chance in 1657 after hearing about the Pascal-Fermat correspondence. Both Huygens and his most famous commentator, Jacob Bernoulli, used the Latin expectatio and sors as synonyms, although sors, or “lot,” can mean both capital invested and expected payoff.53 The reason for the interchangeability of the two terms is that in a fair game, as we have seen, one should pay or invest exactly as much as one anticipates receiving in prizes.54 Huygens opened his treatise with the mathematical formula for expectation: “If I may expect either a or b and either could easily fall to my lot, then my expectation should be said to be worth (a + b)/2.” He then set out to “not only demonstrate this rule, but first derive it” and, in doing so, offered an explicit proof that probabilistic expectation is the fair price of a player’s lot.55 Huygens’s proof hinges on the device of an equivalent fair wager, for which the player would willingly pay the same amount as his expectation in the original game. Because the player is indifferent between the two bets, the expectation, or the amount wagered in the second, must also be the fair price of the first.56 Unlike subsequent thinkers, Huygens established the fairness of the equivalent wager not by the players’ equal expectations—which would have rendered his argument circular—but by the indistinguishability of their initial positions.57 They wager the same amount, the fair price or expectation value of the first bet, and have equal chances of winning the total sum. They then all bilaterally agree to perform various symmetric trades, promising to pay each of the others a specified amount in the event that one wins. Their initial identity and reciprocity in turn ensures that every player’s odds of winning the total amount are the same.58 Commenting on Huygens’s text, Jacob Bernoulli offered a different demonstration of the fairness of mathematical expectation as a wager’s price, based on what he called “reasoning that is more popular  .  .  . and more adapted to common comprehension.”59 Bernoulli, born in Basel in 1654, was the first in a line of prominent mathematicians in his family. Celebrated now for his pioneering work on empirical probability, he was also an early adopter of differential calculus and was well known in international mathematical circles in his time. His Art of Conjecturing, published posthumously in 1713, set out to build on Huygens’s work and thereby extend the application of mathematical methods into the popular field of games of chance.60 Subtly modifying the idea of the equivalent wager, Bernoulli defined a person’s expectation as “just as much as he will acquire without fail”—not after the real wager has been run, but in a kind of hypothetical alterna-

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tive wager in which the parties together claim the whole pool and then agree to divide it up proportionally among them. For example, to find the expectation of a wager in which one has an equal chance of winning a or b, Bernoulli’s argument posits that each amount is hidden in one of two hands, and two players each choose a hand and keep its contents. In reality, of course, after the game is played, one player will receive a and the other b, but in Bernoulli’s alternative scenario, we imagine that the total pool, a  +  b, belongs to both players in common. In that case, the two players “will acquire without fail and ought therefore to expect” the total amount hidden, or a + b, and this is their expectation. “But it must also be conceded that each of us has an equal right to what we expect” since the two parties’ odds of winning either a or b are identical. “Therefore it follows that the total expectation should be divided into two equal parts, and to each of us should be attributed half of the total expectation,” or (a + b)/2.61 Thus, while Huygens defined expectation as the price one would pay for an equivalent fair wager, Bernoulli defined it in terms of one’s fair portion of the total share of the bet, or the amount to which one is legitimately entitled given the initial conditions of the game. Where the players wager the same amount and stand the same chance of winning, each has a legitimate claim to an equal share—even if the amounts they ultimately win will differ. Where they wager different amounts or have different chances of success, their just claims on the total will correspondingly differ as well.62 Expectation on Bernoulli’s account thus becomes the numerical expression of a kind of right, deriving from the players’ collective entitlement to the total amount and from their initial relationship to one another. The proportion between the parties’ odds and their legitimate claims on the total amount at stake is what ensures the sought-after equality between them, and with it the justice of their agreement.63 Equipossibility and the Distributive Turn Given what were undoubtedly well-known assumptions about contractual equity at the time of their writing, it is unlikely that early probabilists would have taken pains simply to defend the notion that a party’s earnings should be proportional to her investment. Rather, the central innovation of their approach vis-à-vis the doctrine of aleatory contracts was its claim that one can rigorously quantify each party’s lot in terms of the number of equally possible outcomes. Prior to this discovery, commentators who approached the so-called division problem arrived at such varied results that some concluded it was simply unsolvable.64 These early demonstrations

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were intended to show that the new method does reliably and precisely generate a wager’s fair price. A number of modern commentators have credited Leibniz as the first to define probability in terms of equally possible cases, meaning that the events in question have the same proclivity to occur.65 In his 1678 manuscript “On Estimating the Uncertain,” Leibniz set out to justify the use of expectation as the fair price of a game. There, he defined a fair game as entailing the “same proportion of hope to fear on either side,” which is the case when “players do similar things in such a way that no distinction can be drawn between them, with the sole exception of the outcome.”66 This is what scholars have called an aleatory condition, as opposed to an epistemic one, in the form of rules that result in each player’s equal chance of winning.67 Leibniz then generalized from this scenario to any set of equally possible outcomes, defining the player’s expectation as “that part of the claim . . . which we get by setting it in proportion to the number of [equipossible] outcomes,” or as the “aliquota portio,” proportional part of the total.68 Huygens had also understood his equivalent wager as fair because all of the players are identically situated and indistinguishable until the final outcome is revealed. Since each wagers the same sum and is equally likely to win, each one’s expectation is his proportional share of the total and equal to everyone else’s. Yet Leibniz introduced the language of distributive justice into his argument for the fairness of a probable expectation. “Let us suppose,” he wrote, that in a game of chance “the whole pool pertains to all and that everyone’s hope is equal; if the players broke the game off and wanted to distribute the pool according to the hope or the claim to it, with the intention of profit, a man’s share would be owed to each one,” or in other words the total pool divided by the number of members.69 Leibniz went on to clarify that “if several people share a thing, or if a thing is common to several people through the same claim, each man’s claim is his share of the claim to the whole thing.”70 Thus, while Huygens’s account of the justice between two players in a game of chance is transactional or corrective, meaning that it aims to equalize the financial standings of two sides of a transaction, Leibniz’s argument suggests a version of distributive justice, according to which each player’s claim is determined by his proportional share of a common pool. The original definitions of both corrective and distributive justice come from Aristotle. Corrective justice, as Aristotle influentially put it, entails equalizing those involved in voluntary transactions, such as buying and selling goods, and involuntary ones, such as theft and other crimes. The

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method for arriving at justice in such cases is arithmetic, which means finding “the middle term of the larger and the smaller” by subtracting from the party who has too much and adding to the one who has too little.71 According to Aristotle, such justice concerns the terms of the transaction alone, without regard for any distinguishing characteristic of the parties. Since “it makes no difference at all whether a decent person robs a base one, or a base person a decent one,” the law “looks only at the difference that stems from the harm done, and it treats persons as equals.”72 The challenge for realizing justice of this kind is to equate quantities or goods that are unequal, like the skills of a doctor and those of a farmer.73 Distributive justice, meanwhile, concerns the distributions of money, honor, or any other divisible good among members of a political community.74 This type of justice requires distributing common possessions in geometrical proportion, or “with the same ratio that the contributions have toward each other.”75 Unlike corrective justice, distributive justice on Aristotle’s account corresponds to some understanding of merit, in accordance with which the parties claim an equal share of the pool. The challenge for this kind of justice is therefore the persistence of disagreement about what kind of merit should be determinative: Democrats “say it is freedom; oligarchs, wealth; others, good birth; aristocrats, virtue.”76 Aristotle’s distinction was well known among medieval and early modern commentators. Historian Joel Kaye has shown that the idea of a geometric model in particular proved influential in fourteenth-century theories of economic exchange.77 By the time probability theory emerged, commentators had accepted that equity in aleatory contracts should take on a geometrical, or proportional, rather than arithmetic character.78 Such a perspective was not exclusively linked to distributive justice; in Aristotle’s thinking and in others’, it was also applied to reciprocity in exchange.79 Yet for Leibniz, Bernoulli, and others who followed them, proportional or geometric equality in aleatory contracts took on a distributive cast. By imagining the division of a common pool, they presented the problem of probability as one of distributing a shared resource among mathematically defined equals. This, I submit, was a significant move for thinking about the character and fairness of insurance. As just discussed, Bernoulli, like Leibniz, used this line of reasoning to replace Huygens’s fair equivalent wager proof. Pierre Rémond de Montmort took a similar approach in his 1708 Essay d’analyse sur les jeux de hazard (published after Bernoulli had written The Art of Conjecturing but before the latter’s publication). Referring to each player’s “right” over the total amount of money in play, Montmort explained that a party’s claim derives

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from his respective hope of winning the whole.80 Likewise, in determining how much two players ought to wager for a given stake, we calculate each one’s proportional share of the total because “Pierre has no less of a right over [his fair portion of Paul’s wager] than he has over the [amount] that he put into play.”81 This language of distributive entitlement is clearly linked to the doctrine of aleatory contracts.82 The earliest canon lawyers had held that the possibility of loss by both sides distinguished acceptable partnerships from usurious ones because justice required the mutual sharing of profits and losses. Such an account of justice focuses less on ensuring corrective or transactional equality than on fairly dividing a shared resource. Once risk emerged as an alienable commodity, the legal challenge became how to fairly price the good: As a result, many juridical analyses became more explicitly commutative.83 Nevertheless, the original understanding of a just aleatory contract as an equitable partnership remained.84 At the same time, the account of equitable distribution that one finds in these early probabilistic writings entails a significant innovation. In resting their own definitions of expectation on an argument about distribution rather than transfer, Leibniz and Bernoulli put forward a novel interpretation of the basis for distributive claims.85 If, as Aristotle argued, the major problem for distributive justice is defining what kind of merit should be determinative, these authors implicitly resolved it by defining the relevant measure as each party’s potential for gain or loss.86 In other words, it is the individual’s likelihood of success or failure, without regard to merit in any traditional sense, that determines her rightful share of the total pool. This novel interpretation of distributive entitlement was enabled by the equipossibility interpretation of probability widely in use at the time. This view holds that a party’s lot is a ratio of favorable to equally possible outcomes, with the latter defined as both an aleatory feature, namely the equal physical propensity of those outcomes, and an epistemic one, concerning the equal weight we attach to their likelihoods. Each equal possibility in effect provides a unit of entitlement according to which all subsequent distinctions must be drawn. Thus Bernoulli, describing the case of a player who is three times as likely as another to win a game, explained that “it is clearly completely just that someone who wants to take the place of the three players  .  .  . should also put up three times as much” because, for distributive purposes, he is the equivalent of three out of four identically situated players.87 This fiction was designed for normative purposes, as Bernoulli implicitly acknowledged with another stylized example: “If a prince allows two criminals to contend with equal lot to live, then each of them

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will be judged . . . to have 1/2 of life and 1/2 of death. In this way a man could, even in a proper sense, be called half dead and half alive.”88 The sum wagered in a game of chance no more belongs to all of the players in common than a single life belongs to both criminals. Yet the fiction of collective ownership and of a corresponding right to one’s proportional share serves the ethical goal of translating arbitrary outcomes into equitable apportionments. We cannot know in advance who will win and who will lose, and individual results will surely diverge; but we can equalize ourselves beforehand in such a way that the outcome, no matter how differential, still seems fair. This idea, which I refer to as probabilistic justice, implies that the type of equality to which distribution should respond is a form of positional identity vis-à-vis chance, mathematically expressed as an expectation or probability value. The latter determines how much each party should contribute and justifies claiming common resources when the uncertainty comes to pass. These early thinkers did not distinguish expectation from probability, and as a result the determinative quantity in their analyses is a product of investment and likelihood, understood as a single economic entity. Yet I submit that the concept of probability itself, and in particular the notion of an equally possible outcome, provided the crucial unit of measurement for distribution. This unit could be used not only to determine an individual’s rightful share but also to compare it quantitatively to that of others. While understandings of probability and expectation changed considerably in the wake of these early analyses, the basic idea that a fair distribution secures equality despite the effects of chance proved remarkably influential in the theory and practice of the welfare state. It did so thanks to the idea of mutual insurance and its account of distributive justice among probabilistic equals. As Lorraine Daston points out, it was in the context of mortality statistics that thinkers first began to explicitly single out probability and to understand expectation as a composite rather than an irreducible economic entity.89 It is therefore to these developments that we now turn.

Life Insurance and Probabilistic Justice The doctrine of aleatory contracts, particularly as appropriated and interpreted by mathematical probabilists, formatively influenced thinking about insurance. While in practice, many who took out policies through the mid-eighteenth century, and even beyond, did so with speculative intent, probability theory supported an alternative tradition of thinking

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about insurance as a tool for distributive justice. This tradition relied on the original insight that equal expectations give rise to equal claims. In the case of insurance, and in particular life insurance, the equally likely outcome in question was the death of any single member of a mortality class, calculated from a growing body of government-collected statistics. The idea of deaths as equally likely outcomes, and of similar individuals as probabilistic equals, meant that the logic outlined by Leibniz and Bernoulli could be applied beyond games of chance, to insurance and other contracts that depend on mortality calculations. As we will see, however, insurance remained subject to two distinct interpretations: one, a bilateral contract for the exchange of a risk, and the other a burden-sharing partnership among any number of similarly situated individuals. While commercial insurance lends itself to the first interpretation and mutual insurance to the second, I contend that all types of insurance inherited this conceptual ambiguity, from the earliest treatments of aleatory contracts and, even more deeply, from the ambiguous character of probability itself. Probability at once attempts to quantify good sense, to guide personal conduct in an uncertain world, and to measure empirical likelihoods, on the basis of which parties can be equalized and their distributive shares defined. The history of thinking about insurance reveals an evolving attempt to harmonize these two understandings. Equity in Empirical Probability Theory The very first calculations of mathematical expectation were based on idealized scenarios involving coins, dice, cards, and similar games, for which a fixed number of equally possible outcomes could be identified and their relative frequencies tabulated a priori, without the need for empirical observation. Although the early probability theorists perceived the potential usefulness of their calculations beyond such stock examples, they did not yet have the tools for applying those calculations to events for which the evidence was solely empirical in nature. Jacob Bernoulli was among the first to explicitly recognize this difficulty. How can anyone, he asked, count “the number of diseases, as if they were just as many cases, which may invade at any age the innumerable parts of the human body and which imply our death? And who can determine how much more easily one disease may kill than another—the plague compared to dropsy, dropsy compared to fever?” For this, one has no choice but to turn to observation: “What cannot be ascertained a priori

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may at least be found out a posteriori from the results many times observed in similar situations.”90 Bernoulli’s suggestion that likelihoods could be gleaned from repeated observation would inaugurate and provide a foundation for the entire theory of a posteriori probability. His contribution, now known as the weak law of large numbers, showed that as the number of trials of a given phenomenon increases to infinity, it becomes increasingly likely that the difference between the true and the observed ratio of outcomes will fall within a specified interval of one’s choosing. Assuming one already knows the true probability of an event, then, Bernoulli set out to determine how many observations one needs to approach what he called moral certainty, or the degree of probability sufficient for use in practical affairs, that the observed probability will fall within a given interval surrounding the true one. Bernoulli did not definitively provide a mathematically rigorous way of solving the inverse problem—that is, how to infer from an observed ratio of outcomes an unknown true probability of events. He did, however, suggest a commonsense solution: “If, for example, there once existed three hundred people of the same age and body type as Titius now has, and you observed that two hundred of them died before the end of a decade . . . you could safely enough conclude” that Titius is twice as likely to die as to live in the next ten years.91 Bernoulli described this way of inferring future probabilities from past observations as what “everyone consistently does . . . in daily practice.”92 The introduction of large numbers of prior observations would simply make such commonsense inductive inference more reliable. The first treatments of a posteriori probability were in the domain of annuity and life insurance mathematics, where a growing body of governmentcollected statistics made Bernoulli-style inference from repeated observation possible. Annuities are financial products in which an individual pays a sum and receives some form of regular payment in return; in the case of life annuities specifically, the annuitant receives a fixed amount annually for the remainder of his years. Like life insurance, then, such annuities involve a wager on the length of the purchaser’s remaining life. Yet while the insured acts from the judgment or fear that he will die soon, betting to that effect against the insurer, the annuitant anticipates surviving beyond his expected mortality and thereby getting the better end of the deal. Both products rely directly on empirical probabilities, specifically the mortality prospects of the purchaser. Both were therefore important to the development of a posteriori probability and were frequently discussed together during this period.93

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Like the early treatments of games of chance, these analyses were explicitly driven by concerns of contractual equity and set out to calculate expectation as the fair price of an annuity or insurance contract.94 They also, like treatments of a priori probability, tended to base their calculations on the equally possible case.95 For example, Johan de Witt’s 1671 Treatise on Life Annuities, one of the first attempts to apply mathematical probability to such contracts, begins by demonstrating a formula for expectation that strikingly resembles Huygens’s, all the way down to the fair equivalent wager.96 De Witt, who at the time was the chief statesman of the Netherlands, embarked on his analysis in an attempt to generate annuity prices that would avoid the unfair and financially disastrous results of previous government practices. Following his contemporary and occasional consultant Huygens, de Witt commenced his treatment by demonstrating the validity of mathematical expectation. In justifying the traditional formula, he relied even more explicitly than Huygens on the equal likelihood of possible outcomes. He then showed how the same model can be applied to mortality prospects as well. An annuitant, “having purchased and sunk a life annuity on a young nominee, has in possession, or in his favor, as many different expectations or chances as there are half years in which the death of the nominee may occur.”97 Assuming that mortality remains constant in the first fifty years of life, then “the first hundred different expectations or chances . . . may result with the same facility, and relative to their probability are equal.”98 After setting out a few more rough assumptions about the distribution of annuitant deaths by age, de Witt tallied each individual’s chances of semiannual death over a lifetime, divided the present value of the total potential annuity payment by this number, and arrived at the contract’s expected value. It is not an accident that the first life insurance mathematicians chose to express mortality prospects in terms of equally likely cases.99 They did this by basing their calculations on mortality curves, which allowed them to regard the chance of annual death as equally likely at least through the prime of life and, in de Witt’s case, as some multiple of that baseline in other periods. In turn, they were able to calculate expectation using the established—and, at the time, only available—method of dividing the total amount at stake by the number of equal chances of “winning” it. De Witt’s work, which was in fact a report to the States General of Holland advising the government on how to price its annuities, ultimately proposed a single annuity price equal to the total sum that the government could anticipate paying divided by the number of annuitants.100 It was not until 1693, when English scientist Edmund Halley devised his

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seminal table of deaths by age and used the results to calculate annuity values, that expectation as a function of individual life expectancy began to make its way into mathematics. Prior to Halley, in 1662, John Graunt had constructed a life table using vital statistics on the population of London. A number of mathematicians readily perceived the utility of such a table in applying probability calculations to the problem of life expectancy. Yet Graunt’s analysis was hindered by defects in his data, including ignorance of the ages of the deceased. By contrast, Halley’s statistics were taken from Breslau, where registers of births and deaths by age and sex had been kept since the end of the sixteenth century. As a result, while de Witt, using Graunt’s data, had begun from the chances of death, taking this as his probability distribution, Halley began with the distribution of survivors. This allowed him to calculate annuity prices as a function of the nominee’s age, an innovation that made a lasting mark on the development of actuarial practice.101 Indeed, while a number of mathematicians had attempted to interpret mortality data in terms of probabilities, Halley’s approach proved uniquely influential in life insurance mathematics. The explanation for this, I suggest, is not merely that Halley began with more refined data but also that his method and calculations more effectively promoted the long-standing goal of equity in aleatory contracts, including life insurance, single-life annuities, and reversionary annuities. These devices had considerable potential to help individuals facing economic insecurity, especially due to the loss of income and the lack of property in land or other rents.102 Getting the mathematics right, in terms of both aggregate financial stability and fairness, was consequently a matter of great importance to thinkers who looked to use these tools for moral and political purposes.103 Halley’s report notes that the purchaser of an annuity “ought to pay only such a part of the value of the annuity, as he has chances that he is living; and this ought to be computed yearly, and the sum of all those yearly values being added together” equals the total value of the annuity.104 In other words, it is only fair to charge an annuitant for the annuity’s expected value to him, which is its present value multiplied by his odds of living through each subsequent year. Rather than referring to the individual’s equal chance of dying over the course of a certain period, as in de Witt’s analysis, Halley’s account refers to the individual’s equal chance of dying relative to everyone else his age. As Halley put it, “as the number of persons living after that term of years, to the number dead; so are the odds that any one person [that age] is alive or dead.”105 By defining equally likely cases in terms of the survival of members of

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a given age group, Halley offered a new account of mathematical equality that could be used for economic and in particular distributive purposes. Although the calculation of life expectancy would remain a subject of debate, Halley’s discussion found important echoes well into the next century. Abraham de Moivre, the foremost probabilist of his generation, used Halley’s data and a version of his method for calculating annuity prices in his textbook, The Doctrine of Chances, originally published in 1718. As de Moivre explained, “Now it is very obvious that there being A persons of the age given, and one year after B persons remaining, that the probability which the person of the given age has to continue in life, for one year at least, is measured by the fraction B/A.”106 Individuals in the initial group A thus amount to equally probable instances for the purpose of calculating each member’s odds of survival. Richard Price, a pioneer of actuarial methods and an advisor to the first statistically informed life insurance society, also used Halley’s table and commended de Moivre’s technique. Writing nearly three-quarters of a century after Halley, Price offered a clue into the normative significance of his predecessor’s innovation. In a 1769 letter to Benjamin Franklin, Price explained the two different meanings of “expectation of life.” One refers to “the number of years which, upon an equality of chance, a person may expect to enjoy” and is the amount of time in which half of his peer group will pass away. This period, however, “does not coincide with what writers on annuities call the expectation of life,” except on the assumption of an arithmetic or uniform decrease in survivors over the course of the human lifespan. Mathematicians therefore use a different definition, namely, “The mean continuance of any given single, joint or surviving lives, according to any given table of observations.”107 This is calculated as the sum of the probabilities that an individual will survive to the end of the first, second, third, and so on years until the end of his life. The difference between the two definitions turned out to be crucial for calculating annuities. It also reflects a difference in purpose.108 Whereas life expectancy in the first sense offers a form of rational expectation for the individual, a number beyond which he cannot reasonably expect to live, in the second sense it takes its bearings from the group, beginning with “the number of years which, taken them one with another, they actually enjoy, and may be considered as sure of enjoying.”109 Price’s language in the second case evokes the same idea of common possession and equitable distribution employed by Leibniz and Bernoulli, but as applied to life prospects. Each individual’s life expectancy in this sense is the “share of life due to a person.”110 Moreover, Price explained that it makes no difference math-

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ematically on this view whether annuities are paid for life to every member of the group or whether they are paid to an alternate group every member of which manifests the life expectancy calculated for all. “The number of years enjoyed by them all will be just the same,” and so in the absence of  interest “there would be no difference in value” between the two sets of payments.111 The new interpretation of probabilistic equality enabled by Halley’s life table thus aligned a posteriori calculations with the earliest a priori ones. Its salience highlights how distributive considerations remained as important in life insurance mathematics as they had in earlier treatments of games of chance, all the way down to the equivalent wager with its shared resource, a portion of which is “due” to all. The Birth of Statistical Life Insurance In practice, it took more than half a century before the insights of mathematical probability found their way into annuity and life insurance contracts. While some early insurance cooperatives and commercial providers did make rudimentary use of demographic data, they did so by simply limiting their coverage to groups of people who shared similar traits, such as those in the prime of life or in the same occupation.112 Like de Witt and other early probabilists, many insurers regarded the chance of death as roughly constant between adolescence and midlife, leading them to disregard the need for a breakdown of mortality risk by age.113 This meant that their schemes were limited in scope and met with wildly varying success.114 A number of historical explanations have been offered for the puzzle of why the insurance and annuity industries made so little avail of contemporary mathematical developments. Lorraine Daston has argued that for both sellers and the public to consider insurance a fitting topic for mathematical analysis, insurance in particular had to be severed from gambling, which required the emergence of new social attitudes toward risk.115 More recently, David Bellhouse has argued that the early analysts of a posteriori probability were not concerned primarily with insurance practices but with property rights, which often had life-contingent provisions and therefore depended on life expectancy calculations.116 As we will see in the next chapter, the question of property was central to discussions of annuities in the mid- to late eighteenth century and played an important role in early proposals for social insurance as well. My focus here is slightly different, however, in that I emphasize how the account of equity present in early probabilistic writings became crucial to the justification of actuarial life

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insurance once the two finally converged. This account, with its focus on both the prudence and the fairness of mutual insurance, provided normative support on which champions of the practice readily drew. The first insurance provider to use statistical probabilities to set its premiums, and thereby to accommodate a wider range of customers than any one company or cooperative had previously been able to do, emerged in the final third of the eighteenth century.117 The Society for Equitable Assurances on Lives and Survivorships, or Equitable, received its founding impetus from mathematician James Dodson. A student of de Moivre, Dodson had been denied admission to London’s Amicable Society on the ground that, at over the age of forty-five, he was too old for coverage. As a result, he set out to establish a life insurance association that would grade premiums on the basis of age and therefore be able to accept older customers without jeopardizing its viability.118 The preamble to the Equitable’s deed of settlement declared the “great benefits” to be derived from life insurance based on “premiums . . . proportionate to the chance of death attending the age of life to be assured,” as well as “to the time such assurance is to continue.”119 Given the importance of contractual equity to probability theory, including early life insurance mathematics, one need not look far to understand why Dodson chose to call his company the Society for Equitable Assurances.120 By placing individuals into groups within which their expectations could be considered equal, age-graded life insurance sought to avoid the perceived unfairness of prior plans. Calculating prices on the basis of average mortality by age would ensure both that individual subscribers were probabilistically equal at the commencement of the contract and that the society itself would have enough funds to pay those who lived the longest.121 William Morgan, one of the Equitable’s first actuaries, explained the approach as follows: Assume, based on mortality data of the time, that one out of every fifty 39-year-olds in London will die before reaching the age of 40. If fifty Londoners each purchased a life insurance policy promising $100 in the event of death within the year, that policy (without factoring in interest) would cost each 1/50 of the total value, or $2. The insurance company would thus collect $100 in total and distribute it to the family of the one who happened to pass away.122 As in the wagers of a priori probability, then, the principle supporting statistical life insurance schemes is that those who end up “losing” the bet about their own longevity compensate those who “win.” Here the psychological impetus for participation is even clearer, however, since it directly reflects the image of an equitable partnership found in the doctrine of alea-

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tory contracts. The arrangement begins with the assumption that the insured parties are interchangeable because their individual mortality is the average for the class and thus identical across the group.123 Since they all face the same odds of death, they agree in advance to use their collective resources to compensate one another for losses that any one of them will incur. In presenting itself as a society rather than a company, the Equitable explicitly set out to reflect this image of mutuality. Once each insured party entered into the group, he in a sense became a common owner of the total pool. In fact, after running a surplus for years due to its conservative mortality estimates and other factors, the Equitable began to regularly distribute some of its excess funds to members in rough proportion to the values of their policies.124 The idea of a risk-spreading partnership always assumed that there is safety in numbers, even if the partners were only two instead of one. What was novel in statistical life insurance was its awareness that security requires not just a few partners but a critical mass of participants whose aggregate experience manifests the projected probability. As Bernoulli had shown, the greater the number of observations of a given phenomenon, the less the uncertainty in the result. The Equitable’s prospectus reflected this in stressing that life expectancy, while uncertain in the individual case, “in an aggregate of lives is reducible to a certainty.”125 For the finances of such insurance to work, at least in theory, the group of insured has to manifest an average mortality that approaches the one on which their contributions are based, and this becomes more likely as their number grows. Bernoulli’s original insight and its subsequent iterations became the mantra of a new approach to protecting the individual from any number of dangers. The promise of predictability entailed in the long-run frequency, in which short-term deviations give way to regularity, seemed to hold the key to security and peace of mind even in the face of life’s most frightening realities. We cannot know what will happen to any individual, goes the logic, but we can know with mathematical precision what will happen in the aggregate, and we can take responsibility for our fates in light of that knowledge. Life insurance was the pioneer and primary exemplar of this argument since it was the first (and for some time the only) insurance practice to consistently make use of statistical averages.126 With it, a new interpretation of risk began to emerge. Where early marine insurers had taken a prudential, particularized approach to quantifying a ship’s likelihood of success, life insurance underwriters now relied on abstraction and aggregation. Once individuals were grouped by age, they were assumed to be alike in every other relevant respect, such that their chances of dying

42 / Chapter One

at a particular time could be considered equal.127 With the large-numbers approach to probabilities, in other words, risk became social, both in its definition and in its use: Only by placing the individual within a group of probabilistic equals could his own expectation be calculated, and only by joining with enough of his peers could that expectation be used as a tool for individual security. Mutualism with and without Risk Probability theory thus offered an image of distributive justice as tied to rigorously calculated and largely impersonal risk assessments. Risk on this account belonged to the individual, who could transfer it to an insurer or mutual society for a suitable premium. Yet statistical risks also abstracted considerably from the individual’s particularities, focusing on a small number of his features and disregarding others. This abstraction was what allowed for the calculation of probabilities from empirical observation because only by isolating features such as sex, age, and location was it possible to generate sufficient data and with them reliable averages. The abstract and impersonal character of such probabilistic justice stood in contrast to another popular model of mutual support around the same time: that of the “box clubs” or, as they were later known, friendly societies. Friendlies had first emerged in England as local groups that brought together neighbors or members of the same trade for socializing and the pledge of assistance in the case of need. From their inception, England’s societies were voluntary, and they remained largely local both in scale and in character through the early 1800s.128 Some scholars have traced their origin to guilds, which in the words of one nineteenth-century treatise “were originally instituted by the mutual agreement of friends and neighbors, and had no further object than the relief of brethren in times of distress,” though they, too, also involved a great deal of “feasting and conviviality” among their tight-knit members.129 Whatever the friendlies’ precise origin, it is generally agreed that their modern variety dates to the late seventeenth or early eighteenth century, and that their number began to grow in the early 1700s. Formed among men who knew each other or were in some sense part of the same community, the friendlies usually charged equal fees and paid a flat benefit to any member who encountered a situation of need, most notably sickness, death of the breadwinner (including the lack of burial expenses), and old age. They also used a portion of the dues collected for club meetings, which members saw as central to the overall benefits of be-

The Origins of Risk and the Growth of Insurance / 43

longing. In fact, these lively gatherings were so important to the ethos of the friendlies that many retained the character of a local club, where members came to drink and socialize along with pledging their mutual aid, well into the nineteenth century. True to their name, then, the friendly societies were guided more by norms of neighborliness and camaraderie than by those of market transfer or contractual justice. The element of financial self-interest, while clearly present, was bound up with social ties and communal aspirations that prioritized members’ equal standing over individualized pricing and benefits. Yet the flip side of this egalitarian ethos was often a demand for homogeneity and behavioral compliance, lest any member end up imposing a disproportionate cost on the group.130 For example, the societies typically restricted their membership to men from the same village or trade, within a limited age range, and without any known propensities to become ill or disabled. They also monitored their ranks to make sure no one was engaging in the kind of behavior that could result in excessive claims.131 The friendly societies thus consciously ensured a degree of uniformity through admissions and behavioral standards that not only promoted social cohesiveness but also justified the equal financial burden each member was expected to shoulder. The friendlies therefore represented an alternative model of mutuality as more personalized and communal than probabilistic life insurance. Rather than envisioning the transfer of a quantified risk, they grouped people who were roughly similar, who knew each other well, and who could police one another’s compliance with shared norms of responsible conduct. While probabilistic insurance abstracted from individual particularities to form its groups of burden-sharing equals, mutual societies could rest on a much thicker form of identification or affinity, grounded in a lived sense among members that they shared a similar fate.132 Thick identity had its downsides, however. Because the friendlies achieved their egalitarian aims with a number of rather exclusive practices, many participants came from the better-off sections of the working classes, even at the height of the movement’s popularity.133 From this perspective, one advantage of probabilistic insurance is that it is impersonal and impartial: It depends on calculation rather than fellow feeling or the fallible people who enforce it. The potential scope of its application is also much greater, as statistical risk classes can transcend localities and affective ties.134 As we will see in the next chapter, these were among the arguments for the movement to reform friendly societies along actuarial lines—that is, to align members’ payments with their personal expectations or risks—which

44 / Chapter One

began in the late eighteenth century and took direct inspiration from the success of the Equitable and similar companies. The same considerations, we will see, motivated the original idea of social insurance. Publicly orchestrated insurance schemes promised to combine the mathematical rigor of statistical insurance with the communal spirit of the friendlies. They would spread a kind of independence and virtue to the lower reaches of the working class—those often excluded from voluntary mutual aid—by encouraging foresight, savings, and a sense of familial duty. They would also replace the friendly societies’ isolated pockets of fraternity with the more encompassing and equalizing protection of the state. A unique constellation of probabilistic ideas supported this vision, I will argue, the aims of which found further expression within the probability calculus itself.

T WO

Probabilistic Justice and the Beginnings of Social Insurance

As we saw in the last chapter, the statistical turn in mathematical probability eventually helped life insurance to take off as an industry, allowing advocates to downplay the speculative or wager-like aspect of the contract and cast it instead as a fair risk-reducing partnership. From the time of the Equitable’s founding, many proponents of life insurance presented it as a way for the responsible bourgeois to provide for his family’s long-term welfare by tapping into the certainty of aggregate regularities.1 Such mutualistic insurance, founded on the impersonal identity of equal probabilities, could at once promote individual welfare and the common good of fair, reciprocal protection. In the words of the Equitable’s prospectus, “the assured being at the same time mutually assurers one to the other, the interest of one might be the interest of both.”2 This chapter will show how the same ideal of a union between selfinterest and the common good also inspired both the friendly society reform movement and the first proposals for social insurance in the late eighteenth and early nineteenth centuries. Probabilistic insurance promised to replace vulnerability and dependence with foresight and selfsufficiency. Chapter 3 will consider in detail the more technical arguments that supported the push for friendly society reform and state-run insurance schemes during this period. In keeping with the claim that the discipline of probability is often as much a moral and a political enterprise as a mathematical one, it argues that one of the most significant innovations of the period, known as inverse probability or the probability of causes, reflected its advocates’ practical aim of effecting an alignment between individual reason and empirical likelihoods. The vision of social insurance that emerged—methodologically individualist but politically technocratic and

46 / Chapter Two

eventually statist—reflects the mathematical apparatus that was designed, in part, to bring it about. First, however, this chapter will show how actuarial mutual insurance, with contributions and benefits determined by mathematical expectation, came to be a political tool and not only a means for commercial benefit or voluntary mutual aid. The first part of the discussion will focus on Great Britain, where life insurance and friendly societies have long histories and where the movement to reform the latter on actuarial lines was particularly prominent and successful. The second part will look to contemporaneous proposals to implement actuarial mutual insurance on a national scale, which originated in England and France but made an especially powerful impact in the latter. Both efforts set out to bring order and mathematical discipline to the allegedly haphazard affairs of the working classes, and both did so by understanding risk as precisely calculable for large groups of people who share salient features. The origins of social insurance can thus be found in a newly socialized understanding of risk, enabled and encouraged by the increasingly statistical cast of mathematical probability itself. This account is not the first to trace the earliest formulations of a modern welfare state to developments in probability theory.3 Yet it does expand on and advance earlier accounts by emphasizing three points. First, it shows that early proponents of social insurance did not perceive a decisive normative difference between commercial and voluntary mutual societies on one hand and forms of social insurance on the other. At their best, all such schemes could reflect what I have been calling probabilistic justice and its alignment between individual benefit and the common good. To be sure, these thinkers were aware that the profit motive could influence the character of commercial schemes. William Morgan and Richard Price, whom we will take up in what follows, both emphasized the value of distributing profits among the insured, as was the practice of the Equitable, whose model they sought to promote.4 The point, however, is that insofar as the Equitable was a life insurance company and not a friendly society or national insurance scheme, its use as a model for noncommercial plans highlights the continuity I am claiming. Second, and as a result, these accounts were heir to a particular set of difficulties arising from the ambiguous character of probability itself. In keeping with the actuarial spirit of their movement, advocates assumed that responsible insurance schemes would grade contributions according to the characteristics of the insured, foremost among them age, the feature for which the most exhaustive data were available at the time. Yet as critics would point out, aligning premiums with such isolated characteristics

Probabilistic Justice and the Beginnings of Social Insurance / 47

ignores other factors that may influence both the choice-worthiness and the fairness of insurance schemes. In other words, probabilistic justice, for all its apparent impartiality and mathematical rigor, could not and cannot evade the practical and, in some cases, political question of who should be considered an equal for the purposes of the insurance contract. The third point, which will be the focus of chapter 3, is that the way in which probability, and therefore risk, is understood has significant implications for the justification and design of social insurance. The account of probability that became dominant during this period entailed its own distinctive vision of social insurance that mirrored advocates’ moral and political aims. Reflecting on the probabilistic foundations of this vision helps to explain both the rationalizing faith of its exponents and an important reason their hopes were ultimately unfulfilled. Throughout, I suggest that probability theory helped to constitute a policy paradigm, one that began to establish itself with the movement to reform friendly societies and found its full expression in the welfare state. Political scientist Peter Hall defines a policy paradigm as the interpretive framework within which policymakers work. Such a set of “ideas and standards . . . specifies not only the goals of policy and the kind of instruments that can be used to attain them, but also the very nature of the problems they are meant to be addressing.”5 The notion of a policy paradigm thus helps to elucidate the relationship between ideas and policymaking: Political actors, Hall explains, work within the terms of a dominant political discourse, or a set of concepts that make sense to the parties involved. It is the nature of such discourses to privilege some lines of policy over others. As a result, the struggle for power among organized interests, political parties, and experts takes the form of competing efforts to influence the terms of the discourse. As Hall puts it, citing social policy scholar Hugh Heclo, actors involved in changing policy both “puzzle,” trying to solve collective political problems, and “power,” vying for influence in the process.6 Social insurance may be understood as a policy paradigm in this sense, specifying both the overarching goal of public policy—broadly speaking, to harmonize the interests and choices of individuals with fairness and security for the group—and the instrument used to attain it. More deeply, this set of ideas also helped to frame the nature of the social problem in distributive terms, as the need to reconcile the logic of commercial prudence with an equitable distribution of the burdens of commercial development. As we will see in the following chapters, this paradigm evolved through the late nineteenth and twentieth centuries in conjunction with evolutions in probability theory itself. Yet the nature of the challenge,

48 / Chapter Two

which is itself a mirror of the unresolved duality of our concept of probability, remained the same.7

Precursors to Social Insurance Social Insurance and the Liberal Idea The idea of social insurance could be said to have emerged together with modern liberal political thought. To be sure, early accounts of the social contract such as those put forward by Thomas Hobbes and John Locke did not envision the exchange or transfer of a calculable entity called risk, and in this sense they clearly differed from insurance as we have been considering it here. Yet there is a demonstrative and even mathematical rigor to the reasoning process that brings about agreement on these accounts, founded as it is on uncontroversial propositions and the universal good sense that flows from them.8 Indeed, early modern contract theory was preoccupied with the problem of uncertainty, born of epistemic doubt and disagreement, and its implications for political life. As Emily Nacol has recounted, Hobbes adopted a “geometrical” mode of reasoning about politics to replace individuals’ prudential judgments about the future with universal and authoritative knowledge about the means to collective security. Locke, while more accepting than Hobbes of the persistence of individual probabilistic judgments, also theorized the social contract as a means of reducing uncertainty and promoting the stability of the commonwealth. Both thinkers were concerned deeply about the problem of disagreement resulting from the limitations of human knowledge.9 Although their political prescriptions diverged, both used the mechanism of contract to secure agreement and with it a kind of common good that could withstand the destabilizing effects of future contingencies. Mutual or group-based insurance arrangements similarly tame future uncertainties through a fair present agreement. It is not surprising, then, that the logic of the social contract and that of mutual insurance resemble one another in various ways. Both imagine individuals as equally vulnerable to harm in the absence of the contract; and both hinge on an abstract but personal entity, a right or a risk, that participants give up or transfer to secure protection. That both may rest in practice as much on the emotional basis of fear as on the counsels of scientific or mathematical reason only heightens the resemblance. At the same time, as we will see, the first social insurance proposals

Probabilistic Justice and the Beginnings of Social Insurance / 49

differed from early social contract theories in their explicitly distributive focus. They aspired to realize a vision of equality as the absence of dependence, in particular financial dependence, and to systematize citizens’ selfprotection via the rigorous, impartial dictates of mathematics. Probabilistic mutual insurance is at once a voluntary contract that reflects a reasonable or prudential response to uncertainty and a means of spreading the burdens of that uncertainty across a group, reducing its differential effects. As such, it reflects the two central commitments of modern liberal government. The first is to some understanding of liberty, especially in the form of economic enterprise or property acquisition and the prudential judgments they require. The second is to an understanding of equality, in the form of an abstract potential or a material endowment or some combination of the two. The political resilience of insurance, and its unique distributive character, derive from the way in which it combines these aims. One of the earliest proposals for something like social insurance helps to demonstrate this claim. It comes from Daniel Defoe, who in his 1697 An Essay Upon Projects envisioned a wide-ranging, borderline-compulsory system of mutual and local insurance entities to protect economic providers and their families from financial ruin. Defoe recognized the relevance of probability calculations to his proposals and referred to William Petty’s Political Arithmetic, though his argument does not reveal a deep engagement with the mathematical literature. His proposal comprises two main parts: a system of pension offices for the working classes and mutual insurance or friendly societies for specific categories of people. Discussing the first, Defoe observed that “innumerable circumstances reduce men to want,” including fire, shipwreck, injury, and the like, as a result of which they may find themselves dependent on charity “without any procuring of [their] own.” To ensure that “all mankind . . . shall gain for himself a just claim to a comfortable subsistence,” then, Defoe proposed that workers pay a small sum to a local office and, in return, receive “an assurance” that in case of injury, illness, or other incapacity they will be given medical care or a subsistence income.10 He suggested that these offices be located in and supported by parishes, in a place convenient for the workers themselves to reach, and overseen by dedicated managers and clerks responsible for receiving and registering deposits. Such a system would allow “all persons in the time of their health and youth, while they are able to work and spare it,” to “lay up some small inconsiderable part of their gettings” as security against later need. Alternatively, “if God so bless them, that they nor theirs never come to need it, the overplus” of their contributions “may be employed to relieve such as shall.”11

50 / Chapter Two

In the same spirit, Defoe also proposed friendly societies for merchant sailors disabled at sea, as well as for the widows of “inferior clergy, or of shopkeepers and artificers” who lose their source of income along with their spouses.12 Here, Defoe insisted that fairness requires disaggregating individuals into appropriate risk categories: Since “a seaman or a soldier is subject to more contingent hazards than other men,” they are “not upon equal terms to form such a society; nor is an annuity on the life of such a man worth so much as it is upon other men.”13 It is therefore “necessary to sort the world into parcels,” and as men’s “contingencies differ, every different sort may be a society upon even terms.”14 Mutual insurance of this sort is an act of “equity, as well as charity; for as it is kind that my neighbour should relieve me if I fall into distress or decay, so it is but equal he should do so if I agreed to have done the same for him.”15 Defoe stressed that such mutual aid differed from the premium insurance offered by the commercial offices of his time. While emphasizing that payment for the acceptance of risk is a legitimate commercial custom, he noted that in practice it often devolves into gambling. By contrast, mutual insurance, where “every one who subscribe, pay their quota,” could serve the public interest without such speculative pitfalls.16 At the same time, mutual societies on Defoe’s account do not oppose the spirit of commerce. Rather, they are a salutary consequence of that spirit, one of the many “projects” spurred by necessity and enabled by the merchant’s ability “to contrive new ways to live.”17 To the “true-bred merchant,” the “most intelligent man in the world,” one can “trace the original of banks, stocks, stock-jobbing, assurances, friendly societies, lotteries, and the like.”18 Defoe thus captured the ambivalent character of insurance as a practice that both reflects the ethos of private enterprise and seeks to mitigate some of its effects. Defoe’s proposals did not have much political influence while their author was alive, perhaps because probability theory was still in its infancy and statistical data quite limited at the time.19 Yet they found resonance with later friendly society reformers, whose proposals we will take up a bit later.20 By then, the success of statistical life insurance had demonstrated that disaggregation could allow mutual societies to achieve greater inclusiveness without sacrificing their financial stability. What is more, because the theory underlying such insurance stressed its fairness and nonspeculative character, there was no reason its model should be applied only to commercial insurance. In fact, it seemed just as well suited to cooperative welfare schemes, which aimed not to make a profit but to offer security through communal self-help—and, by the same logic, to state-sponsored schemes as well.

Probabilistic Justice and the Beginnings of Social Insurance / 51

Richard Price: Property and Political Arithmetic The previous chapter emphasized the distinctions between early friendly societies and actuarial insurance, arguing that the former represented a model of mutual aid that called on strong feelings of identity among members who were expected to share in one another’s fate. We also saw that such mutual aid required a fair amount of exclusivity and behavioral compliance, which limited the friendlies’ reach, particularly among poorer segments of the working population. The movement to reform friendly societies along actuarial lines grew from the recognition of their salutary effects and a critique of their alleged failures. Bearing its first fruits in Great Britain toward the end of the eighteenth century, and subsequently taking root in France, the movement was inspired by the success of the Equitable and the new image of life insurance it fostered. Essential to this image was the reliability of probability values derived from mortality data.21 As we will see in greater detail in the next chapter, contemporary developments allowed mathematicians to calculate predictive probabilities from the observed frequencies of events, such as births, illnesses, and various civic phenomena, with more precision than had previously been thought possible. Moreover, they did so in a way that promised guidance both in particular cases and in the aggregate, or in other words for both individual decision makers and for the insurer or state. Once mathematical calculations could be relied on in this way to accurately predict the mortality experience of subscribers, insurers could in principle offer coverage to large groups while charging each individual a premium that closely tracked his own risk. So too could friendly societies accommodate greater and more diverse membership without compromising their fairness or financial stability. Good sense guided by calculation would thus align with reciprocity and security for all. Among the first and most prominent leaders of this movement was Richard Price, who had served as an early mathematical advisor to the Equitable and whose nephew and protégé, William Morgan, later became its actuary. Price, whose support for the French Revolution would later make him the target of Edmund Burke’s Reflections on the Revolution in France, was admitted to the Royal Society in 1765 for his research on probability. In 1771, he published the first of several editions of an influential reference work, Observations on Reversionary Payments, which laid out actuarial calculations for premium life insurance and annuities. Penelope Ismay has pointed out that Price was not originally interested in friendly societies per se but set out to fix the largely middle-class insurance schemes that had

52 / Chapter Two

spread throughout the eighteenth century. Nevertheless, Ismay shows, he also proposed a model for financing friendly society benefits that, while actuarially flawed in some respects, powerfully influenced contemporary discourse about the relief of poverty.22 Indeed, more than a technical manual for would-be actuaries, Price’s tract formed an important part of a much larger political project. At least three elements of this project drew support or inspiration from life insurance mathematics; they therefore highlight the close connection between probability theory and a prominent strand of political thinking during this period. It is worth pausing to consider each in turn. The first is Price’s advocacy of mutual insurance as means of promoting property ownership and economic independence.23 By the time Price wrote Reversionary Payments, the connection between mortality calculations and property rights had been well established. As David Bellhouse has shown, many early mathematical calculations of annuity values were connected to leases for land, which in England were often granted for a set term of 21 years or three lives. In this context the landowner was like an annuitant, with payments received in the form of rent, and the present value of the annuity was part of the value of the land. The original connection between annuity prices and property was thus forged in the early seventeenth century to support landowners who, due to changes in land management policy such as the government takeover of ecclesiastical lands, the selling of Crown estates, and the enclosure of fields, may have had new impetus to calculate the value of their leases.24 Price, for his part, used mortality calculations and their associated practices to promote security and independence for owners of mobile rather than landed property. He was not the first to do so: Edmond Halley had noted that his calculations could be applied to reversionary annuities for the support of “Clergy-men’s widows and others,” who frequently lacked access to land or other rents, to provide them with a measure of financial security after their spouses’ passing.25 Half a century later, the Equitable advertised the great benefits of life insurance for those “whose subsistence depends upon the life of the person assured,” and who therefore wish to “make some form of provision for their families” when their income ceases. Such clergymen, lawyers, artisans, manual workers, and “others who support themselves by their labour” would gladly pass on to their loved ones “a portion of those benefits which their labour, whilst living, was used to procure for them.”26 Later, advocates of the new or reformed friendly societies in the first decades of the nineteenth century would also appeal to the prospect of property ownership, recasting members as “joint

Probabilistic Justice and the Beginnings of Social Insurance / 53

proprietors” of society funds and owners of insurance policies calculated, thanks to actuarial tables, at a set rate for each class.27 Price made a similar argument, but in the context of a much broader appeal for liberty and self-government. For Price, applying mathematics in general—not only the theory of probability—to public affairs promised to foster a virtuous and free citizenry, one that would be capable of opposing the incursions of a despotic state.28 For instance, in the last chapter of his Observations on Reversionary Payments he discussed at length the national debt, which he feared would breed corruption by making some citizens— those with an interest in the preservation of public funds—overly conservative and submissive to government.29 Reducing the debt was therefore necessary to prevent undue “dependence on the crown” and discourage “acquiescence and servility.”30 On the question of how to accomplish such a reduction, Price proposed a sinking fund, which would pay down the debt while in principle protecting public money from corrupt appropriations. Mathematically informed policy, as Price envisioned it, could thus operate as a kind of check both on the powers of the state and on the temptations of citizens to place narrow self-interest above fairness and the common good. This broad faith in the power of calculation, including life insurance mathematics, also informed Price’s treatment of mutual societies. Historian Peter Buck has argued that Price looked to annuities to serve the same function that property played in the classical republican tradition.31 Reacting to the enclosure and engrossing of English farmlands, Price worried that the great majority of his compatriots would be deprived of the independence that property ownership allows. Whereas “in former times the number of occupiers of land was greater, and all had more opportunities of working for themselves,” now many were forced to work for others and the price of labor had correspondingly decreased.32 By turning small farmers into wage laborers, the British crown had reduced self-sufficiency among the lower classes and increased economic inequality overall. Enter annuities: Like land, they could encourage republican virtues and guarantee individual liberty over time. By encouraging effort and foresight, and securing workers’ earnings, annuities would promote a kind of propertied independence despite the trends toward urbanization, corruption, and inequality that Price elsewhere lamented.33 The same arguments could be made for mutual life insurance, particularly in the wake of the Equitable’s remarkable success. Indeed, insurance promised even greater intertemporal security than annuities in that it provided for the family of a wage earner after his death, and by the time of Price’s treatise it was on the way to losing its earlier association with gam-

54 / Chapter Two

bling. The Life Assurance Act of 1774, passed just three years after the first edition of Reversionary Payments, explicitly distinguished insurance from wagers by requiring a legitimate financial interest for all valid life insurance contracts.34 After this time, one could legally collect on a policy only if a person relied on the insured for income or was a creditor who would lose if the insured died before repaying his loan.35 Price’s own discussion does not distinguish clearly between life insurance and annuities, either on practical or on moral grounds; both types of society could generate fair payment and benefit schedules provided they made judicious use of life expectancy calculations.36 This in turn brings us to the second salient aspect of Price’s use of probabilities in political life: his effort to spread mutual insurance practices across social classes and especially to the poor.37 The notion that economic inequality could threaten liberty or independence was an important theme in the writings of liberal advocates of commercial society in the later eighteenth century. As Emma Rothschild has noted, Adam Smith spoke of inequality as a form of oppression, equated low wages with inequity, and lamented the psychological disparity that accompanies the division of labor. Condorcet, as we will see further on, also emphasized the link between inequality, insecurity, and dependence.38 For his part, Price objected to economic inequality less as an evil in itself than as an impediment to popular liberty and self-government. “The maxim, therefore, ‘that all men are naturally equal,’ refers to their state when grown up to maturity, and become independent agents, capable of acquiring property, and of directing their own conduct.”39 Without property, citizens fall into dependence and are poorly suited for political participation. With too much property, some individuals can coopt power and use it for their own interests rather than the common good.40 It was in America that Price saw the possibility of a republican society based on relative equality in land ownership and economic circumstance. “There is an equality in society which is essential to liberty, and which every State that would continue virtuous and happy ought as far as possible to maintain.”41 He praised those American states in which citizens occupy a “middle state between the savage and the refined, or between the wild and the luxurious state.” There an “independent and hardy Yeomanry, all nearly on a level,” maintain an “equal government, which wanting lucrative places, cannot create corrupt canvassings and ambitious intrigue.”42 He also emphasized the dangers of institutions and practices that allow citizens to amass unequal property, including hereditary honors, primogeniture, and foreign trade.43

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While America stood a chance of realizing the proper conditions for republican government, however, Price found Britain to occupy a very different position. “There is a degree of political degeneracy which unfits for such a constitution,” he noted. “Britain, in particular, consists too much of the high and the low (of scum and dregs) to admit of it.”44 A country in this condition will likely require practices that reproduce or approximate propertied independence in other ways, especially for the most vulnerable. “The lower part of mankind are objects of particular compassion,” Price wrote, “when rendered incapable, by accident, sickness, or age, of earning their subsistence.”45 The fact that so many existing annuity societies failed to meet their obligations rendered reform particularly urgent, both for ending pernicious dependence and for extending the prerequisites of self-rule as widely as possible. Finally, Price understood mathematical probability as integral to the progress and ultimate perfection of humanity, offering a testament to the advancement of reason and a tool for the continued improvement of political life. In 1763, Price published an essay by his friend the late Reverend Thomas Bayes on what became known as inverse probability. There, Bayes had pioneered a method for calculating the chance that the probability of a future event will be within a certain range, based on a set of prior observations. Invoking the physical device of a flat, square table and a series of balls rolled thereon, Bayes analogized the unknown probability to the horizontal coordinate of a single ball rolled across the table. A second ball is then rolled repeatedly, with each time it lands to one side of the original ball counted as a success; these rolls represent the observed trials. Thanks to this setup, the resting place of the original ball is uniformly distributed within the square and the total number of successes of the second ball has a binomial distribution. Bayes was then able to compute the probability that the location of the first ball falls within a certain range given the number of observed favorable outcomes.46 Compared with the independent treatment of French natural philosopher Pierre-Simon Laplace, which we will take up in the next chapter, Bayes’s solution to the inverse problem was relatively neglected until the twentieth century, and he himself did not attempt to apply it to particular examples.47 Yet Price readily grasped its far-reaching potential as a guide to judgments about uncertain phenomena, particularly in the wake of David Hume’s skeptical treatment of the problem of induction.48 Whereas Hume had profoundly questioned the logical basis of inferences made from prior experience, Price found in Bayes’s method a potent tool for forming rational expectations, based on past occurrences, about the outcomes of uncer-

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tain events. In his introduction to Bayes’s essay, Price explained that his friend’s contribution was “by no means merely a curious speculation in the doctrine of chances” but addressed a problem that must “be solved in order to [provide] a sure foundation for all our reasonings concerning past facts, and what is likely to be hereafter.”49 Price moreover concluded that Bayes’s finding revealed, with “distinctness and precision,” to what extent recurrent events stem from the “stable causes and regulations in nature.”50 The inverse (or, in Price’s terminology, “converse”) method thus promised to uncover the guiding presence of natural laws and to free judgments from the burden of epistemic doubt. Far more than a mathematical exercise, then, for Price probability offered a means to individual and political liberation.51 On the individual level, it promised to encourage the proper use of reason and foresight, allowing people to become masters of their own minds and futures. On the political level, it promised to promote an enlightened citizenry that would support judicious, mathematically informed policies. Finally, it appears to have supported Price’s faith in the continued improvement of the human condition. Not only could mathematical advancement be seen as proof of the progress of reason, but the inverse method supported an expectation of further progress based on observation of what had already been achieved. “Nothing can direct us better in judging of the manner in which future improvements are likely to proceed,” Price explained in a speech on divine providence, “than reflecting on the course of human improvement as it has hitherto taken place.”52 Indeed, in light of such evidence, the “happy termination of human affairs in this world . . . is an expectation no less credible and probable in itself than it is encouraging.”53 I suggest that for Price, as for others at the time—in particular his correspondent Condorcet, whom we will meet a bit later—mutual insurance provided an important example of the perfecting potential of mathematics. Whereas under speculative and mismanaged schemes “‘the gain made by some . . . will be so much plunder taken from others,’” mathematically sound arrangements will draw responsibly from all and return to each his due.54 Although Price considered a fairly wide range of possible financing options in his Reversionary Payments, he described as “equitable” primarily those in which contributions were graded by age.55 By making “the benefit which a member is to receive to depend . . . on the value of his contribution” in this way, these schemes could be both prudent and fair, consistent with the demands of “reason, justice, and humanity.”56

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Friendly Society Reform: Social Insurance Writ Small Promoting responsible insurance practices was therefore a central objective of Price’s Observations on Reversionary Payments, as well as his involvement with the Equitable.57 In addition, he helped to devise a 1773 bill that would have allowed parishes in England and Wales to sell life annuities at probabilistically determined prices and, where necessary, charge them to the parish as a security to poor purchasers. He envisioned that this bill would use friendly societies as a model for publicly supported mutual relief, and as part of his advocacy he supplied the tables from which annuity prices were to be calculated.58 Although this proposal, as well as a subsequent one of 1789, met with defeat in the House of Lords, a successful reform act of 1793 rendered Price’s tables the standard reference for friendly society contributions until 1825.59 The 1793 legislation, sometimes called the Rose Act after its champion, George Rose, granted important benefits to friendly societies and their members. One of these was to free members from some of the strictures of the laws of settlement, which established when a parish (or unit of administration under the poor law) was liable to provide relief to a particular person, as well as the means of expelling someone who did not have a legal right to relief where he lived.60 By explicitly recognizing that friendly society members were willing to work and industrious enough to save, the law made it significantly easier for them to obtain legal settlement. It also granted legal standing and privileges to societies that submitted to an official registration process, which involved depositing their rules with justices of the peace and meeting certain requirements regarding the formation of tables and the investment of funds.61 Several subsequent bills determined which authorities would be charged with examining the societies’ rules and permitted registered societies to deposit their capital into savings accounts or to invest it with the Treasury.62 As the attention afforded to friendly societies grew, so did their number. While in 1803, there were nearly 10,000 such societies in the United Kingdom, with a combined membership of 704,350, by 1815 total membership had increased to over 925,000.63 Despite their growing popularity, however, many societies were still relatively unstable, creating “inextricable financial embarrassment,” in the words of French social insurance advocate Émile de Girardin.64 Parliament, trying to remedy matters, passed an act in 1819 giving judges several new rights, among them the power to decline authorization to societies in districts where another group was already organized on the same basis; to decline societies whose financial

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components were not approved by two professional mathematicians; and to ensure that no society would be dissolved until two actuaries decided that doing so would be advantageous to all its members.65 An additional act passed in 1829 empowered barristers to certify that society rules conformed to law, and another of 1846 broadened legitimate society functions to include any eventuality that could fall under the probability calculus. The latter also established the foundations of a centralized system in the form of an official registration process, in which societies submitted their tables to an actuary in order to qualify.66 By 1872, in the wake of such official state encouragement, there were close to 1,900,000 reported members of friendly societies in England and Wales, and nearly 400,000 in Scotland and Ireland.67 Given the direction that friendly society reform took, it is difficult to deny the influence of probability theory, and specifically life insurance mathematics, on the movement. With the help of proper calculations, the thinking went, friendly societies, like the new life insurers, could encourage virtues such as industry, frugality, and responsibility.68 Advocates argued that participants in friendly societies not only had to work hard and save to afford membership but also would not have to turn to their parishes for relief. Introducing actuarial calculations would reinforce these virtues, replacing the original societies’ spendthrift conviviality and ad hoc distributions with the rigorous counsels of mathematics. Societies that successfully forecast their liabilities through the use of mortality tables and probability calculations would guarantee their viability in a way that others purportedly could not. And members who could understand their benefits as a form of property, calculated as a function of their individual risks, would be rewarded for their personal efforts and further encouraged to save to purchase higher levels of coverage.69 It is important to note that the reformers’ vision was neither immediately nor ever fully realized in practice. Many societies resisted actuarial reform well through the nineteenth century, preferring to collect and distribute funds as needed rather than in accordance with calculated risks. Nevertheless, the probabilistic model of forward-looking mutual support offered what many saw as a compelling alternative to existing poor relief. The poor law system relied on local knowledge of recipients’ characters and work histories, which enabled parishes to determine whether any given individual deserved support. At a time of economic flux and increased internal migration, as laborers and their families crossed parish boundaries in search of work, contemporaries looked for ways to promote reciprocity among those without preexisting social ties.70 Reformed friendly societies

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appeared to fit the bill, relying less on personal knowledge and more on impersonal risk classification, all the while rewarding the kind of foresight and self-denial needed for survival in a commercializing society. As for their friendliness, the rough and implicit justice of the early societies was to give way, under the influence of these reforms, to the more exacting mutualism of disaggregated groupings. One relatively early pamphlet criticized existing societies for excluding members above age thirtyfive and argued that the “greater hazard” posed by older members could be accommodated by grading admissions fees or requiring periodical payments by age, as in “the practice of insurance offices.”71 Another popular treatise, from the height of the reform movement, cited the “manifest” injustice of “requiring men of different ages to pay a like rate,” and found the practice at odds with the feeling of “equity and benevolence” on which the friendlies rested.72 Its author, Charles Ansell, emphasized the importance of basing mortality calculations on “persons placed in like circumstances, except as to age,” to match the observed experience with the projected one.73 The implications of this reasoning are clear: The more precisely one can classify observations into risk groups without sacrificing their number, the more accurate a society’s projections and the more equitable its benefit scheme would be. Britain did not yet systematically collect the type of data Ansell apparently had in mind, such as family history, social class, and physical environment. Yet he was able to promote an actuarial approach to sickness in friendly societies: Alongside mortality curves based on the experience of English clubs, he published morbidity tables from the same population detailing the number of illnesses and the mean duration of illness by age, and he compared these findings to those of Scottish club members. Reformers apparently saw no conflict between risk segregation and the friendly societies’ mission of communal aid because, in their view, actuarial insurance is an inherently mutualistic practice. Probabilistic equals who survive longer than the average pay for those who, by no fault of their own, are afflicted sooner. It is also inherently communal, in that only by joining together with a large group of peers can one ensure that the projected average is realized. Self-interest thus aligns with a common good, as the simple act of saving a small portion of one’s earnings guarantees security to both oneself (or one’s family) and the association. As a result, it became possible during this period to present mutual insurance as an obligation, a sign of responsibility and self-sufficiency, and even a civic duty. In 1825, a select committee of the House of Commons declared mutual insurance preferable to private savings since the individual who saves “is really the speculator,” betting that he will stay healthy dur-

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ing his productive years and live only long enough to exhaust what he has saved. The insured, by contrast, while reducing his own monetary reserves, guarantees his and others’ security: Whenever there is a contingency, the cheapest way of providing against it is by uniting with others, so that each may subject himself to a small deprivation, in order that no man may be subjected to a great loss. He, upon whom the contingency does not fall, does not get his money back again, nor does he get for it any tangible benefit; but he obtains security against ruin and consequent peace of mind. He, upon whom the contingency does fall, gets all that those, whom fortune has exempted from it, have lost in hard money, and is thus able to sustain an event which would otherwise overwhelm him.74

According to this rationale, it is not enough to simply have foresight and look after one’s own good. Responsibility means tapping into the power of the average so that one’s exposure is buffered by the reliable experience of the group. Some argued that mutual insurance was not only safer but also nobler than private savings, combining economic good sense with a kind of fellow feeling or generosity. “The principle of the savings bank is that every man is to save for himself,” explained one English pamphleteer in 1817. “The principle of the Friendly Societies is, that every man is to save for himself, if he needs it; but if not, for those whose necessities may be greater than his own.”75 The same view was voiced in 1839 by French jurist JosephMarie  de Gérando and cited approvingly in 1852 in the Dictionary of Political Economy, a work of French liberal political economists. As Gérando put it, “The provident society is a confraternity; mutual assistance is an act of mutual benevolence; it joins to prudential combinations the merit of a good action, since the portion of savings that is not collected by the member who has contributed them profits his associates.”76 Such statements imply that thinkers of this time were well aware of a possible conflict between self-interest or commerce and reciprocity. They saw in the idea of probabilistic justice, and the practice of mutual insurance in particular, a key to its resolution. All of these arguments for actuarially reformed friendlies found clear echoes in early arguments for social insurance as well. The latter were equally inspired by the probabilistic account of justice, imagining the state as one large mutual insurance society. If the original friendlies reflected a voluntary, self-policed, and therefore limited form of risk sharing, their re-

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formed cousins would show how the paternalistic power of the state and the impersonal dictates of mathematics could rationalize self-help for the benefit of all. In this sense, the idea of reformed friendly societies can be seen as social insurance writ small, and it was not a stretch to propose state-run mutual insurance based on the same principles.77

The First Social Insurance Plans: Mutual Insurance Writ Large Early Proposals In England, one of the first proposals in this vein came in 1772 from Baron Francis Maseres, a lawyer and mathematician with interest in actuarial subjects. Maseres’s scheme, which he set out to implement through an act of Parliament, would have given workers in manufacturing areas the chance to buy annuities through their parishes, to be paid out of the poor rates of the parishes themselves. The idea garnered support from Richard Price, who argued that Maseres’s plan (with some modifications) would not only promote industry among workers but also “ease parishes of a considerable part of their present burdens” in providing poor relief.78 As the proposed act put it, the opportunity to plan for their own futures by purchasing annuities would encourage workers to “become more sober and virtuous in their ordinary course of life” and, in so doing, “increase . . . the riches and manufactures of this kingdom.”79 Although it was rejected by the House of Lords, the plan provoked considerable interest in both insurance principles and friendly societies among the public.80 Several years later, English clergyman John Acland used Price’s data to propose another plan for national insurance similar in spirit to Daniel Defoe’s. The plan, “founded on the basis of the friendly societies” and published in 1786, would have created a single compulsory mutual society for all of England. Acland had apparently learned from the failure of an earlier scheme, enacted in 1769, that had proved itself financially unsustainable due to what is now known as adverse selection, or the oversubscription of participants who know they are likely to incur the qualifying event.81 He therefore recommended that participation be mandatory, risking “the odium of so unpopular a proposition” to ensure that the society would not incur greater liabilities than it could afford.82 He also proposed a progressive benefit scheme, offering “the lower classes of subscribers  .  .  . an allowance, beyond what their own contribution would itself afford,” on the ground that by participating in the scheme they saved public funds that would otherwise be spent on their relief.83 Individuals would be free to

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choose to insure themselves for any sum within a given range, and participation would entitle them to a weekly payment if they were rendered incapable of working. Acland argued that this scheme would benefit the individual and the public alike, in part by preventing workers from becoming undue burdens on the commonwealth. “It seems but just that every man should be obliged, out of his present abundance, to take so easy a method of securing to himself such a subsistence, as  .  .  . would insure the public from his ever becoming a burthen to it.”84 Like the reformed friendlies, such a plan would reflect both personal responsibility and the limited altruism of the shared risk pool. In addition, its large public scale would allow for “a national security for its accumulating capital,” compound interest on its funds, and “what is of no small weight, a very considerable resource, to eke out the poor man’s subscriptions, in the gratuitous contributions of the richer subscribers.”85 In short, just as voluntary mutual insurance was less risky and more collectively beneficial than private savings, compulsory social insurance would on this account be more secure, more encompassing, and even more altruistic than the friendlies. Meanwhile, in France, the 1780s and 1790s also saw a variety of national insurance proposals. By this time, as Gareth Stedman Jones points out, the success of the Equitable had promoted a number of imitators there, and the government also took interest in insurance as an important source of public revenue.86 One of the first plans to emerge from this climate was that of André-Jean de Larocque, who in 1785 proposed a system of general savings accounts that would invest funds generated by regular workers’ contributions and return the proceeds as annuities. A second came from Emmanuel-Étienne Duvillard de Durand, a civil servant and mathematician who, with Condorcet, belonged to the elite Society of 1789 that set out to reform the French constitution.87 Duvillard began his proposal for national life insurance with the observation that “wise and prudent men . . . have always been disposed to seize the occasion to draw from the long life of others a remedy for the inconveniences that can result from the shortness of their own.  .  .  . They have often reunited in societies for this purpose.”88 His plan would have offered various types of age-graded life insurance and annuity policies to all citizens who chose to purchase a plan. It would also have created a government office of “calculation and information” to establish such insurance and to promote mutual benefit associations aided by statistics and mathematical expertise.89 These plans testify to the appeal of insurance, both to an ethic of individual prudence and to considerations of reciprocity and a common good.

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For the most part, thinkers during this period understood the practice in what I refer to as liberal terms. This means, first, that they understood the insurance agreement as intended to protect the welfare and property of the individual. Second, they regarded participation as a reflection of personal responsibility, in particular the ability to look successfully after one’s own affairs. Finally, they implicitly presented insurance as a bilateral contract between the individual and the insurance provider—one that, while involving groups of similarly situated individuals, would not call on any sense of familiarity or thick identification with the other members of one’s group.90 As we will see in the next chapter, these individualist commitments, combined with the attempt to justify a moral duty to insure, also found direct expression in the main currents of contemporary probability theory. Few better exemplify these tendencies than the Marquis de Condorcet. Condorcet: Probability and Perfectibility Shortly after the appearance of Larocque’s and Duvillard’s proposals, Condorcet articulated his own plan for probabilistic social insurance along similar lines. In his late and unfinished The Sketch, published in 1795, Condorcet cited Price, along with Anne-Robert-Jacques Turgot and Joseph Priestley, as the “first and most brilliant apostles” of the new doctrine of “the indefinite perfectibility of the human race,” which would eventually change social relations by putting an end to the arbitrary dependence and persistent inequality caused by ignorance and prejudice.91 Condorcet believed that the probability calculus would play a central role in this process, providing the tools to illuminate and conquer the workings of nature, to improve individual reason, to rationalize political economy, and perhaps above all to promote equality of conditions and the “true perfection of man.”92 The next chapter will discuss in greater detail the mathematical developments that inspired Condorcet’s faith. For now, we will focus on one of its most striking political expressions. Condorcet introduced his proposal by recognizing the insecurity of workers’ livelihoods and arguing that the dependence and suffering they experience whenever they lose their work could be “in great part eradicated” through publicly orchestrated mutual insurance. Such methods had “already been successful” thanks to “the application of the [probability] calculus to the probabilities of life and the investment of money.” But they had not yet “been applied in a sufficiently comprehensive and exhaustive fashion to render them really useful . . . to society as a whole.”93 The three schemes that Condorcet went on to propose closely resemble

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actuarial insurance both in their spirit and in their workings. The first is a kind of social security, which would guarantee the elderly “a means of livelihood produced partly by their own savings and partly by the savings of others who make the same outlay, but who die before they need to reap the reward.” The second would secure “for widows and orphans an income which is the same and costs the same for those families which suffer an early loss and for those which suffer it later.” And the third would provide children with “the capital necessary for the full use of their labor,” which increases “at the expense of those whom premature death prevents from reaching this age.”94 Technically, these schemes are designed to function more like annuities, in that they rely on the fact that some participants will die before collecting their benefits and therefore subsidize those who end up living longer than average. Yet they also have all of the major characteristics of insurance: a payment calculated as a function of at least one of the insured’s characteristics, designed to compensate for a prospective misfortune or loss, and made to a party whose sole role in the agreement is to shoulder the burden of that loss. Condorcet justified the need for such programs on the ground that those who depend on their own labor to survive are far more vulnerable to uncertainty than those whose income derives from other sources and “whose resources are not at all subject to the same risks.”95 The inequality and dependence that result from this state of affairs are therefore unnecessary and undeserved, a proper target for ameliorative efforts. While it would be “foolish and dangerous to wish to eradicate” all inequality, since some is the result of “natural and necessary causes,” social insurance promises to reduce arbitrary inequality and “prevent those periodic disasters which strike at so many families and which are such a recurrent source of misery and suffering.”96 Together with widespread access to credit and education, these schemes would promote a kind of universal self-sufficiency, such that everyone is able to “manage his household, administer his affairs, and employ his labor and his faculties in freedom.”97 Whatever inequality does survive will be in everyone’s interests, promoting “the progress of civilization . . . without entailing either poverty, humiliation or dependence.”98 On Condorcet’s account, then, the purpose of social insurance is to prevent severe inequality and its concomitant dependence. Although his argument is fundamentally a liberal one, emphasizing the responsibility, self-sufficiency, and welfare of individuals, it contemplates both compulsory and voluntary schemes without any apparent sense that the former might violate individual freedom. The liberalism of this account therefore hinges not on the voluntary decision to insure but on the assumption that

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insurance is a rational choice (whether or not it is in fact chosen) and on the claim that it provides a kind of freedom one could not secure without it. As we will see in greater detail in the next chapter, this account also rests implicitly on a conception of risk as calculable for individual events and of insurance as a bilateral contract between insurer and insured. While requiring collective participation, then, insurance remains on this view a tool for securing one’s own property and welfare through calculated provision against the vicissitudes of chance.99 Thomas Paine: Welfare without Insurance Yet another important early proposal for welfare policy came from Thomas Paine. Stedman Jones notes that both Condorcet and Paine offered a “distinctively modern form of radicalism” that started from a “future-oriented theory of commercial society.”100 Both men embraced commerce and saw in the mechanism of reciprocal interest an important means to improve the human condition. Both also sought ways to render commercial society more humane or, perhaps more accurately, to realize its full potential by promoting enlightened independence among all of its members. Central to this project was a kind of welfare state: In Rights of Man, issued in two parts in 1791 and 1792, Paine advocated providing a series of tax-financed payments, including old-age stipends, educational assistance, and maternity benefits, to all citizens who chose to claim them. Paine argued that such support, which “is not in the nature of a charity, but of a right,” a universal entitlement for all citizens, would eventually supersede “the poor laws, those instruments of civil torture.”101 There are clearly similarities between Paine’s plan and other proposals we have considered. Like many early advocates for social insurance, Paine sought an alternative to existing poor relief. Like others, he set out to present beneficiaries not as passive recipients of aid but as holders of an entitlement, whether contractual or moral, to relief. And like others, he wanted to rectify the unequal distribution of property that left some in a state of economic and political dependence. Yet Paine’s scheme also differs in important respects from those we have considered thus far. First, there is the striking fact that he referred to his proposed old-age payments as a tontine, providing “little more than the legal interest of the nett money” the individual has paid in taxes.102 Tontines, which offer a kind of annuity, involve an annual payment that increases with age yet reverts to the government on the beneficiary’s death. Although tontines had been relatively prominent both as a source of public finance and in private benefit schemes since

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their introduction in the mid-seventeenth century, many had ended in failure, and government tontines were banned in France in 1763.103 They subsequently came to be associated with gambling, in contrast to the purportedly sober and prudential spirit of insurance.104 In addition, Paine made no attempt to render his proposed benefits contingent on prior contributions, nor did he stress the need for any sort of probabilistic accounting of the various risks involved. Instead, he proposed to finance assistance and public services through progressive taxation, making benefits available to anyone who demands them. Neither of these features necessarily removes Paine’s proposals from the social insurance tradition. In principle, tontines do provide a form of insurance, namely insurance against the risk of living longer than expected. While the actuarial knowledge required to administer them is less involved than what is required for life annuities, the insurer must know how long the oldest member of the group is likely to survive, and the subscriber should know the life expectancy of other members relative to the subscriber’s own.105 Moreover, as we will see in the following chapters, later advocates of social insurance also contemplated tax financing for their schemes without abandoning the notion that such policies provide reciprocal protection in the face of unavoidable or undeserved hardships. This is both because the determination of what constitutes a contribution for social insurance purposes came to be seen as flexible, and because the demand for actuarial fairness in social insurance is typically not as exacting as in commercial insurance markets. Yet Paine did depart rather decisively from insurance principles in a subsequent contribution to welfare theory, his Agrarian Justice, written in 1795–96. This work proposes to create a national fund, supported by an inheritance tax, out of which all citizens would receive a lump sum at the age of twenty-one and everyone at or over the age of fifty would receive annual fixed payments. Paine described these benefits as compensation for the loss of all men’s “natural inheritance” following “the introduction of the system of landed property,” which “has absorbed the property of all those whom it dispossessed, without providing, as ought to have been done, an indemnification for that loss.”106 Paine’s radical critique of the agrarian property distribution led him to view these payments as “not charity but a right, not bounty but justice.”107 Their purpose was to offer a form of redress for the suffering caused by what was essentially the theft or destruction of common property through private appropriation. Like contemporary proposals for social insurance, Paine’s plan for a basic endowment would protect workers from the risk of destitution and

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compensate citizens for arbitrary inequalities. Yet whereas in principle insurance offers protection against a future loss, Paine’s program sets out to redress a prior injustice. Whereas insurance grounds entitlement on a prior contribution that is in some sense proportionate or related to one’s benefits, Paine’s scheme draws funds from those who no longer have anything at stake and redistributes them to those who have contributed nothing. Whereas insurance equalizes individuals insofar as they share certain characteristics, Paine’s account assumes a kind of primordial equality— expressed in the assumption of original common ownership—that has nothing to do with their likeness. Finally, while insurance operates in the realm of contract, Paine’s proposal frequently invokes the language of tort. It is also noteworthy in this context that Paine objected strenuously to the idea that current politicians might make decisions that bind future ones. “Every age and generation must be as free to act for itself, in all cases, as the ages and generations which preceded it,” he wrote in a retort to Burke.108 The difficulty of securing commitment over time is a serious problem for social insurance since neither voters nor the politicians who represent them can bind subsequent voters to their own preferred policies.109 As a result, social insurance programs rely heavily on commitment mechanisms, such as trust funds, which ensure that payments made into the system today will be available for distribution tomorrow. Paine would regard such mechanisms with suspicion at best, particularly given evidence that they obligate future political actors in a way that general tax policy, for example, does not.110

That Paine did not propose a version of social insurance in Agrarian Justice does not necessarily rule him out as a progenitor of the modern welfare state.111 Yet it does remove his endowment scheme from the line of thinking under consideration here, which aimed to realize a vision of distributive justice as forward-looking mutual support among probabilistic equals. Like the liberal political tradition out of which it grew, this vision set out to align individual interest with a common good through universal fear or concern for the future, combined with the industrious and orderly behavior to which it can, when properly channeled, give rise. A risk-sharing association governed by the impersonal laws of mathematics was both an encapsulation of this vision and a tool for its realization. The idea of social insurance as it emerged at this time also raised a distinct set of questions and challenges related to the vision of probabilistic justice that supported it. As the discipline of mathematical probability became increasingly statistical toward the end of the eighteenth century, the

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justification for insurance came to rely heavily on the stability of long-term averages and the security of large numbers. Insurance could now be seen as a means of spreading or pooling risks among a large group of similar individuals: As the insurer takes on more and more risks of a similar nature, the theory goes, the insurer’s side of the transaction looks less and less like a wager, while the insured’s payment decreases to reach his own mathematical expectation, based on the average risk of his class. In principle, the virtue of spreading or pooling risks in this way lies in its ability to align what the insurance association must collect from each member with the amount each should pay according to his personal risk assessment. At the limit, insurance ceases to resemble a gamble or even a risky venture and is simply a prudent and fair arrangement for the mutual sharing of burdens. In reality, of course, such perfect alignment may not be attainable, even among noncommercial insurers. This is the case when a risk pool is relatively small, increasing the chances that its members’ claims will exceed the projected average, or when members are grouped imprecisely, meaning that the less risky end up subsidizing some of their peers. The challenge for probabilistic justice on a statistical view of risk is that the latter condition is almost invariably met. Likelihoods calculated from statistical data selectively choose certain features and ignore others that may meaningfully distinguish individuals.112 The question of who should be considered an equal for the purposes of determining contributions and payments is therefore a matter for the judgment of insurers, and in the case of social insurance a political question. This question saw a number of suggested resolutions in late-classical writings about insurance and the policy proposals made in their wake. The next chapter will look in detail at the mathematical developments that supported these works. As we will see, probability theory during this period entailed an uneasy union of methodological individualism and statistical aggregation. This combination reflected its expositors’ (ultimately unsuccessful) attempt to align the epistemic and aleatory aspects of probability and, in so doing, to harmonize individual judgment with the regularity and stability of averages. Their effort is noteworthy, first, in demonstrating how moral and political goals continued to inflect the probability calculus well after its earliest articulations; and second, in highlighting the lasting practical implications of the two sides, or Janus faces, of probability.

THREE

The Promise of Probability

One of the central arguments of this book is that thinking about probability, and by extension risk and insurance, has always been bound up with moral and political aims. In the case of classical probability, as we saw in chapter 1, it was the legal tradition of aleatory contracts and its understanding of equity that inspired the birth of the discipline and the concept of mathematical expectation. In the school of probabilistic thinking that followed, as I will now argue, it was a particular version of enlightened liberalism that motivated important elements of the probability calculus. The school of thought in question, which I refer to as late-classical or a posteriori probability, enjoyed prominence in England and France from the last decades of the eighteenth century through the middle of the nineteenth.1 It applied elements from the classical method to calculate predictive likelihoods on the basis of prior observations. Exponents of this approach, most famously Pierre-Simon Laplace, continued to use the device of equiprobable cases but gave it a new epistemic interpretation, grounding it in individual judgments rather than observed chances. At the same time, these thinkers increasingly understood probabilities in statistical and therefore aleatory terms—that is, as the properties of groups of individuals who share certain characteristics and whose experience is predictable in the aggregate. This combination entailed important consequences for the theory of insurance. On one hand, it allowed thinkers to maintain an individual, prudential rationale for the practice. On the other hand, it helped them to reimagine insurance as a means to political ends, including distributive fairness, social harmony, and public order. The resulting account presented insurance as a responsible economic choice, entered into for personal protection, while also touting its social benefits.

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The first part of this chapter focuses on the mathematical technique that most directly supported this vision, known as inverse probability or the probability of causes. This technique, which calculated the aggregate experience of groups without abandoning the relevance of probabilities for individual decisions, directly inspired thinkers who sought to apply probabilities to political affairs. The second part of the chapter examines the implications of this new apparatus for thinking about insurance. Together, the two sections aim to show that some of the most significant innovations of the period reflect exponents’ normative assumptions and practical aims, including an understanding of responsible decision making as avoiding unnecessary risk and a faith that such prudence could be made to serve the common good. The final section of the chapter considers how and why this quest to align personal prudence and liberty with a common good through insurance practices was ultimately unfulfilled. In part, this outcome stems from ambiguities in what is now known as actuarial fairness, or the notion that individuals should pay premiums that correspond to their particular risks. As we saw in the last chapter, this idea was central to the justification for mutual insurance in the latter part of the eighteenth century. Yet it has a number of difficulties, including that personal expectations do not necessarily align with the probability value calculated for a class. Whether they do so will depend on a number of factors, including how the individual is classified and the value she personally assigns to the risk. The thinkers we will consider here grappled with this problem in light of their faith in the rationalizing power of mathematics. Rather than resolving it, however, their solutions point to the persistence of a deeper theoretical question, namely the relationship between the epistemic and aleatory faces of probability. Indeed, by the middle of the nineteenth century, many thinkers within the probabilistic tradition had come to emphasize the aggregative character of the calculus, and with it a technocratic, top-down model of social insurance. While continuing to focus on the individual as the target of statistical reforms, this view elevated the role of state over voluntary schemes and downplayed the power of probability to promote personal enlightenment and independence. This tendency resulted, in part, from the failure of probability theory at the time to convincingly align individual judgments with statistical averages. It may also explain why it took a new account of probability—the frequentist interpretation that we will take up in chapter 4—to reimagine the individual and collective justifications for

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insurance in a way that, I will argue, helped to motivate many early welfare programs in Western Europe and the United States.

The Practical Aims of Late-Classical Probability Inverse Probability This section delves into the mathematical tools that supported many theoretical accounts of insurance from the late eighteenth through the mid-nineteenth centuries. It focuses in particular on inverse probability, a technique that assigns probability values to “causes” or underlying frequencies on the basis of empirical observation. This was one of the most significant innovations of mathematical probability around the turn of the nineteenth century. It lent support to attempts to calculate probabilities for social and political phenomena, for which statistical data was increasingly available, and encouraged many paeans to probabilistic mutual insurance such as those we encountered in the last chapter. It also rested on a newly epistemic interpretation of equiprobability, and with it on a distinct view of the relationship between individual judgments and empirical likelihoods. As we saw in the last chapter, mortality data had provided a crucial input for probability calculations since the latter half of the seventeenth century. Yet it was only around the turn of the nineteenth century that official statistics began to include a variety of other social phenomena. The governments of France and Great Britain each attempted a general census for the first time in 1801. In France, an official statistical bureau was established in 1800, the Ministry of Justice began compiling and publishing its own statistics in the 1820s, and official publications of economic data began to appear in the late 1830s. In Britain, a statistical department was added to the Board of Trade in 1833, and civil registration of vital statistics began in 1837.2 Such data would provide fodder for the statistical turn of mathematical probability, which gathered strength through the first half of the nineteenth century and is our focus here. Pioneered independently by Thomas Bayes and Pierre-Simon Laplace, inverse probability calculates the likelihood of an unknown composition or state of the world given the observed outcomes of events. It is a form of induction and the foundation of what one would today call statistical induction. For its pioneers and early adopters, particularly Laplace and Condorcet, it seemed to hold the key to a range of potential applications of

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probability calculations to civic affairs, not least of all through the practice of insurance. The effort to calculate predictive probabilities on the basis of empirical observation was certainly not new to the late eighteenth century. In a short manuscript on the history of probability, Condorcet credited Jacob Bernoulli for perceiving the crucial difference between games of chance and natural events, and for taking the first step toward applying the calculus to empirical questions of practical import.3 Bernoulli had found that for trials satisfying the axioms of the binomial distribution—that is, where a series of independent outcomes can each yield only a positive or negative result—the observed frequency of a given outcome converges to the true probability as the number of observations increases to infinity. His result was an approximation theorem: It could estimate the degree of likelihood that, given a number of trials, the observed frequency of events would differ within certain limits from the true one.4 Abraham de Moivre subsequently improved on Bernoulli’s approach, demonstrating that where one can assume an underlying frequency, “the ratio of happenings will continually approach to that [value], as the experiments or observations are multiplied” and finding the number of observations required to determine that value within given limits.5 Yet while these earlier treatments had suggested the possibility of a theory of statistical induction, they had not yet offered the mathematical tools required for its implementation. Those tools came from the independent work of Thomas Bayes and Pierre-Simon Laplace. Bayes, whom we met briefly in the last chapter, was born in London in 1701 or 1702 to a prominent religiously nonconformist family. A Presbyterian minister, he was elected to the Royal Society in 1742, possibly for an unpublished book on differential calculus as well as an article on trinomial divisors.6 His interest in probability may have been sparked by an earlier work by Thomas Simpson that analyzed, in the context of astronomical observations, the distribution of errors and the reliability of the mean versus any single observation as a measurement of a phenomenon.7 Bayes expressed doubt about Simpson’s assumptions, but the latter’s step of solving a probabilistic problem by focusing on physical observations rather than games of chance proved important for subsequent developments in probabilistic inference.8 Bayes’s now-famous paper on the inverse problem, published posthumously by his friend Richard Price, found the chance, given a set of prior observations, that the probability of an uncertain event will fall within a specified range of values. He thus sought to address the problem left unsolved by Bernoulli and de Moivre, which was of utmost practical importance to thinkers of this time, namely,

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how good an estimate of the population as a whole is any given observed outcome? Although Bayes’s contribution came first, Laplace’s was originally better known and more influential, and therefore is the focus of my discussion here.9 Born in 1749 in Beaumont-en-Auge, Normandy, into a gentrified farming family, Laplace moved to Paris at twenty to join the circle of scientists surrounding Jean le Rond d’Alembert, and he quickly set out to distinguish himself in mathematics. Although he was not, according to biographer Roger Hahn, politically inclined as a young man, he was enlisted into the Revolutionary-era effort to rationalize the French calendar, currency, and census, and he was later appointed minister of the interior by Napoleon Bonaparte.10 Over the course of his life, he made important contributions to pure mathematics, physics, and celestial mechanics, including applying the Newtonian theory of gravitation to the solar system. In later years, his political views grew more conservative, according to Hahn, and following Napoleon’s defeat he readily switched his allegiance to the new monarchy, eager for a return to peace and stability in France.11 Laplace was one of the most important probabilists of his era, publishing a comprehensive treatise, the Analytic Theory of Probability, in 1812, and its more popular introduction, the Philosophical Essay on Probabilities, in 1814.12 He has been seen as a transitional figure away from the classical account, with its partitions of equipossible sets, toward the statistical one that would subsequently prevail.13 Among his more influential contributions was his theory of the probability of causes, which he and his contemporaries believed held applications for physical and social phenomena alike. In an early memoir on the subject, dated 1774, Laplace analogized realworld events to black and white balls in an unknown proportion selected at random from an urn.14 Assuming that the balls are replaced after each draw, Laplace first set out to determine the probability that the true ratio of balls in the urn is a given number x, in light of the observed outcomes. Thus, if one had witnessed that out of one hundred drawings, thirty balls were white and seventy black, Laplace showed how to determine from this finding the probability that the true proportion of white balls is three to ten, or any other ratio one might choose. So far, Laplace’s result is the equivalent of what is known as Bayes’s theorem, with the assumption that all ratios or “causes” are a priori equally likely.15 That is, given very restrictive assumptions, Laplace showed how one can calculate the probability that some observed phenomenon (say, a record of 51 percent male births in a county) results from a particular underlying state of affairs (for example, an equal likelihood of male and

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female infants in nature as a whole). This finding is not predictive, however, so Laplace pressed on, seeking to derive the probability of drawing another white ball given prior draws of p white and q black balls. After a series of transformations, he found the probability of drawing another white, accounting for all possible values of x, or the unknown composition of the urn. This formula, which became known as the Rule of Succession, allows the practitioner to calculate the probability of a desired future outcome given certain empirical inputs and the assumption that all possible prior states of the world are equally likely to have “caused” the results.16 Laplace then further generalized his result to the probability of drawing m white and n black balls from the urn given p and q prior draws. Nor did Laplace stop here. He went on to simplify his results even further, showing through a series of approximations that where p and q are very large and m and n very small, one can conclude that the true underlying ratio of balls approximates p:q. In other words, under certain conditions, one need no longer assume that the underlying ratio of balls is unknown but can reasonably operate as though the underlying or realworld frequency of events equals the observed one. In asserting the identity between “real” probabilities and long-term observed ratios, Laplace confirmed and further encouraged the movement away from the classical understanding of probability. Another important contribution from this memoir is Laplace’s discussion of the problem of finding the best mean for a set of observations. In the two decades prior to this work, Simpson and others had proposed that the difference between any given observation and the true value of the phenomenon is symmetrically distributed. Picking up on this insight, Laplace set out to determine which curve best represents these errors, which he assumed would be symmetrical around the true value and decrease in number as the size of the error increases.17 Thus, given a set of observations— for example, the time at which an event occurs—Laplace sought to model the errors, or distances between the observations and the true time, and then use this curve to determine a single value that could represent the population. Stephen Stigler argues that Laplace’s treatment of this problem made way for his theory of the probability of causes because, by focusing on the differences between observations and the true value rather than on the true value itself, it provided an example of how reasoning could move from effect to cause rather than the other way around.18 Both innovations, in allowing for the probabilistic estimation of phenomena for which direct measurement is not possible, proved crucial for the emergent project of applying the calculus to social affairs.19

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Epistemic Equiprobability The techniques just discussed focused on the aleatory face of probability, measuring events in the physical world and estimating their true values or underlying causes. Yet they also rested on an epistemic premise that was no less crucial to probability theory at this time. As we saw, the attempt to determine unknown and predictive frequencies on the basis of observed evidence—the central project of inverse probability—requires assigning prior odds to the possible “causes” in question. In Laplace’s case, this took the form of assuming what is now known as a uniform prior distribution. If one imagines a different urn for every possible proportion of balls, this premise posits that an urn containing exclusively black balls is as likely to be the true “cause” of the results as an urn containing only white ones, and the same for all possible proportions in between.20 Laplace never offered an explicit justification for this assumption, though he continued to employ it in many of his calculations.21 The only plausible explanation to be found anywhere in his work stems from what has come to be known as the principle of nonsufficient reason or indifference.22 Although not an argument for the equal likelihood of causes per se, this principle states that, absent knowledge to the contrary, one ought to assume that all possible events are equally likely to occur. “When we wish to make use of this theory,” Laplace wrote in his 1774 memoir, “we regard two events as equally probable when we see no reason that makes one more probable than the other.”23 There was no real need for such a principle in the realm of a priori probability, where all likelihoods are considered to be known in advance.24 It was only with the transition to a posteriori probability, and in particular the effort to infer unobserved or underlying likelihoods from empirical observation, that a mathematical expression for the calculator’s ignorance became necessary. Laplace, for his part, seems to have believed that the principle reflected the skeptical, open-ended nature of the scientific enterprise and thus strengthened the link between inverse probability and the natural sciences.25 Indeed, it appears to have grown directly from epistemological currents of the time, combined with the continued need of the calculus for a common denominator of equally likely possibilities or outcomes. By this time, probability had long been linked to an associationist epistemology, which presented knowledge of the natural world as a product of connections between experiential facts.26 While such knowledge could never attain demonstrative certainty, the more one observed a connection between two events, the more likely one could consider it to be that

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they would link in the future. Laplace and his contemporaries understood mathematical probability as the scientific expression of this reasoning process—and thus, in Laplace’s formulation, as relative “in part to this ignorance” (i.e., of true causes), “in part to our knowledge” (as derived from experience).27 In this light, the principle of indifference appears as a practical tool, the precondition for scientific reasoning rather than its conclusion.28 By giving numerical expression to the calculator’s initial ignorance, it allows him to generate inferences that would be unavailable without it. As such, the principle also entailed a distinct interpretation of the equiprobability model at the foundation of mathematical probability theory. Originally understood as an aleatory condition, a representation of the actual chances of an event, in Laplace and his followers it became an epistemic one, a representation of ignorance regarding those chances. Only with sufficient experience would calculations based on this representation come to correspond with probabilities in the world. Laplace was not the only thinker to employ some version of this principle. In his own discussion of inverse probability, Condorcet noted that “what we call probability, is nothing but the relation of the number of combinations that lead to the event to [the number] of combinations that do not; combinations that our ignorance causes us to regard as equally possible.”29 Bayes’s argument was more complex, based on the fact that his table setup generated a uniform marginal distribution of outcomes—that is, the results of the observed trials, or ball rolls.30 Yet he, too, maintained that knowing nothing about the probability of an event requires assigning equal expectations or subjective weights to each member of the relevant set of possible outcomes.31 Richard Price followed suit, noting, for example, that prior to all experience, it would be as “improbable as infinite to one” that any given event should naturally follow another “because there would be an equal chance for any one of an infinity of other events.”32 Each author thus rested his empirical approach on an epistemic premise, linking the understanding of probability as a mental state to the process of calculating odds from observation. It is my contention that this effort to bridge the two sides of probability mirrors the moral and political aspirations of its exponents, and especially their faith in the promise of mathematics to align private judgments with a harmonious social order, either through the actions of individuals or through the interventions of the state. The principle of indifference allowed for the continued application of probabilities to singular events even as calculation focused ever more on long-run frequencies. It allowed

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for such application in two ways: first, by providing the basis on which the Rule of Succession’s predictive probabilities rested; and second, by stating that for any eventuality about which one is uncertain, one can reasonably assign equal probabilities to its possible outcomes in the absence of prior evidence.33 And yet, as we will see, the presumed harmony between the epistemic and aleatory aspects of probability was ultimately just that—presumed. To begin with, there is the practical problem of ensuring that individuals possess the kind of knowledge to ensure their proper use of probabilities. To this end Condorcet, ever the liberal, became deeply concerned later in life with promoting universal mathematical education.34 Such enlightenment would support personal independence and prevent tyranny, and also increase the likelihood that the outcomes of social decision procedures— which require aggregating heterogeneous preferences—would be fair.35 Meanwhile, other thinkers in this tradition, notably Laplace and his student Siméon-Denis Poisson, tended in their treatment of moral and political subjects to emphasize the authority of expert calculation over individual judgment. As a result, their politics took on a more explicitly statist hue despite the emancipatory spirit of the age.36 In addition to the practical problem of enlightening individual judgments, there is the theoretical problem that a mathematical likelihood derived from empirical observation will not always provide a sound guide to individual choice. This problem is not unique to a posteriori probability, but it was heightened by this period’s emphasis on large-scale observation as the basis for calculations. As we will see in the next section, the technical bridge provided by epistemic equiprobability found a parallel in the idea of moral expectation, or the subjective utility associated with a given risk. Both attempted to connect the individual with the aggregate, and both had implications for the understanding of insurance.

Between Individual Choice and Social Responsibility Toward the end of the eighteenth century, a distinctive rationale for insurance came to prominence in probabilistic writings. Rather than simply a transfer of risk, insurance was now theorized as a means of spreading risks across a group of similar instances or individuals. This idea emerged from the line of thinking first inaugurated by Jacob Bernoulli, which emphasized the stability of probability values derived from repeated trials, and received further support from Laplace’s work on the probability of causes. Since the frequency observed for the group approaches its true value as the

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number of trials increases, individual risks could be tied to statistical averages. In addition, the theory of errors implied that an insurer is likely to experience greater uncertainty in outcomes when the number of insured in any given class is smaller.37 This means the insurer is best served by taking on a large number of relevantly similar cases, who together will manifest losses that approximate their mathematical expectation. The logic supporting the case for risk spreading was therefore not entirely new.38 Yet the notion that the insured would benefit from combining with others who share relevant features and paying a premium that corresponds to the mathematical expectation of the group was a distinct idea, with its own promise and challenges. Today, it is often referred to as risk pooling, in which the insured join forces to tap into the regularity of large numbers.39 As articulated by thinkers of this time, the argument for risk pooling is that once the insurer can spread its risks over the group and accurately predict its expenses as a result, the insured will be able to pay a premium that closely approximates her expected loss, and which need not be inflated to compensate for the insurer’s uncertainty. This idea consequently seemed to offer mathematical proof of the alignment between self-interest and distributive justice, or between personal prudence and the common good. Yet it also raised the question of how the individual’s expectation, which is meant to express a value relevant specifically to her, corresponds to the average calculated for the group. This question lies at the heart of probabilistic mutual insurance and therefore of the policy paradigm that is the focus of this book. Late-classical probabilists offered their own distinctive answers—which, as we will see, both supported many midnineteenth-century proposals for social insurance and inspired a number of powerful critiques, leading to the new interpretation of probability that we will take up in the next chapter. A New Rationale and Its Challenges Few thinkers in the late-classical tradition better exemplify its harmonizing aims than Condorcet. He embraced Laplace’s 1774 memoir and the project of a posteriori probability as supporting his ideal of an enlightened liberal society, in which individuals contemplate and pursue their own welfare reasonably, independently, and without political compulsion or fear. Applying the probability calculus to facts that we have not seen ourselves “teaches us to find out and to measure the true strength of our reasons for believing” them, shedding the light of reason on “objects which have too long been abandoned to the seductive influence of imagination, self-

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interest and passion.”40 Mathematically guided reason could thus vanquish that “empire usurped . . . by passions over truth, by active ignorance over light,” replacing mere opinions with the compelling logic of calculation.41 Probability calculations further promised to align these enlightened individual judgments with collectively beneficial outcomes. “What are we to expect from the perfection of laws and public institutions  .  .  . but the reconciliation, the identification of the interests of each with the interests of all?”42 Mutual or social insurance was only one expression of this hope: Condorcet also sought to use probabilities to guide judicial decisions and voting rules, and, in so doing, to resolve the problem of social choice—that is, how to combine individual judgments into a single decision that could reasonably apply to all. Yet insurance is arguably a paradigmatic expression of Condorcet’s hope, at once a contract entered into for personal benefit and a means for promoting security and equality among a potentially unlimited number of persons. To understand why Condorcet labored to maintain an individual contractual rationale for insurance, it is helpful to consider the significance of economic liberty in his thought. As Emma Rothschild has shown, Condorcet and contemporaries Adam Smith and Turgot regarded commerce and industry as components of individual freedom, and in particular freedom from the economic, religious, and political incursions of the state. Like Turgot, Condorcet saw in market relations the prospect of liberation from insecurity and fear, a realm in which individuals could reliably pursue their own ends based on knowledge that they alone possessed.43 Far from being a cold and isolating place, however, the market on this account develops out of and is sustained by reciprocal interest. It calls for awareness of one’s own and others’ sentiments and facilitates the mutual satisfaction of needs. Condorcet’s account of insurance should be read in this light, as the exchange of a probabilistic expectation for the sake of personal, familial, and communal security. What is more, as we saw in the last chapter, mutual insurance on Condorcet’s view promised self-determination, especially for those who found themselves vulnerable to dependence and political oppression. In this respect, the case for various forms of insurance echoes the case for economic liberty more broadly. Such arguments place the individual at the center of their normative vision. Yet expectations determined on the basis of empirical aggregates are not simply or strictly individual risks. Rather, they are calculated for a group and rest on some understanding of similarity or equality among those who are classified together. Without such equality, whether assumed or empirically demonstrated, the individual may consider it unfair to pay

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the same premium as his peers. The argument for statistical insurance as a harmonizing force therefore depends on how one understands such probabilistic equality, and with it the relationship between individual expectations and those calculated for the group. Condorcet’s analyses of probability and insurance grappled with this relationship. The first of his proposed resolutions presents insurance as a market transaction. In an article on the pricing of maritime insurance contracts, Condorcet proposed finding the fair price of an insurance policy by determining the long-run average amount that a merchant could pay while still profiting in business and the long-run average amount that an insurer had to earn for his enterprise to be sustainable, or in Condorcet’s words, “to have a very large probability of gaining.” The fair price of the insurance derives from “a certain concurrence established” between these two amounts.44 This use of long-run probabilities reduces the price of the policy by making the insurer’s outcome more certain. The risk of the insurers thus “spreading itself over a number of objects much larger than that of the insured, they can, in conserving a very large probability of gain, content themselves with a much smaller profit.”45 With this account, Condorcet had reimagined probabilistic justice as a limit problem, in which individual events yield disparate results but any discrepancy between the two sides decreases as the number of trials becomes infinitely large.46 Similarly, in one of his contributions to the Encyclopédie méthodique, he defined the equality of two players in a game of chance as the equality of their long-run expectations, which can be attained only when the game is repeated a large number of times. The implication is that no game can be fair when played only once; the only safe choice is to spread one’s bets over a large number of trials.47 Condorcet used the metaphor of a game repeated an indefinite number of times to describe a variety of economic, legal, and political phenomena.48 In the realm of commercial transactions, this metaphor supported an account of equilibrium pricing as the subjective valuation of the parties, adjusted over time in the course of repeated exchange.49 Condorcet understood this iterative process as one of the central mechanisms by which, in a market context, individual judgments and choices could be coordinated to produce socially beneficial outcomes. As he wrote about the grain trade, “The greater the freedom, the more there will be shops, the more there will be capital employed in the exchange of wheat, the more there will be men habituated to occupy themselves in commerce. There results from this that liberty will bring about the greatest equality possible in the price.”50 Probabilities are essential to this process, governing the parties’

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estimations of their likely benefit and, by extension, the equilibrium price. “As the difference between the prices is equal to the expenses, to the compensations which the merchant is entitled to claim for his risks, and to the profit which must be returned to him, the effect of these three causes of price inequality will become the weakest that is possible.”51 In this respect, Condorcet’s analysis of insurance is an extension of his treatment of probabilistic expectation more broadly. Yet insurance is also a special case in that it can be understood both as a voluntary transaction, governed by the laws of market exchange, and as a noncommercial tool for promoting distributive equity. These two accounts are not incompatible, but they do imply different approaches to risk. While the first invokes a bilateral exchange between parties whose situations or desires are different, the second suggests a sharing of burdens among parties who are the same, at least in some respects. Condorcet and the other probability theorists under consideration in this chapter did not, as far as I have discerned, explicitly differentiate between these two accounts of insurance.52 Nevertheless, a noteworthy precursor to the distinction emerges from the first portion of Condorcet’s Mémoire sur le calcul des probabilités, the earliest-dated of a six-part mathematical and philosophical treatment of probability written over the course of the 1780s. In the wake of his friend d’Alembert’s critique of mathematical expectation, which we will take up in the next subsection, Condorcet conceded that this concept involves substituting an average value for a real one and may therefore be of little use as a guide to individual cases.53 Yet, he explained, in two types of scenario, a substitution of this sort may reasonably be made. The first involves voluntary exchanges in which one party agrees to trade a probabilistic expectation for a certain sum. Here, commercial prudence governs the transaction, and because the exchange is voluntary, neither party will agree to a price that is disadvantageous to her. In the aggregate, this “rapport of reciprocal needs establishes a common price,” such that “in a large number of similar exchanges, there exists between the two parties the greatest equality possible.”54 As a result, the substitution of an expectation—the market value—for a real one is not arbitrary “because there exists between the goods exchanged a species of equality, an average value that forms what one calls the price of things.”55 The second scenario in which averages may reasonably be used in the place of real values involves involuntary exchanges, in which one party exposes another to risk and the latter demands a price prior to the exposure. Such cases are regulated by the law of equity, which strives to generate “the least inequality possible” in the conditions of the exchange.56 It can

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do so by fixing the terms of the agreement fairly, such that in a series of multiple trials, each player’s probability of total gain or loss will approach one-half.57 Condorcet’s discussion here is rather short, but it appears that the two scenarios differ primarily in that while mathematical expectation in the first case invokes an actual mass of similar transactions, giving rise to an average price in the market, in the second case it is based on a hypothetical rather than an actual repetition of cases. In other words, in involuntary exchanges we suppose that equality would result from many such trials, even if the parties themselves engage in the transaction only once. What is particularly interesting about this discussion for our purposes is that insurance could belong to either category of exchange. Condorcet’s manuscript on maritime insurance presents it as a voluntary transaction regulated by a long-run empirical concurrence, or average market price. Indeed, one can imagine that for some risks, including those of overseas trade, a concurrence price would both exist and not be entirely hypothetical from the parties’ point of view. That is, in such cases the parties might engage in enough similar transactions that the price would reflect their own experience and needs. Yet there are also cases for which insurance more likely falls into the second category. Some risks, such as the loss of subsistence income, are clearly not undertaken voluntarily, and often there is not a market or concurrence price for them. Moreover, even if there is such a price—as is perhaps true of mortality risks, for example—a purchaser cannot possibly have enough personal experience with the hazard in question for the average value to relate specifically to him. In these cases, it may make more sense on Condorcet’s terms to understand insurance as an involuntary exchange regulated by the law of equity. By emphasizing the fairness of both types of exchange, Condorcet affirmed their choice-worthiness for the individual alongside a broadly social result. In both cases, he hinted at but did not explicitly defend a kind of identification with similar instances that would enable the individual to substitute the average value for her own. By contrast, many of Condorcet’s contemporaries, particularly those influenced by Laplace, went a different route. They invoked a personal utility value, or what they called moral expectation, to reconcile individual decisions with aggregate regularities. Moral expectation offered a bridge of sorts between the epistemic and aleatory faces of risk, analogous in this respect to the principle of indifference. It also allowed thinkers to affirm the caution and good sense of those who choose to insure. Combined with the increasingly statistical tendencies of probabilistic thinking as the nineteenth century progressed, this idea eventually supported a kind of moral education or discipline, in which citizens

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are made to see the personal value of public order and are recruited thereby into the projects of an aggregating state. Mathematical and Moral Expectation Condorcet had grappled with the difficulties posed by empirical probabilities to theories of contractual equity and offered a response that reflected both the voluntary and the involuntary aspects of bearing risks. Laplace and the thinkers who followed him echoed this contractual orientation and rationale for insurance practices, but they advocated a different approach to reconciling individual judgments with statistical probabilities. Their approach focused more on the desire for security, and on the caution to which it gives rise, than on the demand for personal independence. In this light, Condorcet may be seen as the pivot between the social insurance tradition we considered in the last chapter, with its emphasis on property ownership for the sake of self-rule, and the one that eventually emerged from the statistical turn of late-classical probability. Moral expectation, the idea on which these later thinkers relied, has a long pedigree in the history of probability. It dates back to the solution proposed by Daniel Bernoulli (Jacob’s nephew) to a problem called the St. Petersburg paradox. This problem, which received influential formulation in a letter from Nicholas Bernoulli (Daniel’s cousin) to Pierre Montmort, published in 1713, involves two players in a coin-toss game. The rules of the game state that Peter tosses a coin and agrees to give Paul a cent if heads turns up on the first toss, two cents if heads first turns up on the second toss, four if on the third, and so on. If heads does not turn up until the nth toss, Peter owes Paul 2n–1 cents. According to the standard method of calculating expectation, Paul’s expectation in this game is the sum of ½(1), ¼(2), 1/8(4) and so on to ½n(2n–1) for any value of n. The series, and therefore Paul’s expectation, are thus infinite since there is a nonzero chance that even a fair coin will produce an infinite chain of tails. Yet, as Daniel Bernoulli pointed out, “any fairly reasonable man would sell his chance” in this game “with great pleasure, for twenty ducats.” In other words, the accepted method of calculation places “Paul’s prospects at infinity though no one would be willing to purchase it at [even] a moderately high price.”58 There consequently appears to be a conflict between mathematical expectation understood as the determinant of contractual fairness, which would require valuing Paul’s stake as infinitely high, and the considerations that actually motivate a prudent decision maker. As a solution to this paradox, Daniel Bernoulli proposed the distinc-

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tion between mathematical expectation, with its goal of contractual equity, and moral expectation, which takes into account an outcome’s anticipated value to the particular actor. In the case of the St. Petersburg game, he argued, Paul’s expected benefit from playing depends on his level of wealth. The value to him of an additional dollar will be greater the smaller his initial fortune and will increase with diminishing margins as his base income goes up, a phenomenon that can be represented graphically by a concave utility curve. Bernoulli was thus able to explain the difference between the dictates of contractual equity and the empirical psychology of risk taking by personalizing the value of the wager to the decision maker himself. “From this,” he concluded, “we can see what a tremendous fortune a man must own for it to make sense for him to purchase Paul’s opportunity” for even a modest sum.59 Assuming that personal utility curves for money are always concave, Bernoulli offered a new, logarithmic formula for calculating the utility values of various risky trades: “Any gain must be added to the fortune previously possessed, then this sum must be raised to the power given by the number of possible ways” of obtaining it, after which these terms are multiplied together and a root is taken according to “the number of all possible cases.”60 This formula indicates that many games of chance judged fair by the standard of mathematical expectation will in fact involve negative utility for both players. For example, imagining a game in which two players, each possessing 100 ducats, both wager 50 with an equal probability of winning, he used his formula to determine that the moral expectation of each one is less than 87 ducats—the square root of the multiple of 50 and 150—meaning that each will suffer an expected loss of 13. “Indeed,” he explained, “this is Nature’s admonition to avoid the dice altogether.”61 As Daston points out, Bernoulli’s argument can be understood as an attempt to shift the focus of mathematical analysis from equity to utility, or (what would become) economics.62 Unlike the original probability calculus, in which “no characteristic of the persons themselves ought to be taken into consideration,” moral expectation accounts for “the particular circumstances of the person making the estimate.”63 The former is the province of the law, the latter of the individual. Statistical life insurance, by contrast, implicitly shifts the focus in the other direction, to equity understood from the perspective of the insurance company or social planner. Among the first to recognize this was Jean le Rond d’Alembert, a rare (and controversial) early philosophic skeptic about the ability of probability theory to model or guide prudential reasoning. Analyzing the rules for calculating lifespans, d’Alembert pointed out that

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the same numerical average might result from a number of different life prospects. For example, he wrote, one method of calculation holds that if twenty-five out of fifty people die within a day and twenty-five live for another twenty years, at the end of which they all die as well, the expectation of each member of the group will be twenty divided by two, or ten years. The same expectation will result if, on the other hand, all fifty live for ten years and then die together as a group. Yet, d’Alembert noted, it is one thing to know with certainty that one will live for ten years and quite another to know that one has a 50 percent chance of living for twenty. In this case, expectation defined as the average lifespan fails to capture the difference.64 D’Alembert’s critique of statistical averages thus returned to the perspectival dichotomy raised by Daniel Bernoulli. Averages may be useful to an insurance company or social planner acting on behalf of the aggregate good, but they are less useful to the individual acting on behalf of her own good. D’Alembert put the point particularly starkly in his discussion of the smallpox inoculation controversy raging at the time. Envisioning a scenario in which inoculation causes the death of one out of every five people but increases the lifespan of the other four to one hundred years, d’Alembert argued that no individual would freely choose this policy even though the state would prefer it. While the latter takes the perspective of the aggregator, “considering all citizens indifferently,” for the individual “the interest of his particular conservation is foremost,” and an increase of the average lifespan is not determinative.65 The conventional approach to calculating expectation goes astray, on d’Alembert’s view, because it does not properly weigh outcome values in accordance with their probabilities. Multiplying the two together assumes they are equally significant, but prudence requires considering the likelihood of success or failure in relation to the potential reward or loss, a relation that d’Alembert called the risk. Where the probability of gain is extremely small, a reasonable person will not pay any significant amount for the wager, even if the potential gain itself is enormous. Similarly, in the case of inoculation, what determines the reasonableness of the choice is “uniquely the relationship between the risk on one side, and on the other the augmentation of the average life, or above all the advantage that this augmentation will procure relative to the time and the age at which one will enjoy it. The difficulty is to determine this relationship.”66 The decision of whether to insure one’s life is far less stark than d’Alembert’s inoculation example, and the expectations determined from mortality tables do convey more information than the average lifespans he describes. Yet his concerns about the limitations of aggregation and

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abstraction apply to statistical life insurance as well. Distributive justice on the probabilistic account hinges on the parties’ abstract potential to “win” or “lose” the common resource pool. Where probabilities were based on coin tosses and similar examples, it was easy to imagine that these potentials could be calculated, and the parties equalized, with mathematical precision. As empirically derived probabilities replaced a priori ones, however, it became more difficult to understand expectation as the precise expression of a party’s payoff. For the life insurance company, like the state, the benefits of treating individuals as at a certain point interchangeable are clear. For the individual, by contrast, there is quite a bit of information that the insurance company’s aggregative stance may fail to capture. Late-classical writings about insurance from Laplace onwards consistently invoked moral expectation as a solution to this difficulty. The idea that the individual could derive a subjective but still calculable benefit from the contract helped to justify insurance as both personally reasonable and collectively fair. The next section takes up these arguments in greater detail and, in so doing, considers how the earlier, more traditionally liberal rationale for social insurance gave way, almost imperceptibly, to a statist one. A Social Duty to Insure? Laplace and his followers continued to tout the advantages of spreading risks well through the first half of the nineteenth century. For example, in his most popular work on probability, Laplace explained that mutual insurance is the equivalent of sending small amounts of money on several ships rather than putting the entire sum onto one. Such insurance “always leaves some doubt about the loss to be feared. But this doubt decreases as the number of associates increases,” since their collective experience can be reliably calculated. As a result, the “moral advantage” of such insurance “increases more and more” with the number of participants, and “ends up by coinciding with the mathematical advantage, its natural limit.”67 French mathematician Sylvestre François Lacroix, popularizing Laplace’s ideas in 1816, reiterated that “the characteristic property of insurance is to tend to bring back to an average value the benefits of all enterprises of the same type,” just as “would occur naturally for the merchant who takes part in a very large number of enterprises, and the property owner who would have possessions disseminated in a large number of distant cantons.”68 Augustus De Morgan, the British mathematician and disseminator of Laplace’s ideas in England, relied on the same logic in an 1838 work when he

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noted that “it is more prudent to play twenty games, staking one shilling upon each, than to stake a sovereign upon one game.”69 Correspondingly, insurance is no longer a gamble when the insurer, rather than wagering only once, is allowed “to extend his traffic” and “begin to feel the average” of his loss.70 As both d’Alembert and Condorcet had recognized, however, this argument is much more naturally aligned with the perspective of the state or the insurer, both of which engage in numerous similar transactions, than with that of the individual insured. Statistical probabilities, wrote Condorcet, are relevant primarily “for states, whose interest embraces a large mass of men.”71 Although in theory the individual’s premium will equal her expectation provided the pool is large enough, there is still the difficulty of identifying the proper reference group and therefore the average that best represents her experience. Condorcet, for example, presumed in his account of maritime insurance that each insurer and merchant will have sufficient experience that referring to an average personal profit makes sense, or that both can somehow incorporate the experience of similar insurers or merchants in making their own decisions. Neither presumption is obviously sound, however, and Condorcet did not explicitly justify them. The difficulty becomes even more pronounced in the case of insurance for death and other singular eventualities, for which no individual could possibly have enough experience to generate an average of her own.72 The idea of moral expectation appeared to resolve this difficulty, with three noteworthy implications for the theory of insurance. First, the presumed concavity of utility curves justified caution as a prudent response to uncertainty. As we have seen, Daniel Bernoulli initially propounded this view, emphasizing the irrationality of even fair wagers and the value of spreading risks over multiple ventures.73 George-Louis Leclerc de Buffon took the idea even further, describing in his 1777 Essai d’arithmétique morale a phenomenon akin to what contemporary economists call loss aversion. By calculating gains as a percentage of ex post earnings and losses as a percentage of ex ante income, he weighted the latter much more heavily than the former in determining moral expectation.74 He concluded that “the wise man must risk the least amount possible, and the prudent man who through his position or his business is forced to risk large funds must divide them” to reduce the negative impact of any loss.75 Moral expectation thus lent support to the view that those who insure are reasonable and responsible, motivated by a proper concern to avoid their own future suffering. Insurance associations are “very advantageous to morals,”

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Laplace explained, “in favoring the softer penchants of nature” and “offering the means to exchange the superfluous,” meaning a small amount of one’s present income, “against assured resources in the future.”76 Second, moral expectation helped to explain why it may be reasonable to pay more than one’s own mathematical expectation for insurance coverage. As Laplace put it, there is a “moral disadvantage associated with uncertainty,” which renders “insurance, in which one exchanges the uncertain for the certain . . . advantageous.”77 This personal advantage may justify a premium that is higher than the value of the insured’s own risk—particularly if it is necessary for the survival or proper management of the insurance association itself.78 Physicist and statistician Jean-Baptiste-Joseph Fourier, in a work of 1819, relied on similar reasoning in his analysis of insurance. To measure the true benefit of the contract for the insured, Fourier explained, “it is not enough to know the average value,” or expectation, that results from “the indefinite repetition of events of the same genre”; one also has to “consider the personal situation” of each individual and, with it, the subjective value he derives from the contract.79 Unlike Daniel Bernoulli, Fourier stressed that the utility curve “is different for each person,” changing not only with the level of wealth but over time and with the circumstances of the individual as well. Nevertheless, he insisted, it always maintains “its concave form.”80 This view therefore grants considerable leeway for resolving discrepancies that might arise between a premium calculated for one statistical group or another and the mathematical expectation of any particular insured—all the while aligning with what, according to these thinkers, constituted universal good sense. Finally, these arguments suggest an obligation to insure, both to oneself and to the group on which one’s participation depends. Not only is the failure to insure inexcusably self-destructive, since it could plunge oneself and one’s family into misery far beyond the monetary loss incurred, but it also threatens the success of insurance for everyone else, exposing others to gratuitous risk. The “act of association changes completely the personal situation of the parties,” wrote Fourier. “Each one of them, before the treaty is made, runs the risk of losing his entire property; but after the association is formed, they are set up to regard total loss as impossible.” As a result, “One sees very distinctively that the default of the insurance association occasions a real loss.”81 Indeed, thinkers of this period also began to recognize the economic value of the capital created by insurance premiums, which are negligible when taken individually but together constitute a powerful mass.82

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This line of reasoning implies that the individual has an interest in the survival or well-being of the association itself. Belgian astronomer and statistician Adolphe Quetelet, a student of Fourier, influentially pointed this out, noting that those who insure themselves “present to the state a type of guarantee that they respect the public order. They will not, in effect, compromise the future of their families, in exposing without reason the product of their labors to the chances of political dislocations.” Someone who is literally willing to pay a premium for her security will not let potentially disruptive political opinions or passions threaten her prosperity and peace. As Quetelet continued, “I am often surprised that governments do not take a more direct part in institutions that can develop so advantageously the spirit of order and the morality of a nation.”83 Napoleon III and, later, Bismarck would take heed in devising their own social welfare programs. François Ewald identifies in this logic one source of the doctrine of social solidarity, positing an obligation of each on behalf of all.84 This view has much to recommend it, particularly given later nineteenth- and early twentieth-century thought defending social insurance in solidaristic terms.85 Yet insofar as the late-classical account still rested on the exchange of a personal risk, it retained an individualist methodology and orientation. Insurance on this view remains a contract for the quantifiable benefit of the individual insured, even if that benefit extends beyond her strict mathematical expectation to include the psychological value of security for its own sake.86

Social Insurance in Theory and in Practice The mathematical innovations and practical proposals of these thinkers proved influential for understanding the role of insurance in public life. Yet they were also vulnerable to powerful critique. First, the principle of indifference gives rise to various confusions because, in the realm of empirical phenomena, there is rarely one compelling answer to the question of which possibilities should be considered as equally likely cases, and different selections will give rise to different probabilities. To take a very simple example, if there are white, red, and blue balls in an urn, the probability that the first ball drawn will be white will differ depending on whether one considers it equally likely that the ball be white, red, or blue (in which case the desired probability is one-third) or white or nonwhite (resulting in a probability of one-half).87 Statistical questions are rife with such examples. This means that contestable judgments about equality are incorporated

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into such calculations from the outset—judgments that are usually imperceptible to the untrained observer, and which late-classical probabilists themselves often neglected to adequately defend. Second, the notion of moral expectation, while intending to model the foresight and caution of the responsible individual, is normatively indeterminate. Thinkers who employed the concept did not agree on a single formula for modeling prudence, or even on the possibility of finding a formula that would apply to all people. What is more, even if one grants a phenomenon such as diminishing marginal utility or loss aversion as a descriptive matter, this in itself does not tell us how reasonable individuals ought to behave in situations of uncertainty. These difficulties lend support to the conclusion that moral and political aims played an important role in shaping elements of the probability calculus during this period. In other words, it is possible to understand some of the shortcomings of these analyses as results of the practical aspirations that motivated them. The probability of causes, and with it the principle of indifference, was spurred largely by the effort to calculate probabilities for demographic and other civic phenomena.88 Together with the Rule of Succession, they accomplished their task without abandoning the applicability of probability values to individual cases. Meanwhile, accounts of moral expectation sought to reconcile personal prudence with statistical averages, showing that probability calculations could be used to promote individually responsible decisions as well as collectively beneficial outcomes. All of these elements supported a vision in which the judgments and self-regarding actions of individuals align with the common goods of order, stability, and fairness. Such aims found clear expression in late eighteenth and nineteenthcentury discussions of insurance, and the difficulties they raise continue to resonate today. Likelihoods calculated from statistical data selectively choose certain features and ignore others that meaningfully distinguish individuals. In addition, the attractiveness of insurance rests not only on such “objective” factors but also on the personal beliefs and valuations of the insured. The notion of actuarial fairness, so appealing to thinkers of this era and beyond, thus entails difficulties that cannot be addressed without first understanding the dualistic character of probability itself. Indeed, as a result of this duality, probabilistic insurance can be seen as a microcosm for thinking about political life. If there is a conflict between individual judgments, or the liberty to pursue them, and the security of the collective, which of the two should take priority? What does the individual

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owe the group—what, if anything, should she pay beyond her mathematical expectation—and what does the group owe the individual in turn? These questions saw a number of suggested resolutions in late-classical probabilistic writings and the political proposals made in their wake. Some, as we have seen, redefined rationality in terms of utility rather than mathematical expectation, justifying any additional price the insured might pay as a reflection of the psychological benefit of the insurance arrangement. Others redefined justice in terms other than actuarial fairness, prioritizing the security of the group over precision in calculating individual expectations. Both sets of arguments together constitute what I will call the atomist-statist account of social insurance that emerged by the middle of the nineteenth century, particularly in France, and helped inspire some of Western Europe’s earliest welfare laws. This account was atomistic in maintaining the relevance of probabilities to singular cases and in understanding insurance as a bilateral exchange between insurer and insured. Yet it also tended toward political centralization, regarding ever-larger associations and ultimately the state as the most effective aggregators of risk. The fact that the insurance principle enjoyed growing political prominence while accommodating both types of argument can be understood as a legacy of late-classical probability, with its distinctive blend of individualism and aggregation. Mutualism with and without Risk, Revisited But before turning to social insurance, we will pause for a moment to consider parallel developments in other forms of insurance during this time. The last chapter analyzed the movement to reform friendly societies as an outgrowth of a policy paradigm associated with mathematical probability. There, I argued that reformers sought to introduce probability calculations into friendly society operations as part of an effort to align individual reason with a common good. I also noted that these writers tended to blur the distinctions between voluntary, commercial, and state-run insurance schemes, regarding all three as capable of promoting the same ends, provided they were based on sound mathematics. In Britain, however, notwithstanding some legislative successes, it took quite some time before reformers managed to introduce their mathematical mindset into the friendly societies, and even then, they were not entirely successful. Many societies continued well into the nineteenth century to operate on a “providential” basis, according to which members paid

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into a common stock and were compensated as needed, a practice very different from the actuarial ideal. According to Penelope Ismay, members did not share the reformers’ faith in mathematical prediction, but rather regarded the future as largely unknowable and their association as offering protection against needs whose timing and nature could not be forecast.89 Indeed, unlike life insurance companies, friendlies often promised coverage for a variety of eventualities without accounting separately for different types of risk. Nor did the societies agree with critics that their financing methods were unsound, as they were usually able to pay immediate and near-future claims even when they could not satisfy the actuary’s demand for a long-term accounting of costs.90 Finally, the friendlies persisted in devoting considerable resources to ritualized sociability despite elite warnings about allegedly wasteful social practices. As a result of all of these features, members tended to see themselves not as individual participants to a forward-looking insurance contract but as brothers, bound together by trust (fostered in part by selective membership criteria) and a relatively encompassing commitment to one another.91 The difference between this understanding of mutual aid and the probabilistic one highlights different answers to the question of how to promote cooperation and reciprocity under increasingly fluid and impersonal social conditions. Mathematical probabilists proposed to address the challenge through the mechanism of a contract between abstract, mathematical equals. The friendlies, meanwhile, continued to appeal to sociability and affective ties, even as their membership shifted away from isolated local clubs toward geographically more dispersed organizations.92 Moreover, the continued struggle between the two visions, and in particular the friendlies’ protracted resistance to actuarial reform, suggests that individuals facing insecurity may be motivated less by mathematically informed reason than by a desire for belonging and its promise of encompassing support. Indeed, the friendly model garnered many adherents over the course of the nineteenth century, providing mutual aid to a significant part of the working-class population—in other words, to many (but not all) of the same people whom social insurance proposals were intended to help.93 At the same time, as we will see in the next section, proposals for state-run insurance in the first half of the nineteenth century took on an increasingly aggregative orientation. By midcentury, the two visions would openly clash. Contemporaneous developments in commercial life insurance also illustrate discontinuities between the various forms of mutual protection available at this time. Work by historian Timothy Alborn on the British

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market has shown, first, that life insurers’ practice of distributing surplus revenues to policyholders took on a more explicitly profit-oriented character in the first half of the nineteenth century.94 Life insurance offices experimented with a variety of schemes to benefit shareholders or attract customers, promising superior asset management and leveraging their calculable, long-term liabilities into investment options unavailable to other firms. Thus, while bonuses had been justified initially as a consequence of actuarial uncertainty, meaning that insurers had charged more than necessary and returned some of the surplus to policyholders, now companies began to present them as serving an individual savings function. Correspondingly, the notion of mutual burden sharing that featured in many early paeans to statistical insurance was replaced with a promise to the insured that even if he “lost” the bet about his own mortality, his sacrifice would be counterbalanced by the growth and division of company profits.95 Second, the increasing participation of the working classes in the life insurance market in the latter half of the nineteenth century revived the question of how to distinguish legitimate insurance from wagering on a life. Providing a proper burial, which was the main reason that working people purchased life insurance, was not considered an insurable interest under the 1774 Life Assurance Act. As a result, when “industrial” insurance companies began to offer policies to the working classes after 1860, technically illegal policies proliferated, as apparently did the practice of taking advantage of superior knowledge—awareness of a neighbor’s illness, for example—to purchase coverage and profit at the insurer’s expense. The legal treatment of burial insurance during this time therefore highlighted some of the difficulties of attempts to distinguish legitimate insurance from the ever-present specter of gambling.96 Finally, by the mid-nineteenth century, life insurance actuaries had discovered that the overall state of the market strongly influenced the premiums they could set. While too little competition meant that offices could charge whatever they wanted for policies, effectively rendering mathematical probabilities irrelevant, too much competition tempted insurers to charge less than was needed for their long-term viability.97 As a result, by the 1850s, many had recognized the need for regulation of the industry. In 1853, Parliament opted to entrust supervision of corporate practices to actuaries, who were to form a self-regulating profession and provide regular reports on the financial soundness of insurers.98 The same principle was affirmed in 1870. Thereafter, as James Franklin notes, the actuarial profession was “one of the most heavily regulated and institutionalized of the professions based on risk.”99

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While friendly societies continued to take the path of mutualism without risk, then, commercial insurers experimented in trading risk without mutuality. Both tendencies illustrate the same challenge that late-classical probabilists set out to solve: that of justifying group insurance in a way that satisfies the demands of both prudence and equity. Both also demonstrate how readily these two rationales may in fact diverge. In addition, both friendly and commercial insurance continued to rest on exclusivity: Mutual societies often restricted their coverage to the skilled and relatively prosperous, while many commercial insurers refused to extend contracts, even at higher prices, to those they deemed to be of bad character.100 These practices confirm that the sorting and management of risks invariably rests on considerations of who ought to be considered an equal within the burden-sharing community—an important continuity between the various types of insurance, despite their otherwise divergent paths. They also substantiate one of the strongest arguments for social insurance: the power of the state to compel participation and thereby include those who might otherwise be excluded from protection. As we will now see, arguments for social insurance by this time embraced the comparative advantages of national-level governments in managing risks. While the probabilistic paradigm that supported these later proposals remained in substantial respects the same, later writings increasingly emphasized the statistical, and therefore statist, side of the discipline. Causal Laws and Rational Planners I have referred to the account of social insurance that emerged by the midnineteenth century as atomist and statist, in that it adhered to an individualist methodology while affirming the role of the state in promoting socially beneficial outcomes. The former side of the model found mathematical expression in an individually calculable expectation, supplemented for the purposes of decision making by a utility value. The latter side, meanwhile, increasingly embraced statistical observation and aggregate regularities, monitored and managed by a central political authority. As Quetelet explained, from the elevated vantage point of the social planner, “moral phenomena . . . are found to resemble physical phenomena,” products of the causal forces or “general facts, by virtue of which society exists and is preserved.” Each individual, “as a member of the social body  .  .  . is subjected every instant to the necessity of these causes, and pays them a regular tribute.”101 Quetelet represents the culmination of a line of thought that began with the growing availability of social data in the early nineteenth century. Math-

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ematicians such as Fourier and Poisson discovered new regularities in civil and social phenomena such as crimes, jury decisions, and suicides. Poisson is well known for having coined the term “the law of large numbers” to describe the phenomenon whereby a sequence of independent Bernoulli trials (those with only two possible outcomes) converges to its probability with an increasing number of observations.102 He also took advantage of the proliferation of legal statistics to apply the method of inverse probability to find the chances of an erroneous judicial decision given the “cause” of defendants’ culpability. Poisson saw such moral phenomena as akin to natural ones such as births and deaths, and as therefore demonstrating the same aggregate regularities. His approach correspondingly focused on the statistical collective rather than the individual case. “For the guarantee of society,” he explained, “and that which one owes the accused, it is not the probability [of error] with respect to a particular judgment that is most important to determine; it is that which relates to all of the trials” carried out in one or several years.103 With this, according to Lorraine Daston, Poisson “cleared the way for a statistical treatment” of judicial decisions, one that emphasized the demands of public order and security over accuracy in any particular verdict.104 Quetelet, for his part, had learned probability from Fourier while studying astronomy in Paris. He went on to become the foremost promoter and popularizer of the statistical approach to social affairs. Quetelet was enthralled with the idea that social forces generate regularities in human conduct that are analogous to the physical regularities generated by natural laws. He also perceived the power of statistics to define and control populations. His notorious homme type, or average man, a fictional composite of the population averages from various biological and social measures, was as much the object of moral reform efforts as of detached scientific investigation. By examining aggregate data—for example, from savings banks and insurance companies—one could “ascertain the degree of foresight at different periods of life” and understand what conduces to the development of those “virtues most essential to the social state.”105 Enlightened leadership could then alter social conditions in such a way as to, on average, encourage such virtues and minimize their corresponding vices.106 Once individual misfortunes and even vices can be explained as products of social forces—which, moreover, can be altered by a “few men, gifted with superior genius”—the state can modify or mollify conditions on behalf of those who suffer under them. The observation of statistical regularity, “so discouraging at first sight,” becomes “consolatory, when examined more nearly, by showing the possibility of ameliorating the human race, by

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modifying their institutions, their habits, the amount of their information, and, generally, all which influences their mode of existence.”107 Indeed, one of Quetelet’s most famous or notorious statements can be read in this light as a call for proper social engineering: Since the crimes which are annually committed seem to be a necessary result of our social organization, and since the number of them cannot diminish without the causes which induce them undergoing previous modification, it is the province of legislators to ascertain these causes, and to remove them as far as possible. . . . Indeed, experience proves as clearly as possible the truth of this opinion, which at first may appear paradoxical, viz., that society prepares crime, and the guilty are only the instruments by which it is executed. Hence it happens that the unfortunate person who loses his head on the scaffold, or who ends his life in prison, is in some manner an expiatory victim for the society. His crime is the result of the circumstances in which he is found placed.108

Theodore Porter points out that the discovery of statistical laws often coincided with a laissez-faire approach to politics, or the view that governments should let historical progress unfold without impediment.109 Yet Quetelet recognized that social laws are pliable and can be altered through the activities of a legislator. In fact, the argument just quoted is a version of the claim that motivated industrial insurance and workers’ compensation laws, the first frontier of the modern welfare state, in France and other countries through the second half of the nineteenth century. Although Quetelet is speaking about crimes rather than work accidents or unemployment, the crucial underlying move was the same: Once such phenomena can be seen as objective facts or inevitabilities, outside the sphere of individual agency, it is possible to treat those affected as innocent victims of economic progress or the common good. One can even derive a collective responsibility to the individual whose unlucky sacrifice enables the entire system to continue.110 I have suggested that the notion of a duty to insure followed from arguments about moral expectation, insofar as the latter affirmed the subjective value of security and a corresponding concern for the association that provides it. In this respect, Quetelet does not reflect a radical departure from the approach of those who preceded him. Yet the notion that states can manipulate conditions to change the behaviors of their citizens in the aggregate does represent an important shift from the views of the late eighteenth-century thinkers we considered in the last chapter. Whereas

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earlier probabilists such as Richard Price and Condorcet had regarded insurance as a means to self-determination and independence, the later view emphasized the ways in which citizens are shaped by and dependent on the collective. Whereas earlier thinkers had focused on individual virtues such as frugality, foresight, and care for one’s own, Quetelet sought to promote responsibility understood, in part, as attachment to the state. This shift further helps to explain why the distinctions between voluntary, commercial, and state-run insurance appeared more significant by the mid-nineteenth century than they had to Condorcet and his peers. As the primary collector of statistics and the largest aggregator of individuals, the state was best suited to realize many of the benefits of insurance on this later account: to spread its own risks, to promote socially desirable behavior, and to encourage citizens’ loyalty to itself, the ultimate insurer. If insurance is a social duty, however, does this mean it should be compelled? This was a controversial question in mid-nineteenth-century France, especially in the years leading up to and following the Revolution of 1848. Insurance had emerged within a basically liberal or voluntarist paradigm, and despite its increasingly aggregative character it had not yet fully shed the image of a voluntary exchange.111 It could also be said that the argument from personal obligation, insofar as it aimed to cultivate virtues such as saving and familial responsibility, required a choice on the part of the insured. On one hand, then, while the case for social duty denied individual agency in causing or preventing certain misfortunes, on the other it still rested on a view of prudence as foreseeing calamity and taking steps to mitigate its effects. In France, this debate played out in discussions of two important laws, both adopted by the legislative assembly in the summer of 1850. The first created a state pension fund, designed to channel workers’ retirement savings; the second concerned France’s growing network of voluntary mutual aid societies.112 The political controversy concerned whether pension payments should be obligatory. On one side stood the friendly society model, with its spontaneously communal spirit but lack of universality. On the other side stood the possibility of mandatory payments accompanied by sanctions for noncompliance. The republican legislature rejected compulsion in favor of greater freedom for the individual worker. Yet Napoleon III and his advisors sought to reinforce the role of the state and therefore opted for a system of subsidized liberty, or helping those who help themselves. Individual savings and the interest rate they accrued would be guaranteed by the government, and the mutual societies would be recast as intermediaries between work-

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ers and the state. The aim was to generate on the part of individual laborers a sense of shared interest with society as a whole and an attachment to the providing (and provident) state.113 As one politician explained at the time, adopting the liberal position but echoing Quetelet, national insurance creates between the state and the worker a solidarity, a community of interests that cannot but profit the public peace. . . . The worker, once entered into this vast association, is interested for his entire life in the affirmation of society, in the development of public prosperity. His fortune is tied to that of the state.114

If it is true that, as Ewald has argued, these mid-nineteenth-century political developments “found their conditions of possibility in the formation of that probabilistic rationality” developed by Quetelet, it should come as little surprise that they also embody the uneasy union of individualism and social control at work in the tradition that Quetelet represents.115 In theory, the average man, the target of proposed efforts at moral improvement, could over time come to represent an ever greater proportion of the population, as social divisions narrowed and everyone came to resemble that calm and orderly being, “alike removed from excess or defect of every kind.”116 Under such conditions, social insurance could be both equitable and encompassing, individually choice-worthy and collectively beneficial. The state would be one large mutual assurance association, comprising thousands or millions of “average men.” A Social Insurance Moment France’s nascent social insurance laws grew out of the political ambitions of Napoleon III, who saw in insurance a way to build a strong executive that could reduce economic discord and depoliticize government.117 Yet they also reflect a distinct political moment, when the idea of social insurance—and the promise of probability—had found acceptance in diverse intellectual circles. Prominent liberals, despite their concerns about excessive centralization and the undermining of family ties, had expressed support for the idea of a compulsory national pension fund.118 Socialists, meanwhile, drew inspiration from radical economist Jean Charles Léonard de Sismondi, who had urged employers to take responsibility for their employees’ medical care, childcare, and pensions.119 Although implementing social insurance policies was never the primary goal either of the conservative liberal approach that sought reform through moral education and philanthropy or of the radical socialist one that found political expression

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in the 1848 Luxembourg Commission, the practice apparently did appeal to elements of both. The economic and political situation of mid-nineteenth-century France was very different from the one in which the earliest social insurance proposals had emerged. The increasingly obvious disconnect between the ideal of equality and the precarious reality of workers, or what Gareth Stedman Jones calls the “swelling, property-less class whose social struggles could not but challenge the existence of the state,” had provoked new and more radical responses to the problems of poverty and insecurity.120 A new generation of French political economists had emerged, proposing social reform to ameliorate the situation of industrial workers without altogether abandoning liberal economics.121 Several schools of socialist thought had also taken shape, proposing wage setting, a right to work, and collective forms of property to ensure workers’ welfare in a way that, it was thought, private property and economic competition could not. The growing availability and prominence of statistics played an important role in both of these developments: Conservative-leaning liberals used survey data to support their proposals for philanthropic interventions, while socialist economists and workers’ associations sought to capture and quantify human needs in support of higher wages.122 In addition, a new tradition of Catholic social economics had grown in opposition to economic liberalism, advancing a structural understanding of poverty and concern about the distribution of property.123 In principle, these writers tended to advocate charity rather than insurance, and focused less on the independence or self-sufficiency of the working classes than on ensuring their assistance when needed. Nevertheless, in envisioning “the principle of charity applied to all of the relations of social life,” in the words of one prominent author, they also articulated an important strand of welfare thinking that, according to some contemporary historians, would prove influential to the subsequent development of the French welfare state.124 Notwithstanding these very different political, economic, and ideological circumstances, I contend that the philosophical foundations of a welfare state based on insurance principles had been laid by the generation of probabilistic thinkers that began with Condorcet, and that these foundations remained in broad outlines intact through the mid-nineteenth century. To be clear, the continuity I am claiming up to this point exists more in theory than in practice. The reform ideas of thinkers like Condorcet and Paine were by midcentury largely ignored or neglected.125 In Laplace and Poisson, the political applications of probability had already taken on a

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more explicitly technocratic and statist character, which would find further amplification in Quetelet. The friendly societies could be seen to offer an institutional link between the earliest social insurance proposals and the first social insurance laws, thanks to the reform movement that strived to rationalize and bring them under the tutelage of the central government. In practice, however, as we have seen, the friendlies remained strongly associated with a voluntarist and nonactuarial approach for much of the nineteenth century.126 Above all, then, the continuity that I am describing pertains to a set of ideas, or a paradigm: an understanding of insurance as capable of aligning the separate interests of each with the good of all; as educating citizens to live responsibly without abandoning them to their own devices; as both honoring individuals’ contribution to the social wealth and satisfying their basic needs.127 This vision, we have seen, requires a determination of probabilistic equality or, in other words, of who can be considered equally vulnerable or interchangeable in the face of chance. As Michael Freeden puts it, social insurance rests on a “telling reformulation of equality: a specific conception of equality of treatment in the form of social compensation . . . for crucial and dehumanizing lacunae in the human condition.”128 I have argued that this reformulation was first theorized and justified in the context of mathematical probability. The specific way in which it appeared during this period derives from late-classical probability in particular, with its uneasy combination of epistemic individualism and statistical aggregation.129 The growing influence of this set of ideas, or policy paradigm, as well as the ways in which political actors vied over its terms, can be seen in several mid-nineteenth-century French tracts: G. S. Boyer’s Projet d’assurance générale de bienfaisance nationale et de secours mutuel dans les 86 départemens; Raoul Boudon’s Organisation unitaire et nationale de l’assurance; and Émile de Girardin’s La politique universelle, all originally written between 1838 and 1852.130 Their authors came from substantially different schools of thought: Boudon was a follower of utopian socialist Charles Fourier, while Girardin is best remembered as owner of the popular newspaper La Presse, which switched its political allegiance from conservative to republican between 1848 and 1852.131 Viewed in conjunction, however, they point to the salience of the insurance idea in mid-nineteenth-century French political discourse and to its appeal, especially within a broadly liberal politics plagued by the challenges of uncertainty. Boyer’s scheme warrants only a brief note. First published in 1838, it envisioned a single fund for each of France’s eighty-six departments. The

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fund would comprise contributions from all types of worker, to be distributed to any member who incurred a qualifying event and upon retirement. Although Boyer proposed different contributions for men and women and allowed for the formation of separate classes for urban and country dwellers, he otherwise envisioned that participants would pay the same amount, with those who entered the fund later simply receiving proportionally less in benefits. The aim of this rough actuarialism, he explained, was to create an inclusive scheme in which each accident would be everyone’s concern, and “the entire popular mass becomes one’s support in reciprocity.”132 Similarly, Boudon’s proposal, published a few years later, explicitly rejected individualized actuarial fairness in favor of a kind of macro-level actuarialism, based on the principle of mutual insurance and its ability “to reconcile all the interests of the associates.”133 Boudon criticized commercial insurance companies for baselessly disaggregating risks, for their excessive administrative costs, and for being inaccessible to the poorer classes. Nevertheless, he noted that “statistics do offer without doubt a nearly constant average of the annual losses of France,” and on this basis he proposed a plan for national insurance against several enumerated risks to personal property.134 Boudon defended his deliberately approximate approach by noting that too much classification would be administratively infeasible and only increase contributions for the most vulnerable.135 “I insist greatly on this point because one should not be led astray, like those who have come before, by the desire to arrive at a minutely exact distribution, to an abstract justice, that will entail considerable expenses without leading to that end.”136 Such macro-level actuarialism, which applies probabilities to the system’s overall finances but not to individual premiums, has two advantages on Boudon’s account. First, it allows for tapping into large-scale averages and making the scheme secure for the individual in a way that more limited risk pooling cannot. “The chances of probabilities are all the more uncertain as they are established in a narrower circle. . . . As the bases of the operation are expanded, the probabilities become more and more regular, more and more favorable.”137 In this respect, the state has an advantage over other insurers since its pool is automatically larger and it can avoid the high administrative costs of precisely classifying all risks. Second, macrolevel actuarialism makes it possible to regard insurance as a social obligation, a means by which the citizen body as a whole protects the faultless sufferers among them. Insurance is “eminently social; it interests all of the insured in the conservation of the property of each one.”138 Disaggregation by risk category will only create arbitrary distinctions and undermine the

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ultimate goal, which is “that all the population of a town will see itself as struck at the same time, lest an accident be seen as a particular fortune.”139 With regard to what he designated as individual risks, meaning the numerous accidents that could interfere with workers’ ability to earn a living, Boudon eschewed actuarialism even further, proposing a special relief fund that would be supported by universal contributions. He was quite clear, however, that not everyone is equally worthy of such a solidaristic embrace. In recommending social insurance for those “who, by a useful and productive labor, could be exposed to certain accidents and maladies,” he made sure to contrast deserving claimants from “the idle, who sometimes expose themselves voluntarily  .  .  . to certain dangers without any social utility” and to whom society “owes nothing for individual accidents.”140 Whether intentionally or not, Boudon thus offered a useful reminder of the exclusionary side of insurance. Even the most disaggregated risk pool inevitably will rest on a decision about who is, and who is not, considered an equal for the purposes of mutual protection. The final and apparently most successful example of this genre was Girardin’s La politique universelle. Girardin was a journalist and editor, who after launching a number of literary and political magazines in the 1820s and 1830s went on to found La Presse, France’s first popular newspaper. His biographer depicts him as a pioneer of modern journalism and “inventor” of Napoleon III’s ideology of liberal empire, a “socialist of the previous day” (Girardin’s words) who imagined the future of government as technocratic, apolitical, and welfarist.141 At one time, he was closely aligned with French economic liberals, though he also critiqued some of their positions—along with Napoleon III’s early social insurance laws—as inadequate to the needs of the working population.142 In La politique universelle, Girardin envisioned “a society that, reducing everything mathematically to risks judiciously foreseen and to probabilities exactly calculated, has for its unique pivot universal insurance.”143 Mathematical probability “applied to the life of nations, to the case of war and revolution, is the foundation of all high politics. . . . To govern is to foresee; to foresee nothing is not to govern, but to run to one’s ruin.”144 Among the practical proposals Girardin derived from this idea was a “right of work” (as opposed to a right to work), which would guarantee a minimum salary to workers and thereby ensure that they could provide for their own subsistence through labor. Under such a system, “individual foresight combined with universal insurance” will replace charity and governmental relief, and “Fraternity” will be transformed from a “rare and exceptional sentiment” into a “common and ordinary science.”145

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According to Ewald, the success of Girardin’s work came from its presentation of insurance as a way out of liberal individualism that did not fall into socialism, which harmonized liberty and mobility with equality and security.146 Above all, Girardin appears to have expressed in popular form the overarching hope of late-classical probability—that the “exact science” of probabilities, penetrating to the causes of suffering, would at last replace division and revolution with a nonpartisan government of enlightened risk management. In such a world, mystical evil becomes calculable risk, culpable wrongdoing becomes accidental harm, and a providential God becomes L’État providence—the foreseeing, calculating, and providing state.

Although these pamphlets were the work of practical, political men rather than philosophers of probability, they highlight the presuppositions and challenges of the theoretical approach considered throughout this chapter. Late-classical probabilists aspired to a rational social order in which individual choices would align with a common good. A posteriori likelihoods calculated on the basis of observation would be predictive in both the singular case and in the aggregate; they would guide individual reason with the same force, and to the same ends, as they would the initiatives of enlightened social planners. Mutual insurance embodied this promise of harmony between personal and collective benefit, the promise of a regime that turns individual prudence into universal security. As these works attest, however, the hope expressed by the earliest proponents of social insurance had taken on a different guise by midcentury, entailing a rather more limited understanding of both freedom and the common good. Even where the targeted risk group is broad, as in both Boudon’s and Girardin’s proposals, social insurance restricts its protections to the responsible and deserving, defined as those who have already taken steps to reduce their own risks. As Girardin put it, “As soon as I insure myself, I no longer need for someone else to relieve me; just as it would be wrong to relieve me if I made the mistake of not insuring myself.”147 Insurance as a surrogate for virtue means that one cannot transgress the bounds of responsibility and still maintain a claim to aid. This is fraternity “made a science,” its obligations precisely delineated and deviations curtailed. Protection is thereby limited to those who have relatively little need for it, those who have earned it by choosing to insure in the first place. In effect, this is the vision I have attributed to Quetelet: a society of average men, equivalent and interchangeable in their propensities and vulner-

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ability to misfortune. Too much deviation, too much freedom, mean that individual choices might not promote a common good because those who see themselves as superior will prefer not to insure, while those who can’t muster the right amount of self-control will unduly burden the group. Like the principle of indifference, the most distinctive tool of late-classical probability, this approach seems to rest on a kind of epistemic and contractual freedom, a view that the individual can make sound calculations and rational decisions on his own. Yet in practice it conceals behind a veneer of mathematical rigor what are often arbitrary or relative judgments—determinations about which events are to be considered equally likely or who is to be considered a probabilistic equal.148 Freedom thus invites paternalism, as the common sense of everyday induction cedes its authority to expertise. In the political realm, one can see this development playing out in the struggle between mutual societies and the state that began with Napoleon III’s reforms and continued throughout the development of centralized welfare provision.149 Far more than simply a battle over membership and resources, this conflict concerned the proper locus of decision-making authority, whether it ought to be the citizen or the expert, the distinct individual or the aggregating state. As the next chapter will argue, the interpretation of probability that supplanted the late-classical one over the course of the nineteenth century offered a different solution to the difficulty of aligning individual judgments with statistical averages. This account was less individualist in its methodology and more democratic in its political expression. It also left a significant impression on the theory and practice of welfare in the twentieth century and beyond.

FOUR

The Collectivization of Risk and the Early Welfare States

The last two chapters considered the philosophical origins of social insurance, as it was envisioned at the end of the eighteenth century and gained prominence through the first half of the nineteenth. That period saw a growing concern for the implications of new economic realities, in particular their influence on the working poor, reliant as they were on wage labor and vulnerable to any number of disruptions as a result. Actuarial mutual insurance, both of the commercial and the reformed friendly variety, promised to reduce this vulnerability through the newly theorized mechanism of risk spreading or pooling. The corresponding image of insurance as a prudent agreement, which also fairly distributes the burdens of uncertainty across a group, paved the way for the idea that it could be used on a political scale to both individual and public benefit. The period that will be considered in this chapter—from the second half of the nineteenth century through the early twentieth—saw an intensified political interest in social insurance to promote security for the working classes, cultivate a kind of social cohesion, and preserve capitalism despite the clear hardships of the poor. At the same time, this period also witnessed the emergence of a new rationale for mutual insurance, one that focused less on contractual benefits for individuals and more on the wealth and welfare of groups. A pivotal moment in this shift, I will argue, came in the 1840s, with the advent of a new understanding of probability as the observed frequency of a series of events. Frequentism, as this account is known, emerged as an alternative to the late-classical interpretation that we have been considering. Emphasizing the aleatory or objective side of probability, it insisted that calculation and prediction are possible solely with reference to an observed series, or class, within which individual instances are unpredictable.1

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Frequentism affirmed the value of mutual insurance but modified its justification. Above all, it replaced the idea of personal expectation with the class-based sharing of a wholly collectivized risk. On this view, risk as a quantified and manageable likelihood could no longer apply directly to an individual. Instead, both the assignment of a probability value and, by extension, the fairness of insurance for the individual had to rest on her prior identification with some reference group or class. That this class had a real but relative existence, capable of being defined and redefined according to available evidence, put insurance on a foundation of what might be called pragmatic solidarity, indispensable yet fluid in nature. In fact, this vision accords very well with the way in which the first social insurance programs developed—namely, as the result of lobbying by or on behalf of changeable risk-sharing groups. Thus, if the early welfare state marked a departure from liberal political ontology, or a concern for individuals as the primary political units, then developments in probability theory around the same time can help to illuminate some of the assumptions and implications of that shift. In keeping with the overall argument of the book, this chapter advances several claims about the interconnected development of mathematical probability and the welfare state. First, it argues that the frequentist account of probability had a distinctive normative cast, proposing a vision of class-based solidarity that is holist rather than individualist in character. Second, frequentism provided a powerful rationale for group-based social insurance shortly before the latter became a political reality. Indeed, the frequentist view arguably found practical expression in some of the actual welfare programs that emerged from the end of the nineteenth century onward. This chapter therefore adds evidence to the case that the interpretation and calculation of risk is also a moral and political endeavor, one that both rests on normative claims and has implications for the shape of the social practices that result.

The Rise of the Collective View of Chance A New Interpretation of Probability The writings of late eighteenth-century probability enthusiasts such as Richard Price and Condorcet had treated mutual insurance as a predominantly voluntary affair, albeit one that would be administered in some cases on a political scale. Supporting this image of insurance as a voluntary contract was an assumption that probability values could be applied directly

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to individual instances, even when they had been determined with respect to groups. As the discipline of probability became more statistical in its orientation over the first half of the nineteenth century, the link between probability values and personal prudence came to appear more tenuous, leading Quetelet, for instance, to declare that while statistics “offer very certain results when applied to a great number of persons,” they “teach us no direct application to an individual.”2 Nevertheless, the probabilists we have considered thus far continued to understand insurance as the exchange of an individual expectation or risk, undertaken for personal benefit, even as they also saw it as a tool for the state to promote public order and loyalty. Beginning in the 1840s, the interpretation of probability that we considered in the last chapter faced a serious philosophical challenge. Frequentism, as the alternative view is known, was initially worked out during the late 1830s and early 1840s, during a rising tide of philosophical empiricism in England, France, and elsewhere. It holds that a probability value is simply the observed frequency with which an event occurs in a series of trials. As a result, the probability itself applies to the series and not to any individual instance within it. In the early 1840s, according to Theodore Porter, four authors in three countries—Robert Leslie Ellis and John Stuart Mill in England, Antoine Augustin Cournot in France, and Jakob Friedrich Fries in Germany—offered interpretations of probability that were “fundamentally frequentist in character.”3 Our focus here will be primarily on the expression of this view in England, where it enjoyed relative prominence and sparked lasting debates that had implications well beyond probability theory. Although frequentism was not a unified movement, several features stand out as broadly distinguishing the frequentist understanding of probability at this time: first, an emphasis on empirical observation over subjective belief; second, a strong critique, if not outright rejection, of the principle of indifference; third, a reluctance or refusal to assign probability values to single instances; and finally, an understanding of randomness as a property of events within a properly defined series. Ultimately, what makes frequentism significant for our purposes is its acknowledgment that all probability estimates are conditional on the prior identification of a series or class. As a result, frequentism supported a collectivist approach to insurance, prioritizing groups of citizens over individuals and demoting claims about personal responsibility for some misfortunes. Frequentism begins with an apparently straightforward proposition: A probability value is simply the observed ratio of successes over the total number of trials in a series of relevantly similar occurrences. This defini-

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tion deliberately breaks from the Laplacean paradigm, and in particular Laplace’s famous dictum that probability relates in part to our knowledge and in part to ignorance.4 Frequentists held that a probability value is not a reflection of the individual’s belief, but rather a measurement of occurrences in the world. As John Stuart Mill put it in the first edition of his A System of Logic, “Conclusions respecting the probability of a fact” rest “upon the very same basis, as conclusions respecting its certainty: namely . . . knowledge obtained by experience, of the proportion between the cases in which the fact occurs, and those in which it does not occur.”5 A year earlier, Ellis had similarly argued that “when on a single trial we expect one event rather than another, we necessarily believe that on a series of similar trials the former event will occur more frequently than the latter.”6 Insofar as we assign a probability value to any event, then, it is on the basis of evidence that, in the long run, it occurs in the proportion expressed by that value. Those who adopted a frequentist interpretation at this time were not united in their epistemological views. Ellis, for example, a Cambridgeeducated mathematician and editor of the works of Francis Bacon, adopted an idealist interpretation of the foundations of probability, maintaining that the identity of probabilities and long-run frequencies is an a priori truth, premised on the regularity of nature. John Venn, by contrast, perhaps the most prominent frequentist of the era, rejected claims of a priori truth and aspired to bring the theory of probability into conformity with experience.7 Also a Cambridge mathematician, Venn published several important books on logic; his first, The Logic of Chance, is a systematic exposition of frequentism that went through three editions between 1866 and 1888. Despite their differences, however, Ellis and Venn shared an insistence that a probability value is a ratio or frequency derived from a series of occurrences, each of which is uncertain in isolation. In Ellis’s words, our judgments of probabilities depend not on the “fortuitous and varying circumstances of each trial” but on the natural fact that “on the long run, the action of fortuitous causes disappears.”8 Or, as Venn put it, probability is concerned with those classes of things “as to the individuals of which we feel quite in uncertainty, whilst as we embrace larger numbers in our assertions we attach greater weight to our inferences.”9 So far, frequentism clearly resonates with the views of the later statistical enthusiasts who followed Laplace. Yet in rejecting the notion that probabilities measure partial belief, frequentists also did away with one of Laplace’s most characteristic innovations: the principle of indifference. On a strictly frequentist view, one cannot represent ignorance with an assign-

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ment of  equal probabilities, since the latter is only justified if the events in question can be said to occur with equal frequency in a series of trials. As Mill put it in 1843, in order to “pronounce two events to be equally probable, it is not enough that we should know that one or the other must happen” but have no grounds for determining which. Rather, “experience must have shown that the two events are of equally frequent occurrence.”10 Frequentism thus emphasized the distinction between probability’s subjective and objective interpretations, putting its weight decisively on the latter. Although the old view of probability as partial belief remained in force in some circles, frequentists took the regularities of social statistics as modeling an alternative view, in which the subjective side of probability is, as Venn put it, “a mere appendage of the objective, and affords in itself no safe ground for a science of inference.”11 Ellis put the point slightly differently, but to the same effect: “I have been unable to sever the judgment that one event is more likely to happen than another, or that it is to be expected in preference to it, from the belief that on the long run it will occur more frequently.”12 As a consequence of these two positions, frequentism also called into question the relevance of probability values to individual events. Frequencies are calculated for a sequence of trials, each iteration of which is wholly unpredictable. “When individual cases are considered,” wrote Ellis in 1854, “we recognize in the determining circumstances of their occurrence an extraneous element,” a kind of contingency that precludes prediction because we cannot know the causal factors at work. This contingency disappears only “when we consider the genus in its entirety” and ignore the individual species.13 Venn articulated the point without regard to causal considerations: “For bearing in mind that the employment of Probability postulates ignorance of the single event, it is not easy to see how we are to justify any other opinion or statement about the single event than a confession of such ignorance.”14 In assigning a mathematical expectation to any individual, Venn explained, the frequentist intends “nothing more than to make a statement about the average of his class.”15 This view reflects a version of epistemological holism, according to which knowledge of the individual case derives from knowledge of the collective. In some cases, including Venn’s, it also reflects a kind of ontological holism, implying the priority of the series as a matter of fact. “Such regularity as we trace in nature is owing, much more than is often suspected, to the arrangement of things in natural kinds, each of them containing a large number of individuals.”16 Although Venn denied the existence of fixed nat-

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ural types, he did suggest that imperfect series exist in nature and that these could be replaced with refined or idealized versions for the purposes of statistical analysis.17 Finally, frequentism was accompanied by a distinctive understanding of what it means for events to be random. Specifically, it supported a view of randomness as a uniform distribution of individual trials within a properly defined series. As Venn explained, randomness presumes some agent, human or other, operating within a set of limits such that it is as likely to generate any given outcome as any other. In other words, over a set of possible outcomes—say, the selection of a ball from an urn or a book from a shelf—the agent must be just as likely to select one ball or book as any other. As a result, “we always encounter, under this conception of ‘randomness,’ at some stage or other, this postulate of ultimate uniformity of distribution over some assigned magnitude,” although the determination of when and how to introduce that assumption is a matter of experience and convention.18 Charles Sanders Peirce, the American pragmatist philosopher, articulated a similar view in defining a random sample as one “taken according to a precept or method which, being applied over and over again indefinitely, would in the long run result in the drawing of any one set of instances as often as any other set of the same number.”19 A Modified Case for Insurance These features of nineteenth-century frequentism had several implications for the theory of insurance, and social insurance in particular. First, frequentism offered a new answer to the question of how risk-pooling arrangements could be justified for the individual, and it outlined the mental disposition necessary to support such arrangements from the individual’s point of view. Second, it encouraged a more explicit awareness of risk classes as the targets of insurance arrangements, which differed from the earlier tendency to regard the individual as the primary unit of social concern. Third, frequentism tended to emphasize the aggregate effects of insurance rather than its benefit in any particular case. Finally, it implied a new understanding of probabilistic equality as the property of individuals within a series, each of whom is as likely as any other to incur a given fate. Frequentism thus operated on both levels of the social insurance paradigm— the individual and the state, or demand and supply—bringing them together in a way that was meaningfully different from previous accounts. Many frequentists, most famously Mill, mollified over time their critique of the principle of indifference, particularly as applied to causal

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hypotheses.20 Yet by insisting on the inapplicability of probabilities to individual events, they had already suggested a radical critique of the classical rationale for insurance. Venn, for example, explained that from an individual perspective insurance cannot be justified for any single event.21 Cournot allowed for the use of probabilities “to fix the conditions of a bet or some random business deal,” but made clear that whatever number the parties happen to choose is simply a “subjective” assessment, which will differ depending on each one’s knowledge and has nothing to do with an actual ratio of outcomes.22 Even Mill continued to maintain in later editions of his Logic that empirical averages, while necessary for practical use, “are of extremely small value as grounds of expectation in any one individual instance.”23 If mathematical probability is of such little use as a guide to single events, what then is left of the justification for insurance? That is, how can an individual reasonably choose whether to insure if there is not a probability value that applies to the specific eventuality she wishes to insure against? Recall that Condorcet had posed a version of this question and suggested that the substitution of an average value for a real one makes sense either when there is a market price for the risk in question or when the terms of the agreement can be fixed such that, in a long run of identical trials, the parties would be equalized. Frequentism offered a somewhat different solution, calling on a kind of enlarged sympathy or prior identification with the class, after which the individual can regard its probability value as her own. Venn, for one, recognized that for insurance to remain individually rational on a frequentist view, it would require a different justification from the one offered by classical probability. One possible approach, he suggested, is for the individual to consider his own actions as a series and to find that the “equalization of his gains and losses, for which he cannot hope in annuities, insurances, and lotteries taken separately, may yet be secured to him out of these events taken collectively.”24 The individual with sufficient experience might thus be justified in substituting an average value for his mathematical expectation in any particular case. This approach is problematic, however, because it is unclear what actions constitute the relevant trials and whether they could in fact amount to a series, which Venn defined as a set of events that are completely uniform with regard to most of their qualities.25 It is particularly problematic with respect to events which the individual will experience infrequently or only once. More promising, in such cases, is Venn’s suggestion to “suppose the existence of an enlarged fellow-feeling,” or an identity with the

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other members of one’s group.26 He offered the example of dying on any particular day of the week: “Here the contingent event is clearly one that does not admit of repetition, and yet would not the belief of every man” assign it a value of one-seventh? What justifies this assignment is a form of expanded interest: While “it is quite true that I have only the opportunity of dying once myself,” Venn explained, “I am a member of a class in which deaths occur with frequency, and I form my opinion upon evidence drawn from that class.”27 On this account, then, the reasonableness of insurance hinges on each person’s ability to see himself first and foremost as a member of his class, and to enlarge his own interest to encompass the group as a whole. This class-based actuarialism is thus grounded in a kind of interpersonal identity rather than an individualized risk. It is also flexible, based on an admission that the insured’s designated reference class—those with whom he is grouped for the purposes of calculating the probability value in question—can vary according to the insurer’s needs and available information, as well as over time.28 On this view, the class exists in nature as a class, but because it is known through observation and not as a consequence of any deeper causal account, there is no reason to fix its existence as such or to consider it as inherently superior to any other observed series.29 Venn offered an illuminating discussion of the relativity of reference classes. Examining Quetelet’s treatment of statistical groups, he accepted that combining the statistics of two distinct classes—for example, the heights of Englishmen and Frenchmen—may result in a distribution that loses its symmetrical form because the averages of the two groups will differ. Yet he noted that the same could be said about each group taken independently, since it, too, is a composite of other relatively homogeneous groups. “What we call a nation is really a highly artificial body, the members of which are subject to a considerable number of local or occasional disturbing causes.” As a result, “whatever objections exist against confusing together French and English statistics, exist also, though of course in a less degree, against confusing together those of the various provisional and other components which make up the French people.”30 In conjunction with the view that probabilities apply to such classes and not to individual events, several frequentists also rejected the idea of moral expectation, which late-classical thinkers had invoked to resolve any discrepancy between the individual’s projected loss and the average premium charged for the group. Cournot, writing in 1843, argued that accounts of moral expectation “are vague and arbitrary,” as well as unnecessary. While the security that insurance provides to the individual is indeed

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a benefit, it “cannot appear on the balance sheet of a particular insured, nor does it directly increase his wealth or the social wealth, considered as the sum of fortunes possessed separately by all members of society.”31 Instead, it is the institution of insurance (in this case, the commercial variety) that increases wealth of both sorts. Insurance allows owners to preserve the value of their goods, and as more people purchase it, the fairer its price becomes. What is more, this benefit need not accrue to any particular individual to serve its purpose since the very possibility of insuring a good at a fair price is enough to raise the price of that good, on average. “We are discussing not accidental causes that determine the conditions of this or that market,” Cournot continued, “but economic laws that produce general and mean results, compensating for random deviations.”32 As we will see in the next subsection, Venn explicitly proposed supplanting moral expectation with utilitarianism, with its aggregative approach to social welfare. Cournot’s discussion in the passage just quoted concerns fixed-premium commercial insurance, which he distinguished from mutual insurance on the ground that the latter can vary premiums over time in accordance with the magnitudes and variance of the risks insured. On Cournot’s account, this feature is particularly advantageous for nonindependent or “solidary” risks—those that are causally related in some way, such as when a single fire burns down an entire city—which can seriously undermine an insurer’s projections, making a fixed-premium office “more or less resemble a gambler’s lot.”33 Cournot’s appreciation of the benefits of mutual insurance relies on a finding of his friend and correspondent I. J. Bienaymé, a leading statistician of the nineteenth century. Bienaymé had calculated the probability that the mean contribution of a participant to a mutual insurance agreement would fall within certain limits given the value insured, the probability of loss, and the number of participants in each risk class. He concluded that it is always beneficial for two or more risk classes to combine into one association since the increase in the number of new members will tend to decrease the variance of each individual’s payments.34 Here too, then, the justification for insurance hinged less on its fairness in the individual case, understood as the justly priced exchange of one’s mathematical expectation, than on the aggregate effects of large numbers of participants in stabilizing the premiums collected from each group. Finally, frequentism suggested a new interpretation of probabilistic equality, based on its understanding of the nature of chance itself. Since Hume, at least, the idea of chance was associated with a mental state of complete indifference between the possible outcomes of a particular trial.35 Frequentists, by contrast, looked for chance in the world and found it in

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the observation of causal independence or the absence of a discernable agency.36 We can know that an outcome is chancy on this view not because we are ignorant about its result beforehand but because repeated trials of the same event generate a uniform distribution in which the individual results are random, or occur with equal frequency. Although the distinction is a subtle one, the frequentist view implies that we can learn from experience that any given risk—say, a work accident or losing one’s job—is randomly distributed within a specific population in the same way that natural events such as deaths are.37 This in turn implies that individual victims of such events are not responsible for their fates because anyone within the class could have just as well been struck. Many of the earliest welfare policies rested on precisely such claims about the revealed randomness of particular phenomena, and about the need for policies that help groups of people who are deemed equally vulnerable to, and therefore blameless for, the unfortunate events that befall them. The Ethical Character of Frequentist Probability We should not overstate the influence of frequentism on ideas about social solidarity or early welfare policy. Except perhaps in England, frequentism never gained wholesale acceptance within the philosophy of probability, and it was therefore somewhat limited in its theoretical influence.38 Venn’s rejection of the principle of indifference in particular, and of the application of numerical probabilities to individual events, met with skepticism even among contemporaries who were sympathetic to his empirical approach.39 Nor was the frequentist approach original or unique in proposing to understand certain phenomena, in particular problems related to economic deprivation, as a function of class characteristics.40 Indeed, there appear to be other and possibly more direct sources of the philosophical holism that emerged at the end of the nineteenth century and arguably supported early welfare legislation by promoting ideas about solidarity and social obligation.41 Nevertheless, a number of indirect signs indicate that a roughly frequentist understanding of probabilities helped to undergird early social legislation. First, the subordination of causal inquiries to the search for large-scale, observed regularities supports the notion of systemic or social risk that was so important in justifying early social insurance schemes. Moreover, it does so without simultaneously invoking a personal contractual entitlement, as previous accounts had done. Second, the demotion of causal analysis and the view of events within a series as random down-

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played individual responsibility and supported the case for compulsory risk pooling, as on this view the benefits of insurance hinge on its aggregate effects and not on whatever personal virtues it may reflect. Finally, the flexible class-based actuarialism of the frequentist account does characterize the shape of many early welfare states, as will be shown in greater detail in the next section. The risks covered by many early social insurance programs, including disability, illness, and unemployment, were often not amenable to fine-grained probability calculations in the way that mortality risks were thought to be. As a result, these schemes frequently pooled risks beyond more conventional actuarial groups, calling on a somewhat more encompassing form of solidarity than both commercial life insurance and friendly societies had done. Frequentism, by acknowledging the relativity of probability calculations to a changeable reference class, and by encouraging the identification of the individual with this class, provided a theoretical model of such solidarity.42 I have thus far focused on indications of what one might call an elective affinity between the philosophy of probability and early welfare thinking. Yet there is also a historical connection of some significance. Utilitarian philosophers and political economists of this time, particularly in England, took considerable interest in the foundations of probability, and some perceived a connection between utilitarianism and the frequentist view. Indeed, both accounts took an aggregative approach to individuals, and both rested on empirically informed, yet changeable, determinations of equality that allowed for such aggregation. Utilitarian skepticism about natural rights also finds an intriguing parallel in the frequentist rejection of a personalized risk, reflecting in each instance an explicit departure from classical liberal thought. This is not to say that a frequentist view of probabilities necessarily lends itself to utilitarian economics, or that the kind of solidarity I am identifying with frequentism necessarily entails a rejection of individual rights. Rather, the more modest point here is that these two families of ideas were worked out in close proximity, with noteworthy overlaps between them. For example, in his final addition of the Logic, Venn recommended utilitarianism as the successor to and fulfillment of the concept of moral expectation, in that it answers the question of which “distribution of wealth tends to secure the maximum of happiness.”43 Venn accepted his predecessors’ assumption about the concavity of utility curves, or the view that the marginal utility of income declines as base wealth increases, as Daniel Bernoulli had initially proposed. Yet whereas earlier authors had invoked declining marginal utility and moral expectation to justify individual deci-

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sions about risk, Venn interpreted them as arguments about the overall distribution of wealth. If the disutility of the losing gambler exceeds the utility of the winner, then overall happiness has decreased, and what is proved is that “inequality is bad, on the ground that two fortunes of £50 are better than one of £60 and one of £40.”44 The real problem with gambling, therefore, is not its disutility to the individual but “its tendency to the increase of the inequality in the distribution of wealth,” a conclusion that recommends the “Socialist’s ideal as being distinctly that which tends to increase happiness.”45 In making these remarks, Venn credited political economist and philosopher Francis Ysidro Edgeworth for having discovered the theoretical successor to moral expectation. Although made to Edgeworth’s chagrin, this reference is revealing of the intersection between probability theory and political economy in the latter half of the nineteenth century.46 If one were to try to trace a direct historical connection between the frequentist interpretation of probability and the interventionist utilitarianism of the early British welfare state, it is likely that Edgeworth would play an important role. Although this is not the place to fully trace that intricate lineage, it is worth pausing briefly to consider his work. Edgeworth was certainly not a conventional frequentist, if such exists.47 Like Venn, however, he was an empiricist when it came to probability, insisting that likelihoods should “rest upon precise experience” if they are to be measurable.48 While he defended the principle of indifference, and was even responsible for persuading Venn to moderate his critique of inverse probability in later editions of the Logic, he did so on grounds that differed substantially from those offered by many of his late-classical predecessors. “In Probabilities,” he explained, “it is often necessary to assume that quantities between which no inequality has obtruded itself in the course of experience may be treated as equal.”49 Yet this assumption, he quickly clarified, rests “upon the loose foundations of common-sense,” not on the statistician’s mental state of uncertainty.50 Specifically, there is a “substratum established by wide experience, that what has held good in two or three  .  .  . experiments will hold good generally.” Equiprobabilities based on such observation will therefore be “respectably grounded upon experience,” and not “so inane as Mr. Venn would have us believe.”51 Edgeworth explicitly related this commonsense assumption of equal probabilities to utilitarian ethics, explaining that in the latter “equality is similarly postulated. The reasoning of Bentham and Prof. Sidgwick, that equality of distribution tends to maximum happiness, presupposes that

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the distributees are equally capable of happiness.”52 Indeed, the application of “intellectual probability . . . appears to be unconsciously performed by the utilitarian who thinks it ‘fair’ to treat as equals those between whom no material difference is discerned.”53 The assumption of equality thus serves the practical needs of the utilitarian calculus in the same way that it serves those of scientific endeavor: It provides a “hypothesis which may serve as a starting point for further observation” and calculation.54 Eventually, such observation and calculation would allow for a truly “scientific hedonimetry,” a project that Edgeworth first laid out in his 1881 Mathematical Psychics.55 There he analyzed the phenomenon of contractual indeterminacy, or the fact that in the absence of perfect competition, more than one desirable outcome exists for any exchange. Under such conditions, either party to an agreement may choose to recontract after the initial bargain is made, giving rise to a general state of uncertainty. The growth of trade unions and cooperative associations, while rational and beneficial to the participants themselves, exacerbates this fundamental problem of economic and social life by undermining competition and reducing the number of actors within a given field. Assuming, then, that individuals prefer certainty to uncertainty, “there would arise” from this situation “a general demand for a principle of arbitration,” a single solution for each type of contract that will ensure the parties’ benefit and the overall social good.56 The central question motivating this analysis and, less explicitly, Edgeworth’s subsequent work in mathematical statistics is how to reconcile the free choices of individuals with the collectively beneficial or utilitarian outcome.57 In Mathematical Psychics, Edgeworth’s answer involves intervention by statistically informed planners who, with the help of data about individual preferences (to arbitrate contracts on the private level) and the characteristics of classes (to arbitrate on the social level), are able to facilitate socially advantageous agreements. Supplementing competition with arbitration in this way means that the “economical leads up to the utilitarian calculus,” and the outcomes of self-interested bargains can be fixed so as to promote overall utility.58 Over time, Edgeworth’s argument suggests, the application of scientific utilitarianism to economic and political life will allow for a “reconciliation between egoism and altruism,” between a contractual regime guided by self-interest and one in which each citizen identifies her own good with that of the whole.59 It is worth noting that while this vision is thoroughly moral in its ambitions, there is nothing inherently egalitarian about it.60 Just as the principle of indifference, with its assumption of equal prior probabilities, would

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ultimately give way to empirical frequencies, the utilitarian assumption of equality could be modified in light of further observation, revealing that particular groups of people are more or less capable of happiness. A truly scientific utilitarianism calls for estimating “the duration of the pleasure, the susceptibility, as well as the number” of all citizens on the basis of extensive observation.61 It also calls for a rejection of those “metaphysical ‘rights of man’” often invoked to justify equality.62 The social contract on Edgeworth’s account is therefore to be informed not by natural rights but by an awareness of statistical groups and their potentially distinct distributive claims. Although Edgeworth would eventually modify his youthful antiegalitarian stance—and even embrace the leveling power of the probability calculus in some circumstances—he continued to emphasize the analogy between probability theory and utilitarianism, particularly as he turned to theoretical statistics in the years after publishing Mathematical Psychics.63 For one, the analogy allowed him to affirm that utility values are measurable, since probability and in particular the normal law provided a means of approximating numerical measurements even where, as in the case of utilities, perfect measurement is impossible.64 More generally, it appears that both the philosophy of probability and utilitarianism suggested an answer to a question that preoccupied Edgeworth throughout his life, namely how to relate particular instances or spontaneous events with an account of general order and stability. As Philip Mirowski has explained, Edgeworth reconceived economic equilibrium as an evolutionary process, resulting in a kind of stochastic order on the model of the gas laws.65 In this context, the theoretical interest of the probability calculus lay in its ability to model the coexistence of free or spontaneous elements within a single harmonious system.66 In conjunction with this view, Edgeworth also proposed an alternative psychological foundation for economic order. “Self-regarding self-interest, the gospel of Adam Smith, is not alone sufficient for industrial salvation: a leaf must be taken from his older and less familiar testament, of which the cardinal doctrine was sympathy.” Edgeworth was quick to clarify that he did not mean a “utopian eradication of self-love,” but rather “mutual understanding, between the parties to distribution.” Over time, “the dispositions of which the gratification constitutes self-interest may become more social,” so that, for example, the extreme deprivation of some will be undesirable to others (in particular their employers).67 Until then, “intellectual sympathy alone might effect much.”68 One finds in such statements an echo of the frequentist case for social welfare, to which we will now turn.

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Frequentist Social Welfare The connection between frequentism and utilitarianism for both Venn and Edgeworth—and, less explicitly, for Mill and Cournot—is not simply a coincidence. As we have seen, the concept of utility, along with the assumption of the concave utility curve, emerged within the theory of probability. It was originally intended to reconcile mathematics with common sense, showing that probability is a reliable guide to decision making as long as certain psychological and moral assumptions are made. Frequentism, too, set out to align probability calculations with “the common sense of mankind,” as Ellis put it, offering what advocates saw as a more compelling basis for practical reason than its Laplacean predecessor.69 Although Venn’s original impetus in writing The Logic of Chance was to distinguish probability from psychology or the laws of partial belief, frequentists never managed to rid the concept of its epistemic face. Instead, at least in the extreme case, they simply rendered that face a derivative of the aleatory one. As I argued in the last chapter, the epistemic commitments supporting late-classical probability had allowed it to remain methodologically individualist and, in this sense, liberal, respecting a kind of personal judgment about probabilities even when not based on empirical observation. Frequentism, by contrast, aspired to place its counsels on the firmer ground of cumulative experience. It did this by rejecting any quantification of ignorance and by defining probability as a measurement of observed events. From the individual’s perspective, this means that many rational decisions cannot be made in isolation, but rather only by first considering the relevant experiences of others. Reason requires seeing one’s own case as an equally probable instance in an ongoing series of trials. American pragmatist philosopher Charles Sanders Peirce was perhaps the most clear-eyed in recognizing this implication of the frequentist view. Peirce explained that “in the long run, there is a real fact which corresponds to the idea of probability, and it is that a given mode of inference sometimes proves successful and sometimes not, and that in a ratio ultimately fixed.”70 Because “probability essentially belongs to a kind of inference which is repeated indefinitely,” a single instance or inference “can show no effect of probability; and, therefore, in reference to a single case considered in itself, probability can have no meaning.” Instead, logicality inexorably requires that our interests shall not be limited. They must not stop at our own fate, but must embrace the whole community. This community, again, must not be limited, but must extend to all races of

120 / Chapter Four beings with whom we can come into immediate or mediate intellectual relation. . . . Logic is rooted in the social principle.71

Peirce gave the example of choosing a card from a pack of twenty-five red cards and one black, or twenty-five black and one red. If choosing red will bring eternal felicity and black everlasting sorrow, one will certainly opt to pick from the first pack. Yet on Peirce’s view, no valid inference justifies that choice when taken in isolation. Because the exercise is carried out only once, no “real fact” gives truth to the statement that if the drawer selects from one pack, a particular color will likely appear. The example therefore illustrates that only by having enlarged interests—by caring “equally for what was to happen in all possible cases of the sort”—is it possible to act logically in choosing from the red pack.72 The practical consequences of this position are significant. Far from sanctifying the right of any individual to judge her own case, frequentism implies the epistemic priority of the community, and with it an argument for a kind of sympathy or altruism. Although this shift will not necessarily lead to different probability values, it does amount to a very different justification for both individual and collective action. The truly reasonable person will ground her decisions in the “social principle.” In other words, only by first expanding our field of concern and understanding our place in a larger series of similar cases will we have grounds to regard the empirical probability as our own and be motivated to act accordingly. Peirce’s vision thus echoes the “enlarged fellow-feeling” on which Venn’s account of insurance rests. Although “fellow-feeling” suggests an emotion, the ultimate basis of this disposition is rational rather than sentimental.73 Specifically, it rests on the decision maker’s knowledge about his own prospects, derived from observation of those similarly situated, and on an understanding of the logical necessity of seeing himself as interchangeable with everyone else in that group. Edgeworth later reached a similar conclusion, quoting Venn to the effect that it is almost always possible to conceive of an event as part of a series, and that our ability to do so improves with experience.74 “‘A man, say, buys a life annuity, insures his life on a railway journey, puts into a lottery, and so on.’ It may be expected, I think, that the class of actions which cannot be regarded as part of a ‘series’ will diminish with the increase of providence and sympathy.”75 These examples are not intended to suggest that many late nineteenthand early twentieth-century thinkers—including utilitarians and those now known as neoclassical economists—understood the more collectivist implications of frequentism or extrapolated from them a case for social insur-

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ance.76 For instance, the economist Arthur Pigou, whose remarks on the subject Edgeworth enthusiastically cited in a 1913 review, did tout mutual insurance as a means for the “voluntary transference” of wealth from rich to poor, or more specifically from lucky to unlucky within an insurance association.77 Pigou admitted that such arrangements are somewhat constrained by claims of actuarial fairness, but noted that the ratio between premiums and risks need not be exact for the arrangement to remain mutually beneficial.78 He thus allowed for a range of advantageous insurance arrangements in which the shared risk pool is defined more broadly and more flexibly than strict actuarial fairness would suggest. Nevertheless, Pigou did not specifically discuss social insurance in this context, nor did he tie his remarks to the interpretation of risk itself. Indeed, the political implications of frequentism remained below the surface in many of these accounts. Instead, as I now hope to show, it was early welfare policy itself that brought them to the fore.

Risk in the Early Welfare States There is no shortage of scholarly explanations for the rise of the modern welfare state, from industrialization and the destructive effects of capitalism, to efforts by nondemocratic rulers to gain legitimacy, to the political power of working-class movements.79 Recent scholarship has shown a particular interest in the explanatory value of risk perceptions and insurance as the motivations for social policies, with good reason.80 As we have seen, the idea of social insurance can be understood as a natural extension of early accounts of the social contract, with their focus on promoting security through collective agreement, and of the statistical revolution that took place during and after the Napoleonic period, when, in Ian Hacking’s words, “counting and measuring became the thing to do.”81 The latter development encouraged recognition of the accidental and therefore undeserved character of many private misfortunes and placed a greater onus on the collective to mitigate their effects. Furthermore, political economists and historians of modern welfare policy have called attention to the influence of risk-prone groups in demanding social insurance to shift the financial burdens of economic hazards, both among themselves and across the polity as a whole.82 Historically, then, ideas about risk have been closely implicated in the development of many welfare states. As fruitful as this recent scholarship has been, however, the literature has not seriously considered how changing understandings of probability and risk may have influenced the models of social insurance proposed or

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adopted. If, as the preceding historical analysis indicates, risk is not a singular or static concept but one that has evolved, reflecting different normative commitments over time, then there is not a single insurance rationale for welfare but several, each embodying a different constellation of epistemic and normative claims. We have seen that this is true in theory, through the differences between late-classical accounts of insurance and their frequentist successors. The discussion that follows endeavors to show that it is true in practice as well. By examining some of the actual debates and policies surrounding the emergence of social insurance in Europe from roughly 1880 through the onset of the First World War, and in the United States up until the New Deal, one can see how reformers adopted, and adapted, the logic of probability and statistics to promote particular political aims. Here, once again, the concept of a policy paradigm helps to illuminate the relationship between probability theory and political outcomes. Ideas about risk, statistics, and insurance were an important part of the arsenal used by political actors during this era to influence political debate. The frequentist understanding of probability and insurance proposed not only a solution to the problem of reconciling economic development and distributive fairness but also a means for bringing that solution about, through collective action in the face of shared risks. This is not to say that the individual citizens who sought economic protection during this era were motivated directly by frequentism or to insist on the influence of this interpretation in shaping particular policy decisions.83 My aim, rather, is to trace an overarching resemblance between probabilistic ideas and social policies, and in so doing to make a prima facie case that frequentism and its associated account of social insurance were among the set of ideas used by political actors seeking to translate the popular demand for protection into public policy.84 This account resonated with new political realities, including the expansion of the franchise and the political clout of mutual societies and labor movements. As a result, while the social insurance paradigm was not new, this particular interpretation was well suited to support the enactment of social insurance schemes during the period in question. The risk-collectivist account of social insurance was not the only one available to reformers of this era. Its predecessor, which we considered in detail in the last chapter, also rested on an understanding of certain accidents as beyond the scope of individual control. Yet while the earlier view saw the individual worker as the primary target of state policy, its successor understood self-defined risk groups as central to the purposes and workings of social insurance. The fact that these two models coexisted in the latter decades of the nineteenth century supports the claim that social insurance

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was by this time established as a policy paradigm, such that political actors were now vying to influence its terms. The success of the risk-collectivist view, I propose, derives in part from the fact that it was better suited to support the demand for social insurance in increasingly democratic polities, explaining and justifying a form of collective action in the arena of distributive politics.85 The Question of Responsibility In the countries that will be considered here, work-injury compensation laws tended to herald the movement toward more generalized social insurance. Such laws began to shift the financial burden of workplace accidents from workers to their employers or the general public, and they hinged on a changed understanding of causation and thus who should be responsible for industrial injuries.86 This development found different expressions across countries and times, but on the whole the late nineteenthcentury trend away from employee responsibility was strikingly common in places as politically diverse as Germany, France, Great Britain, and even the United States. In Germany, for example, employer liability for work accidents was extended in 1871, and in 1881 an accident insurance bill mandated that employers be insured.87 In France, a proposal to establish the presumption of employer liability failed in 1880, but another based on the principle of “occupational risk” succeeded in 1898 in establishing statutory compensation for certain categories of worker.88 In Britain, an 1897 workers’ compensation act allowed those suffering injuries from specific types of work to recover compensation without proof of employer negligence, and another in 1906 extended this coverage to industrial diseases and most previously excluded occupations.89 In the United States, the judicial attack on orthodox causation in tort law, the locus of worker-employer disputes, was encapsulated in 1897 by Oliver Wendell Holmes, who argued that “the question of liability, if pressed far enough, is really the question of how far it is desirable that the public should insure the safety of those whose work it uses.”90 Between 1911 and 1920, most American states enacted workers’ compensation laws.91 In each country except France, full-fledged social insurance programs for sickness, old age, and unemployment were not long in following, all predicated on an understanding of certain eventualities as unavoidable or “social” risks, and therefore beyond the control of any given individual. While the statistical understanding of accidents helped to reshape per-

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ceptions of individual responsibility, it did not imply any particular answer regarding how to manage the risks in question, and in particular whether they should be pooled among groups of workers or shifted onto employers or the state.92 In France and to some degree Germany, the initial answer was to shift risk to the central government, with insurance understood as a direct and material contract between the individual worker and the state. In 1850, a national pension plan for workers was established in France, along with a contemporaneous law regarding mutual societies.93 The former entailed a separate savings-like account for each depositor and was followed in 1868 by similar departments for accidents and death.94 Although the approach remained voluntarist, Napoleon III and his advisors sought to reinforce the role of the central government by directly subsidizing individual savings and recasting the mutuals as intermediaries between workers and the state.95 Bismarck, for his part, claimed to have learned from Napoleon the secret of using of social insurance to tie workers to the state, reportedly embracing the idea when he visited France in the mid-1850s and served as ambassador to Paris in 1862.96 Two decades later, he set out to implement it, passing a series of laws between 1883 and 1889 that, although largely repressive in their intent, significantly departed from the existing poor law system; they are still widely credited as having inaugurated the modern welfare state. It was political pressure from the workers’ movement that most directly spurred Bismarck’s intervention. Michael Stolleis explains that the existing system of poor relief, which granted specific forms of assistance on the basis of demonstrated need, had long failed to solve the problems caused by internal migration, population growth, and industrial poverty. Previous reform efforts had lacked urgency, however, thanks to the geographical dispersion of the poor and the lack of an organized labor movement. By the final decades of the century, conditions had changed: Workers had concentrated in cities and industrial centers, socialism was gaining traction as a political program, liberal thinkers and members of the middle class had come to favor ameliorative efforts for the poor, and industry sought a policy solution that would promote stability while reflecting its interests. In addition, while occupationally based funds existed to provide aid to certain workers in need, enrollment was not always compulsory, and coverage was spotty as a result.97 Bismarck had already set out to quell labor struggles and socialist agitation through legal means. Yet he saw in social insurance a positive complement to these efforts, one that would allow the state to directly promote

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workers’ welfare and redirect their loyalty away from the Social Democrats. He also believed these policies would unify society, including the Catholic Church and business enterprises, some of which had already established occupational pension arrangements.98 The state would thus exert its power to secure the individual worker while tending to the needs of industry and smoothing out class differences.99 Like his reported model Napoleon III, Bismarck maintained that responsibility for individual economic misfortune should be transferred directly from workers to the state. The “soldier of labor,” he noted, just like “the regular soldier disabled by war, or the official,” merited compensation for his sacrifice on behalf of the common good.100 In the case of accidents, he proposed mandatory government-subsidized, state-run employer insurance. The Reichstag, however, rejected both centralization and the subsidy in favor of preserving local insurance institutions and a contribution by the employed.101 Bismarck’s mandatory health insurance law, conceived with the accident bill, also set out to replace voluntary institutions with centralized provision, though he was ill during its passage and as a result it, too, preserved a greater role for voluntarism than he would have liked.102 Finally, Bismarck intended the third law, mandating disability and oldage pensions for all wage earners, to be financed through general taxation, thereby shifting to the social body as a whole the cost of workers’ misfortune. In the end, however, financial and political considerations led to the introduction of a contributory principle.103 Two points about these laws stand out in the context of our survey. First, they reflected a deliberate departure from prior poor relief. They established a contractual right to benefits that was not contingent on a demonstration of need, and they singled out specific groups for attention, in particular the employed and skilled core of the industrial working class.104 They also operated on a principle of differentiated coverage, basing compensation levels on workers’ income. This was related to their goal of encouraging stable employment and savings, giving employees the idea that both they and their employers were investing in their future.105 In these respects, the laws operated within a very different paradigm from the social policies that had preceded them. Second, the difference between Bismarck’s vision and the eventual shape of all three schemes confirms the conceptual and practical plasticity of social insurance. For example, in the case of accident insurance, while Bismarck favored a subsidy to demonstrate public concern for workers’ welfare, the resistance of heavy industries to state intervention ultimately prevailed.106 In the case of health insurance, while Bismarck had intended

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to undermine the autonomy of working-class organizations, establishing the state as the direct benefactor of each worker, the scheme ended up using existing local sickness funds as the vehicles of provision.107 Finally, in the case of pensions, while Bismarck rejected the contributory principle, his ministers and policymakers strongly supported it, and the law that eventually passed the Reichstag deviated even further from his original aim of providing relatively uniform coverage.108 Nevertheless, despite their differences of vision, both sides of these debates operated within an overarching policy discourse or schema that emphasized present payment for future benefits, the institution of a contractual right to relief, and the role of the state as the ultimate guarantor of that right.109 In fact, a number of these disagreements mirror the distinction I have been drawing in this chapter and the preceding one between two models or interpretations of the social insurance paradigm. Bismarck’s centralizing ambitions, like those of Napoleon III, reflected the view that a direct insurance contract between workers and the state would create an identity of interests between the private and the public good. Individuals would get the security they need, while the state would secure their loyalty and with it a form of social order and control. As Bismarck explained in a parliamentary speech on behalf of his proposed pension law, I lived in France long enough to realize that the attachment most Frenchmen feel towards their government . . . is essentially connected with the fact that most Frenchmen are in receipt of a state pension. . . . People there say, if the state comes to any harm, I’ll lose my pension . . . they don’t want to lose it, and so have a vested interest in the state.110

Bismarck may have exaggerated the facts here: France’s original state pension plan was not a major provider of coverage to workers, so it is not clear that many Frenchmen felt the kind of attachment he describes. Yet even if no such widespread sentiment existed in France, the comment illustrates Bismarck’s own statist rationale. He set out to strengthen the state at the expense of both Social Democrats and labor unions, hoping to use insurance to integrate workers as individuals and discourage their activity as organized groups. His opposition to self-help, which also found expression in his rejection of the contributory principle, grew out of a view that a powerful central government could tamp down class conflict. In these respects, Bismarck’s vision differs significantly from the one that came to dominate subsequent welfare legislation in many European countries and the United States.

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The alternative interpretation of social insurance, which I have loosely associated with frequentism, focused on risk classes rather than individuals, accepting and even encouraging their self-identification for the purpose of collective action. This model presupposes an identity among citizens who see themselves as equally vulnerable to a given harm. The distinction at work here did not translate directly into any particular financing or benefit model; as we will see, both visions can result in targeted or universal, tax-financed or contributory schemes. Rather, they differed primarily in their accounts of the relationship between the individual and the risksharing group, with implications for the genesis and justification of social insurance programs. The Subjects and Targets of Social Policy In France, after Napoleon III’s reforms, a version of the risk-collectivist account of social insurance came to prominence in public discourse and policy. Although an early innovator in social insurance, France proved to be one of the slowest countries to develop an extensive centralized welfare state. A host of causes undoubtedly played a role in the delay, including distrust for the state following the Second Empire, a fragmented labor movement and a campaign of political repression in the wake of the Paris Commune, and the relatively slow pace of industrialization.111 Another was the prominence of France’s mutual societies and their ethos of voluntary aid. Whereas Bismarck had staunchly rejected voluntary mutualism, the social insurance paradigm in France long remained connected to its practice and ethical ideal. Often this limited efforts to centralize social provision through the state: In 1910, for example, the French legislature tried to establish compulsory pensions for industrial and agricultural workers, but the measure was quickly undone by a court verdict that nullified the obligation to contribute. In 1925, an attempt to introduce limited unemployment insurance failed as well, as the proliferation and political clout of the mutual societies had created powerful vested interests against state provision.112 The failure of these earlier laws, however, combined with the incomplete reach of the mutuals, did serve as arguments for France’s first major social insurance law, adopted in 1930, providing compulsory health, disability, and pension coverage for all workers in industry and commerce.113 Unlike earlier proposals, this law preserved a large role for existing mutual societies, allowing certain approved funds to provide coverage on either a repartition or full-capitalization basis, depending on the risk.114 Mutual-

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ism in the French context represented not only a powerful political force against state-run social insurance but also an alternate vision of solidarity as more local and more sentimental, even more familial, than what could be achieved through an institution as vast and impersonal as the state.115 The strength of mutualism in France also helps to explain why one of the most influential arguments for social insurance at the end of the nineteenth century set out to transpose the friendly societies’ ethos of mutual responsibility onto society as a whole. This argument did not reflect the atomist-statist vision of Napoleon III or Bismarck, with its strong central authority contracting directly with individual workers. Rather, this was the holistic vision of politician Léon Bourgeois, which saw insurance as emerging from a sense of identity among all members of the social order. Bourgeois served in several ministerial positions at the end of the nineteenth century and became premier in 1895. A supporter of voluntarism, he also forged the compromise position that ultimately persuaded mutualists to accept compulsory state insurance.116 His account of solidarity, published in an 1896 book of that name, presented an understanding of reciprocal dependence among citizens that tried to avoid the extremes of both laissezfaire liberalism and statist socialism. “It is not between man and the state,” Bourgeois wrote, “that society poses the problem of right and duty; it is between men themselves . . . obliged to one another by the necessity of a common goal.”117 Bourgeois regarded a robust, public system of mutual insurance as central to this vision. In a report to the Congress on Social Education in 1900, he advocated the creation of “true mutual institutions, supported by all and open to all, that have for their objective assuring to all men, as much as possible, the support of communal forces and guaranteeing, as exactly as possible, against the risks of communal life.”118 Indeed, his discussion of the social contract as a whole is explicitly reminiscent of the probabilistic treatment of aleatory contracts. The main difference is that, rather than agreeing ex ante to divide their common pool in accordance with each individual’s expectation, the participants in Bourgeois’s society do so ex post, in accordance with the benefits they have already received and the indebtedness to society that they experience as a result. “Man living in society, and incapable of living without it,” Bourgeois explained, “is at every hour a debtor to society.”119 Solidaristic mutual insurance therefore expresses each person’s debt to everyone, both living and deceased, on whose collective efforts his own flourishing depends. While lacking any apparent concern for actuarial fairness, Bourgeois’s account does entail important elements of what I have called probabilistic

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justice. Specifically, it invokes an agreement among equals to contribute to a common pool and redistribute the burdens of misfortunes among them. The equality of the parties is, moreover, a function of their positional identity vis-à-vis chance, and in particular their ignorance of the causal chain leading to various outcomes. This ignorance results in an inability to attribute personal responsibility for many events.120 Individuals’ lives, Bourgeois explained, are “still at the mercy of a considerable number of risks that are themselves  .  .  . the work of society,” such as work accidents and unemployment. “We demand that all of these involuntary risks be insured, and we demand that each one pays . . . his equitable contribution” to the common till that sustains them all.121 Finally, Bourgeois insisted that costs and benefits be calibrated as a function of what each person has received and how much he stands to benefit. “The formula that determines the social link will have to account for . . . the conditions in which each member enters, the benefits he is assured and the costs to which he is subject.” Legislation is “but the practical expression of the equitable division of the profits and costs of the association.”122 These elements place Bourgeois’s thought within the social insurance paradigm as I have been characterizing it. Again, this paradigm does not entail definitive answers regarding how to define the risk pool or apportion the costs and benefits of harms. Bourgeois’s account represents one possible interpretation, and thus confirms both the salience of insurance in principle and its flexibility in practice. As Daniel Béland points out, Bourgeois’s advocacy coincided with two of France’s early social insurance laws, the 1898 law on work accidents and the 1910 pensions scheme, with solidarity appearing as one of their justifications.123 Bourgeois’s account may be understood as an attempt to reconcile the voluntary and communal spirit of the friendly societies with the centralizing tendencies of the age. Yet evidently the French were not yet disposed to regard the entire nation as a single risk pool for mutual insurance purposes, and the alternative—social insurance organized on the basis of classes—still struck many reformers as objectionable.124 It was only after World War II, in 1946, that coverage of various risks was fully centralized and systematized in the form of social security, enlarging the role of the state and dealing a blow to the mutualist movement.125 Until then, French welfare provision remained largely the province of self-defined yet voluntary risk collectives. Elsewhere, reformers and the interest groups they represented had fewer qualms about employing state powers for the benefit of particular classes. In Denmark, for example, the first social insurance scheme—a uni-

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versal, tax-financed pension plan enacted in 1891—was established as a direct result of class-based risk pooling. As Peter Baldwin explains, the law resulted from a protracted political struggle in which the agrarian bourgeoisie, unable to enact desired fiscal reforms, opted to use social policy for its own economic ends. Tax-financed pensions promised to shift the burden of poor relief from local land taxes to the central authority’s indirect consumption levies, and therefore result in lower costs to the farmers. Agrarian employers also preferred a universal approach to appeal to a heterogeneous workforce, as they desperately needed more manpower and relied on a variety of types of labor.126 The pension law was thus one of the primary concessions they extracted for themselves on joining forces with moderate Conservatives to resolve the country’s constitutional crisis. A similar political calculation, but very different outcome, characterized the second piece of Danish welfare legislation, a limited employers’ liability law for work accidents passed in 1897. In this case, farmers rejected universal tax financing because it would have required them to share the burden of hazardous industrial practices in which they did not participate and from which they received no benefit. The resulting law consequently reflected narrow, industry-specific risk pooling rather than the broad coverage of the pension scheme.127 Unlike in Germany, then, where social insurance set out to show workers that the state was a benevolent “institution . . . serving their needs and interests,” early Danish social legislation was a direct product of risk-class mobilization, and in particular the desire of farmers to avoid redistribution to urban industrial laborers, who faced their own specific set of risks.128 The case of Denmark therefore reflects the kind of risk-collectivist welfare that a frequentist account of social insurance would predict: self-defined equals pooling their own risks in the name of collective security, while limiting redistribution to those considered outside of their reference group. The Flexible Actuarialism of Early Social Insurance Over the first few decades of the twentieth century, this flexible, class-based approach to social policy became increasingly common. The political clout of self-defined risk groups grew, thanks to the spread of democracy and the organization of workers themselves, and new hazards and population groups were increasingly incorporated into social insurance schemes. As a result, many welfare states expanded from offering accident compensation and old-age pensions for limited groups of workers, to covering additional economic hazards and wider swaths of the working popula-

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tion.129 These new programs defined their aims pragmatically, expanding or contracting recipient groups and identifying new risks to serve diverse political needs. This pragmatic flexibility accords with the conclusions of frequentism, which acknowledged the reference-class problem and the relativity it injects into probability calculations, and which emphasized the role of experience in revealing whether a risk is randomly distributed. Both frequentism and early welfare programs thus embraced an experimental approach to risk management that rested on certain assumptions about equality but remained open to reevaluating them as needed or desired.130 Early British social insurance offers a powerful illustration of this trend. Compulsory pensions, enacted in 1908, provided flat-rate payments financed by general taxes and paid to every citizen over the age of seventy with an income of less than a certain amount per year.131 In principle, pensions were designed to be universal in reach, although in practice considerations of cost meant that benefits were granted only to the poorer segments of the population and coverage was made contingent on recipients’ character.132 The choice of tax financing as opposed to contributions—Bismarck’s preference for pensions as well—was partly based on the view that the poor could not be expected to save for themselves and partly a capitulation to friendly societies, whose leaders feared that a contributory system would deflect working-class savings and reduce their own ranks.133 Despite their coverage limitations and noncontributory design, however, pensions were intended and largely understood as a significant departure from the poor law system that had formed a central pillar of English social policy throughout the nineteenth century.134 A Royal Commission of 1893 had examined the possibility of public pensions in the context of poor law reform. Yet by 1908, the dominant policy paradigm had changed, thanks in part to the German example.135 Elites had started to heed the demands of organized labor, not only because they feared strikes and protests but also because they perceived new opportunities for partisan advantage in catering to working-class interests.136 For their part, labor groups had rejected poor relief, with its means testing and its focus on deterring claims, and sought pensions as an “endowment” for those who found themselves marginalized from the labor market due to contingencies beyond their control.137 Means tests, which under the poor law had entailed intrusive inquiries into recipients’ means of support, were considered objectionable for humiliating beneficiaries and disincentivizing their saving. Moreover, some unions had instituted pension arrangements of their own and did not want the modest income from those schemes to reduce workers’ public pension allowances.138 While some in the labor movement preferred self-

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help and a more radical change in economic conditions over state aid, the situation of the poorest workers and of women militated in favor of taxfinanced provision.139 In short, then, while the pension law fell short of many expectations, it nevertheless responded to the demands of groups of citizens for protection against economic risks that indiscriminately affected their members. British unemployment insurance, enacted in 1911, exemplifies even more clearly the risk-collectivist account of social insurance. Prior to this time, unemployment had been considered uninsurable, both because it was thought to stem from individual choices rather than economic forces, and because it tended to affect entire groups at once. The depressions of 1879 and 1908, however, had led the British public to conclude that unemployment was indeed a product of forces more powerful than any individual worker.140 As Winston Churchill, then president of the Board of Trade in Asquith’s Liberal government, explained in a 1908 speech, “We have lately seen how the backwash of an American monetary disturbance  .  .  . or some other cause influencing world trade, and as independent of our control as are the phases of the moon, may easily have the effect of letting loose upon thousands of humble families and households all the horrors of a state of siege or a warlike blockade.”141 The solution, according to Churchill, was “that necessary apparatus of insurance and security, without which our industrial system is not merely incomplete, but actually inhumane.”142 Especially in need of protection is the casual unskilled worker, who “has no hope of security and no incentive to thrift,” and who is “embarked in a sort of blind, desperate, fatalistic gamble with circumstances beyond his comprehension or control.”143 Churchill sought to focus the scheme on specific trades, “in which unemployment is not only high and chronic, but marked by seasonal and cyclical fluctuations” that prevent workers from averaging wages or effectively preparing for bad times.144 Restricting compulsory insurance to particular industries would support the sense of mutuality that might not be possible among a more expansive group. While a purely voluntary system would end up with a “preponderance of bad risks,” a universal contributory system, without outside funding, would “almost certainly break down, because of the refusal of the higher class of worker to assume, unsupported, a share of the burden of the weaker members of the community.”145 Britain’s first unemployment insurance scheme correspondingly focused on a limited number of industries and assumed a lateral model of redistribution, with contributions from those currently employed in a given trade financing the claims of those contemporaneously out of work.146 Wil-

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liam Beveridge, who worked with Churchill in the Board of Trade and was one of the main proponents of the scheme, emphasized the equal vulnerability of those covered. Against the view of Sidney and Beatrice Webb, who advocated a reformative approach to the unemployed, Beveridge stressed that many workers faced an unavoidable difficulty of “averaging wages over good times and bad,” and further justified the inclusion of all workers within each industry on the ground of their interdependence: “The regular workman must admit a certain solidarity . . . with the irregular workman, since without the latter the industry by which the former lives could not be carried on.”147 In a sense, this scheme applied the ethos of the mutual societies on a more inclusive basis, thanks to the coercive powers of the state.148 Yet where mutual societies had failed to cover the most difficult risks, the state could mandate workers to share burdens within and somewhat beyond their actuarial class, and furthermore require employers and taxpayers to shoulder some of the costs. In the United States, as in nearly every industrialized democracy, the issue of work accidents played a foundational role in the gradual emergence of the welfare state, providing the classic example of an undeserved misfortune in need of redress. As elsewhere, this problem led to the emergence of various cooperative workers’ associations that provided members with rudimentary insurance-type relief. As John Fabian Witt argues, these associations successfully cultivated a strong sense of mutuality and avoided the challenges inherent to disability insurance, in particular the self-selection of high-risk candidates and the potential for fraud. By the 1890s, cooperatives were also the leading source of life insurance in the United States, reporting a greater number of policies and total insurance than commercial mutual and stock companies combined.149 In contrast to what transpired in both Britain and France, however, the American welfare state did not retain an important role for such voluntary insurance societies in its administration. This was in part a product of the cooperatives’ staunch commitment to voluntarism and rejection of any state role in providing insurance.150 It was also the result of an unfriendly legal climate and a massive influx of poor immigrants, both of which meant that the cooperatives had lost much of their comparative advantage by the time reformers began to push for broad social insurance around 1910.151 The relatively limited influence of cooperative associations, both in principle and as a political movement, may help to explain why mutualism and its version of solidarity played a more muted role in the development of the American welfare state than was the case in Britain and France.

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For example, Isaac Rubinow, one of the most prominent early twentiethcentury advocates of social insurance in the United States, saw compulsory state insurance as fundamentally different from both private insurance, with its profit motive and reliance on individual savings, and mutual societies, which on his account operated on the model of charity rather than right.152 Only a mandatory, publicly administered insurance scheme could “substitute a social guarantee against the results of emergencies and accidents for the purely personal responsibility which is still the rule in many countries.”153 Whereas elsewhere voluntary mutual assurance and social insurance had long been seen as resting on similar philosophical as well as institutional foundations, in the United States the two came to appear much more distinct. The idea of risk pooling on a national scale ultimately seemed more foreign and threatening to Americans’ voluntarist sensibility.154 As a result, of the countries under consideration here, the United States seems least to illustrate the influence of frequentist ideas in the emergence of a national welfare state. Early American welfare did focus on specific risks—injury, old-age poverty, and unemployment—that were understood as social in nature and therefore beyond individual control. But the influence of risk-based classes of workers, whether organized as political movements or in mutual insurance societies, appears to have been more muted in the American context than in Denmark, Great Britain, and even France. One self-defined risk class, however, was particularly well organized and influential in the United States: that of employers.155 In a sense, then, the eventual shape of the American welfare state may be seen to reflect the aleatory collectivism associated with a frequentist account of probabilities, but as shaped to a noteworthy extent by the risks of private enterprise. For instance, American workers’ compensation statutes, enacted in most states between 1911 and 1920, reflected the demands of the private sector, which saw them as less intrusive than minimum standards regulation and welcomed them as reducing the administrative burden of accident litigation and lowering employers’ insurance premiums.156 Even after the New Deal’s expansion of federal provision, welfare policy often reflected the considerations of private employers. For example, as Jacob Hacker points out, the Social Security Act succeeded in part because private organizations had provided only spotty and insufficient pension coverage, and as a result employers had little vested interest in the continuation of the existing system.157 Although many business leaders did oppose the act, they retained an organized influence over its workings, particularly in securing the resemblance of public welfare to private arrangements.158 Moreover, compa-

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nies soon learned to use Social Security to their advantage, combining corporate pension plans with federal benefits to attract and retain better-paid employees.159 The American case is perhaps a reminder, then, that classbased perceptions of risk need not confine themselves to workers, and that their distributive implications are not always or inherently egalitarian.160

The early welfare programs considered in this chapter originated as a response to the plight of workers, in particular the challenges inherent in their reliance on wage labor and the devastation that can arise from its disruption. As the legal scholar A. V. Dicey put it in 1917, explaining the rise of what he termed collectivism in the nineteenth century, “The sale of labour is felt to be unlike the sale of goods. A shopkeeper can keep back his wares until the market rises, whilst a factory hand, if he refuses low wages, runs the risk of pauperism or of starvation.”161 Social insurance, by either compelling workers to save for their own futures or pooling risks and redistributing their costs among designated equals, would ensure that such interruptions in a worker’s earnings would not result in economic ruin. It is not simply a coincidence that insurance, which emerged as a commercial tool to help merchants limit their losses, was appropriated to save industrial capitalism by helping workers limit the downside of their participation in the labor market. Yet the interpretation of risk also underwent a serious modification over the course of the nineteenth century, coming with the help of probability theory to promote an image of interpersonal identity that was empirically based yet flexible, and that could support a collective response to uncertainty. Indeed, the specific risks covered by these early programs were often more uncertain or ambiguous, based on less extensive or reliable statistical data, than the mortality risks that had inspired many earlier proposals for social insurance.162 As a result, these programs often called for a sharing of burdens beyond narrow classes, distributing resources from “winners” to “losers” within relatively expansive and changeable groups.163 This dual character of insurance—its close relation to the logic of contractual exchange and its simultaneous burdensharing potential—rendered it appealing as a framework for social legislation. This same dual character also suggests that efficiency-based and altruistic arguments for social welfare may have a common root, in the pragmatic solidarity of frequentism. The frequentist view is not without difficulties, however, either as a philosophical account of probability or as a justification for insurance. As philosopher Alan Hájek has shown, frequentism is subject to strong objec-

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tions in both its finite form, which defines the probability of an event as the relative frequency with which it occurs in a finite reference class, and its hypothetical one, which focuses on the limiting relative frequency in a counterfactual set of infinitely many trials.164 Four of Hájek’s objections to finite frequentism strike particularly close to the issues we have considered in this chapter. First, frequentism defines all probabilities as relative to a given reference class, none of which is the definitive or canonical one. Second, finite frequentism becomes implausible when that reference class is either too diverse or too small. Third, when people seek to know the odds of a particular event, at least as it applies to them, they are ultimately interested not in their class but in their own particular probability. While statistics about others will provide an insured with evidence of his own probability of dying, for example, they do not provide “the fact that he ultimately cares about,” which “is a fact about himself.” Hájek calls this the “argument from concern.”165 Finally, finite frequentism runs into serious difficulties when an event or attribute has no occurrences, in which case there can be no determinate probability value (a “chance gap”), or when it occurs only once, leading to a misleading probability of 1 (“local determinism”).166 These are significant theoretical weaknesses, although my analysis suggests that within the context of welfare policy some of these features may be practical strengths.167 If one thinks that social policy should be able to adapt to the changing vulnerabilities and demands of different groups, which may themselves change in composition over time, then it makes political (as well as epistemological) sense to embrace the relativity of probabilities and reference classes in designing social insurance schemes.168 In addition, the fact that frequentism recognizes probabilities only with respect to repeated events of a particular kind could be seen as a salutary constraint on the state, which on this view could not legitimately invoke insurance to compel participation in schemes that do not protect against a demonstrated and widely shared risk. At the same time, and for some of the same reasons, the frequentist model of social insurance also entails serious limitations. First, the burdensharing potential of insurance is on this view restricted to those who share an established similarity or who can be persuaded that they do.169 This may not satisfy anyone who maintains that the purpose of insurance is to promote cooperation among people who are different (although, as we have seen, the risk-collectivist account does allow for mutualism beyond narrow actuarial classes, as well as across other social categories).170 Second, and closely related, while frequentism appears to align individual self-interest

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with a common good, it does so within the confines of an agreed-upon class, which need not coincide with the polity as a whole. As a result, as we will see more clearly in the next chapter, risk on this interpretation may not support universal social insurance schemes, particularly in societies with significant social divisions, unless precipitated by some calamitous event that affects the entire citizen body on roughly equal terms. Even then, it may not be capable of sustaining such schemes over any considerable length of time. This observation may help to explain why some twentieth-century theories of justice, most notably that of John Rawls, exclude considerations of probability from the decision procedures that justify their distributive schemes, even as they invoke the mechanism of insurance in a variety of ways.

FIVE

The Egalitarian Welfare State and the Ambiguities of Insurance

In the last chapter, I argued that the frequentist rejection of the Laplacean paradigm, and in particular its contention that probabilities can be assigned exclusively to statistical classes and not to individual events, was associated with a novel defense of insurance. The frequentist account, with its flexible risk collectivism, found practical echoes in the group-based welfare policies enacted in the decades just before and after the turn of the twentieth century. The appeal of such class-based risk pooling was that it could be simultaneously a prudent means of self-protection in a market economy and a kind of circumscribed altruism—a commitment to band with one’s “own” in times both good and bad, similar to the fraternal societies out of which the welfare state grew and which it eventually replaced as workers’ main source of economic security. The years between the two world wars and after 1945 further established the insurance principle as the core of social welfare policy in industrialized democracies. Many of the expansive welfare programs enacted during this era invoked the idea of broad risk pooling to promote social integration, self-respect, and basic security for all. At the same time, these programs inevitably, and often intentionally, departed so much from more traditional insurance principles that in some respects they ceased to resemble insurance at all. As a result, while the rhetoric of risk remained essential to political support for welfare policies, particularly among the increasingly influential middle classes, the normative aims of welfare extended well beyond what empirical risk pooling could achieve. A number of midcentury social theorists consequently concluded that welfare programs ought to abandon or transcend the rubric of insurance altogether. At approximately the same time but for different reasons, developments

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in probability theory and economics also cast doubt on the earlier vision of social insurance as an expression of solidarity among equals in the face of risk. While the frequentist account of probability had supported riskpooling efforts by particular groups, the subjective theory of risk that rose to prominence in the twentieth century offered no clear justification for such collective action. On the contrary, by understanding mathematical likelihoods as, above all, a tool of individual instrumental reason, the subjective account downplayed concerns about equity and tended to define all reasoning as a form of wager.1 I do not suggest that this shift caused the growing concerns about the insurance model in midcentury welfare practice or theory. I do maintain, however, that both trends found expression in the most influential work of twentieth-century political thought, John Rawls’s A Theory of Justice. Rawls’s account of distributive justice can be read in the context of this political and intellectual history as an effort to rescue the normative logic of social insurance, or part of it, from the constraints of probabilistic reasoning. Given the inability of existing accounts of risk to promote or justify the solidaristic welfare state, Rawls devised an account of distributive justice that did away with risk altogether. Like the previous chapters, then, this one identifies a link between evolving conceptions of probability and political responses to uncertainty. In this instance, the move away from an objective or empirical understanding of risk and toward a subjective, ultimately personalized one undermined rather than supported the case for mutual insurance as a beneficial political tool. As prominent strands of economic thought increasingly neglected the mutualistic side of risk, social and political thought looked for ways to advance solidarity without it. What the latter development failed to understand, I propose, is the difficulty of extricating the distinctive logic of probability from political life, as well as the distinctive benefits of social insurance as a distributive regime. Rather than doing away with probabilities, then, I suggest that political theorists should carefully consider the understanding of risk on which our political practices rest. Given that social insurance is likely to remain a mainstay of liberal democratic politics for some time—for reasons that, I have argued, stem from the character of modern liberalism itself—it is important to understand both its malleability and its limits, both the variety of ways in which it has set out to harmonize competing claims and its inability to conclusively do so.

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The Egalitarian Welfare State Emerges The Centrality of Insurance to Postwar Egalitarian Welfare Many histories of the welfare state attribute the emergence of modern social policy to the years immediately following World War II, when, according to the standard narrative, recent memory of the war’s indiscriminate devastation paved the way for sweeping protective legislation.2 Indeed, many of the programs that define the era of universal centralized welfare, or what we might call the egalitarian welfare state, date from 1945 or thereafter. In Great Britain, several major social policy statutes were enacted based on ideas laid out by William Beveridge in his 1942 Social Insurance and Allied Services, popularly known as the Beveridge Report.3 Beveridge and the Labour government that instituted his proposals established the principle of universal contributory coverage, which provided flat-rate benefits to all as a matter of right. This system served as the heart of the British welfare state and as an aspiration for social legislation worldwide. Universal flatrate pensions were passed with broad political support in Sweden in 1946 and in Denmark in 1956.4 The postwar period also saw a variety of efforts to enact similar programs in France and Germany, though these came to fruition only in the 1960s and 1970s, around the time that several new national welfare programs were created in the United States.5 The widespread adoption of universal social insurance programs marked a change in the aims of social policy from helping groups of riskprone workers to providing a basic level of security for all. Both the insurance programs instantiated at this time—which were designed primarily to provide income support—and the social services introduced to supplement them were organized along these lines, offered to everyone at uniform standards regardless of status or earnings.6 As a result, contemporary and recent commentators have stressed a shift during this period from what one early study called the “canon  .  .  . of collective risk, that is the standardization of contributions and benefits” within statistical classes, to the “canon of a subsistence minimum guaranteed through social security,” with the help of state subsidies.7 While this was undoubtedly a noteworthy change, the continuities in social welfare between the pre- and postwar periods were equally significant.8 As we saw in previous chapters, the idea of insurance constituted the core of modern welfare policy since at least Bismarck, and it only grew in prominence as the twentieth century progressed. As a result, more recent efforts to distinguish various eras of welfare provision tend to obscure the

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ongoing prominence of insurance rhetoric across time periods and programs.9 As social security expert Eveline Burns pointed out in her 1949 study of the American welfare system, it had long been common to refer to government programs as “insurance” even when their workings deviated from actuarial and even contributory principles.10 While the institution underwent a substantial evolution over time, covering “not only new risks but . . . new population groups” and eventually guaranteeing a universal basic minimum, it remained through all of these iterations widely understood as “social insurance,” a means to protect the vulnerable by pooling their resources and compensating the blameless sufferers among them.11 If we must divide the history of welfare provision into the periods before and after 1945, then, we should be clear about what distinguishes them. It is not the underlying insurance-based principle that distribution should shield against or compensate for undeserved hardship, a principle common to both eras, but the scope of the recipient group and the accounts of equality and solidarity entailed therein. The Bismarckian (originally Napoleonic) idea of tying workers to the state had already been supplanted around the turn of the century by a more flexible risk collectivism aimed at reciprocity and mutual aid within specific groups of citizens. Postwar social insurance carried the latter idea further, proposing a vision of universal equality based on common exposure to hazards that threaten all citizens’ economic well-being. Why, then, did the insurance principle continue to hold such a grasp on the imaginations of social reformers and politicians even as the aims of welfare provision expanded beyond particular risk-prone groups? Without intending a full explanation, I will suggest a few important factors. For one, path dependence likely played a significant role, in that early social policy decisions heavily influenced what was subsequently considered desirable and politically possible. In most of the countries under consideration here, the first public responses to the plight of industrial laborers relied heavily on insurance mechanisms and their providers, including commercial insurers (as in some workers’ compensation schemes), mutual societies (where they helped administer public programs), and the state. These policies not only helped to legitimize insurance in principle but also created institutional, economic, and legal realities that then proved difficult to reverse.12 While the nature of such path dependence differed from country to country and did not always lead to public rather than private schemes, such initial decisions helped create the conditions for the continued preeminence of insurance as the favored mechanism of welfare provision.13 Another important factor was the advancement of mathematical statis-

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tics, which developed new tools to interpret large-scale phenomena and acquired new prominence between the world wars. Probability theory assumed a more central role in both the natural sciences and economic theory during the 1920s.14 Around the same time, the new technique of random sampling, which allowed policymakers to draw conclusions about an entire nation via surveys of representative groups, gave statisticians considerable importance and authority in increasingly centralized states.15 The discipline appears to have solidified its grasp on policymaking during the 1930s, thanks largely to the economic turmoil of that decade and the perceived need for more centralized planning or technical competence within the state.16 As a matter of sheer political visibility and clout, then, statistical thinking made inroads between the wars that in turn enabled its central role in the policy revolution that followed. Finally, and perhaps above all, it was the conceptual and practical plasticity of social insurance that allowed it to remain at the center of welfare policy both before and after 1945. I have been arguing that each major account of social insurance tried to reconcile in practice a pair of distinct principles: commercial prudence and equity, individual liberty and social order, personal responsibility and collective burden sharing. In its postwar variety, insurance had the appeal of being egalitarian without being too drastically redistributive, and of acknowledging the salience of basic needs without relinquishing individual responsibility or desert. The view that everyone is vulnerable to a given risk meant that welfare could cast off any stigma associated with means testing, a central concern of those who advocated for universal benefits.17 At the same time, the fact that the individual paid contributions out of wages (or taxes) meant that she had in some sense merited coverage.18 This harmonizing character, as we will now see, proved to be at once a political necessity and a theoretical liability. The Amorphous Appeal of Insurance The notion that social insurance could bridge the competing distributive principles of merit and need, individual responsibility and universal security, found expression in the work of its pre- and postwar advocates, not least of all Beveridge. The architect of Britain’s egalitarian welfare state presented insurance as a kind of third way, the key to “maintaining individual freedom and responsibilities” while “giving security against all the main risks of economic life.” If Communism meant guaranteeing an income “at all times to everybody irrespective of his work and services,” and laissezfaire capitalism abandoned workers to the vagaries of the market, social

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insurance promised to protect the hardworking and responsible from disruptions due to “causes beyond their control.”19 In practice, Beveridgean welfare programs did this by accommodating a range of financing and benefit options, including general tax financing or differential contributions combined with flat-rate payments, while still affirming the idea that the individual received what he had paid for.20 Beveridge acknowledged that while such insurance “preserves the contributory principle,” it otherwise differs from voluntary insurance because the state, with its powers of compulsion and taxation, “is not under the necessity of varying the premium according to the risk” or accumulating reserves to fund future liabilities.21 Nevertheless, Beveridge’s writings repeatedly endorsed the insurance principle as enabling a system in which benefits are “earned” through contributions, means tests are avoided, and the state as benevolent planner orchestrates a comprehensive response to a variety of social risks. Not everyone was enthralled with the insurance idea, however. Several decades earlier, Beveridge’s close associates Beatrice and Sidney Webb had explained the power of insurance in similar but far less enthusiastic terms. “We are, at this moment,” they wrote in their 1911 The Prevention of Destitution, “face to face with an obsession of the public mind in favour of insurance. This obsession is not likely to be removed by any demonstration that it depends on a confusion between voluntary and compulsory insurance, which have entirely different attributes, and lead to entirely different results.” Nor would ordinary citizens likely be persuaded that the latter “involves an extravagant expenditure of public funds on persons who would in any event have maintained themselves at the prescribed standard of civilised life.”22 Despite the Webbs’ lack of patience for the prejudices of the British public, however, they understood the political appeal of the insurance principle and were ready to use it as a means to more comprehensive ends. The “more universal and more compulsory” the insurance scheme, “the more quickly and the more certainly” it will give rise to a “Policy of Prevention” because it will increase the public incentive to prevent selfindulgence and other irresponsible behaviors on the part of the insured.23 Until then, social insurance policies relying on the public’s irrational enthusiasm provided what seemed to be a path toward greater social cohesion using familiar terminology and relatively flexible means. The Webbs’ preventative approach never carried the day, and Beveridge’s writings often emphasized the moderate character of insurance rather than laying out a vision that would eventually supersede it.24 Nevertheless, the question of whether social insurance was an end or a means to more com-

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prehensive goals remained a central one among reformers and social theorists in the decades after 1945. The preeminent welfare theorist of this period, Richard Titmuss, in describing his own support for universal insurance programs after the war, explained that he had understood these measures as “connected with the demand for one society,” characterized by universal self-respect and social integration, rather than with the redistribution of wealth for its own sake.25 Titmuss well understood the role of class politics in achieving this goal, admitting that “from some perspectives these major changes in policy could be regarded as ideological pleas to the middle- and upper-income classes to share in the benefits (as well as the costs) of public welfare.”26 The National Health Service, for example, had succeeded in providing “non-discriminatory, non-judgmental” care in large part because the middle classes joined in 1948 and remained thereafter in the system instead of contracting out.27 What Titmuss had less successfully appreciated, by his later admission, was that social insurance qua insurance could neither fully escape such class politics nor, as a result, achieve the broad solidaristic aims he had associated with it. Instead, insurance as tracking both earned reward and basic need persisted precisely because it avoided the full application of either principle. This feature was particularly important in winning over the most important constituency for social insurance programs: the middle classes. As historian Peter Baldwin has explained, To the extent that social policy was to be more extensive, inclusive, or generous . . . it no longer reapportioned resources de haut en bas, but increasingly within one large middle group. Growing more powerful, the interests of this new constituency began to determine the flow of redistribution. . . . In nations where statutory intervention was accepted as normal and desirable . . . it did not take long for the European welfare state to formulate, as among its main tasks, the concern of the middle class for itself.28

In other words, universal welfare policies succeeded not necessarily by overriding class-based risk pooling but by appealing to it, and in particular by tapping into the desire of the middle classes to secure themselves without sacrificing too much to the poor. Even the abolition of means tests— which, it was thought, would follow from granting everyone a contractual right to subsistence-level benefits—was believed to encourage savings and self-help, contributing to the broad appeal of universal coverage.29 In this respect, there indeed existed a serious tension between the aims of social solidarity, which sought to move beyond the more limited equality of re-

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stricted risk pools, and the distributive politics underlying the postwar welfare state. As a result, social insurance soon came under attack from both ends of the political spectrum, as commentators alleged that the rubric of risk tended to conceal or limit the true aims of social policy. The Limits of Universal Social Insurance I have been arguing that if there was a change in welfare policies between the pre- and postwar period, it was in the scope of their application rather than the policy paradigm at work. Yet I have also just suggested that the goal of classless solidarity pointed beyond what the insurance idea was authorized or able to do, even in its most expansive form. The result was a system that depended on a kind of actuarialism in practice—specifically, on the self-aware solidarity of the middle classes—while abjuring it in principle. Indeed, the political success of Beveridge’s proposals hinged partly on their ability to conceal the extent to which they deviated from actuarial fairness, preserving the aura of traditional insurance while obscuring the element of vertical redistribution (transfers from the wealthy to the poor). By the same token, as Baldwin explains, postwar attempts that made their redistributive intentions more explicit failed due to resistance from the property-owning middle classes.30 Universal social insurance, in short, was palatable insofar as it appealed to class-based self-interest and hid the ways in which it betrayed that appeal.31 The claim that social insurance is inherently deceptive or unduly restrictive consequently became part of a prominent critique of the practice in the second half of the twentieth century.32 Libertarians argued that it entails forced income redistribution under the guise of a contract, while socialists took issue with the gap between its solidaristic rhetoric and its ability to lift the poor. Although the flexible or prudential character of risk pooling had originally been one of the political selling points of social insurance, it came during the 1950s and 1960s to appear to some as a liability, concealing or limiting the moral aims undergirding welfare policy. A pioneer of this view was Eveline Burns. Born in London in 1900, Burns received her PhD from the London School of Economics and in 1928 joined the faculty at Columbia University in New York. While teaching there, she was selected to serve on President Franklin Roosevelt’s Committee on Economic Security, where she helped to design the Social Security Act of 1935; she later wrote several important works on the operation of that program and the evolution of social policy more broadly.33 In an article published in 1953, Burns argued that the confusion between social

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and private insurance was creating serious problems in political discourse and public policy. The inclusion within social insurance schemes of nonrisks such as the existence of children, the increasing detachment of benefits from contributions, and the reliance on tax and employer financing had made actuarialism a distant reality. As a result, “in most countries with extensive and highly-developed social security systems, social insurance has become an institution to which the word ‘insurance’ can be applied only at the risk of a serious distortion of the language.”34 The problem, according to Burns, was more than linguistic: Because the process of crafting social policy is an inherently political one, involving conflicting interests and objectives, private insurance concepts “not only provide no solution, but may have the dangerous consequence of partially concealing the fact that these issues and conflicts exist.”35 A few years later, classical liberal economist Friedrich Hayek cited Burns’s work in making a similar point about the obfuscating character of the insurance model. While in principle private group insurance cannot deliberately transfer income from one group to another, he argued, social security systems had come to make such transfers their explicit goal. “No system of monopolistic compulsory insurance has resisted this transformation into something quite different, an instrument for the compulsory redistribution of income.” Indeed, Hayek continued, “it was mainly through decisions that seemed to most people to concern minor technical issues, where the essential distinctions were often deliberately obscured by an assiduous and skillful propaganda, that the transformation was effected.”36 One consequence of this development, in his view, was an increasing gulf between the actual workings of welfare schemes and their public perceptions, a “serious problem” for democracy given that “the immense social security apparatus has been a chief factor in the transformation of our economy” but is “also the least understood.”37 Although Hayek did not oppose all forms of government protection against common risks, he insisted that such protection be conceived as a universal minimum, granted impartially to all on the basis of demonstrated need, not as an effort to distribute resources to those whom the state deems in some way deserving.38 Social insurance presents a danger, on this view, because monopolistic public provision can easily overstep its legitimate aims, all the while evading public scrutiny. Thus, thanks to the “stroke of promotional genius” of calling tax- and debt-financed redistribution “insurance,” democratic citizens had unsuspectingly granted central governments the power to divide “income according to some preconceived notion of justice,” to the detriment of the rule of law and individual liberty.39

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Even Titmuss, who had initially supported universalism to remove the stigma of poor relief, came by 1965 to lament the use of insurance principles in social welfare. Like Hayek, Titmuss allowed that in principle the goal of equity in private group insurance entails a deliberate rejection of redistribution: Participants in such schemes see themselves as having entered into an individual contract, in which their contributions earn no more and no less than their own actuarially determined benefits. In practice, however, Titmuss conceded that all group insurance, both private and social, is redistributive to the extent that its underlying risk ratings are imprecise, a reality that had become increasingly evident over time. The problem, then, is not the occurrence of redistribution, as Hayek claimed, but the fact that without proper awareness and planning such redistribution may end up being regressive rather than serving the poor. Titmuss concluded that the concept of insurance in social welfare should be abandoned in favor of universal contributions, flat-rate benefits, general tax financing, and selective benefits to the needy as a matter of right.40 Both the partisans and the opponents of the egalitarian welfare state, then, have long understood that the rubric of risk and insurance may conceal as much as it illuminates about the workings of these programs and the normative aims behind them. As Burns once again perceptively put it, “the institution of social insurance is a social invention which was brought into being to perform a specific function in a specific economic and social environment.”41 Its resemblance to private insurance allowed for a shift away from individual economic responsibility in certain cases, serving as a bridge between a more traditional liberal ethos and a newer social one. Yet while the private analogy “enabled social insurance to perform this task, its very success carried within it the seeds of its own destruction, or at least very fundamental modification.”42 What these observers may have failed to understand, however, is the difficulty of extricating the insurance idea from the politics of the welfare state. The Webbs and Beveridge were right that the public’s receptivity to insurance as a mean of sorts between distributive extremes would allow governments to achieve more expansive aims by blurring the lines of actuarial fairness. Yet the shared perception of vulnerability and risk remained a critical source of public support for welfare policies, and this foundation became more important as democracy spread over the course of the twentieth century.43 The politics of welfare thus remained closely tied to the logic of risk pooling, even as the normative theory tried to move beyond it. I now wish to switch gears somewhat, to consider contemporaneous developments in mathematical probability and economic thought. We will

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see that at around the same time that proponents of universal welfare sought to transcend the limits of empirical risk pooling in the name of classless egalitarianism, a newly subjective understanding of probability undermined the case for risk pooling from the other direction. Adherents to the subjective view of probability focused on economic rationality and saw risk taking as an omnipresent but wholly private affair. Their accounts therefore abandoned the political understanding of insurance—and in particular its Janus-faced distributive appeal—just as welfare egalitarians did the same.

Subjective Probability and the Personalization of Chance Keynes’s Transitional Account Probability, as we have seen, has always been subject to two interpretations, epistemic and aleatory, which, beginning in the nineteenth century, also became known as the subjective and objective views. The difference between them became the focus of sustained philosophical consideration in conjunction with the emergence of frequentism. In its most rigorous form, frequentism insisted that mathematical probabilities are empirically determined and do not reflect the individual’s state of mind or personal estimations. The alternative view, that probability is a measurement of partial belief, had been central to the understanding of the term prior to the emergence of the probability calculus in the seventeenth century. It continued to play a role in mathematical theory through Laplace and his successors, as long as theorists assumed that epistemic likelihoods (namely, equiprobability assignments under the principle of indifference) were the necessary starting points for determining aleatory ones. After the split that occurred thanks to frequentism, however, the subjectivist view, while famously articulated by Augustus De Morgan in the mid-nineteenth century, was relatively neglected until the early decades of the twentieth. One of the first thinkers to take explicit aim at frequentism and to propose an alternative interpretation of probability was John Maynard Keynes. Along with Beveridge, Keynes is widely considered a founding father of the modern welfare state.44 He is also, if less famously, a notable figure in the history of probability theory. Probability was the subject of his Cambridge fellowship dissertation and of his first major book, A Treatise on Probability, published in 1921. Although his influence with respect to practical applications of probability was ultimately limited, Keynes’s contribution reflects a broader philosophical shift that took place around this time between

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the empiricist view that had been dominant in England since the latter part of the nineteenth century and the epistemic one that would come to prominence, particularly in some areas of economic thought, over the course of the twentieth. In addition, the links between his account of probability and his economic theory lend support to the larger claim of this work that the way in which uncertainty is conceptualized and calculated has ramifications for the design of public policy, and in particular the welfare state. Keynes’s work on probability is not subjectivist in the sense that would later prevail and which we will consider in greater detail in the next two subsections. Yet he did understand probability as pertaining first and foremost to the conditions of individual judgment or rational belief. It is “‘subjective chance,’ concerned with knowledge and ignorance,” that is “fundamental,” he explained, and “so-called ‘objective chance,’ however important it may turn out to be from the practical or scientific point of view, is really a special kind of ‘subjective chance’ and a derivative type of the latter.”45 Pursuant to this understanding, Keynes took aim at frequentism and proposed an alternative account of probability as a logical relation between propositions. His account is logical, he explained, “because it is concerned with the degree of belief which it is rational to entertain in given conditions, and not merely with the actual beliefs of particular individuals, which may or may not be rational.”46 It differs from many subsequent subjective theories in maintaining that only certain classes of likelihoods are quantifiable, but shares with them a focus on systematizing the process of inference by which all probability values are obtained. The contrast between Keynes and Edgeworth, who traveled in the same circles and shared many interests, is particularly illuminating of the changing philosophical tide that interests us here. As we saw, Edgeworth had turned to statistics in the years after publishing Mathematical Psychics with the aim of furthering his project of a scientific utilitarianism. As Stephen Stigler points out, Edgeworth’s statistical essays contain several notable innovations, and some of his articles would serve as “basic references for the theory and application of statistical techniques to social and economic data” until the end of the nineteenth century.47 Yet Keynes would later charge that Edgeworth’s mature focus on the applications of statistics came at the expense of his earlier concern with the philosophical foundations of the discipline. In his obituary for his senior colleague, Keynes recounted that when he pressed Edgeworth to “give an opinion as to how far the modern theory of statistics and correlation can stand if the frequency theory falls as a logical doctrine,” the latter

150 / Chapter Five would always reply to the effect that the collapse of the frequency theory would affect the universality of application of statistical theory, but that large masses of statistical data did, nevertheless, in his opinion, satisfy the conditions required for the validity of statistical theory, whatever these might be. I expect that this is true. It is a reasonable attitude for one who is mainly interested in statistics to take up. But it implied in Edgeworth an unwillingness to revise or take up again the more speculative studies of his youth.48

Keynes in fact had questioned Edgeworth’s views on a number of fundamental questions in probability theory. For example, whereas Edgeworth had generally accepted the “rule that probability implies reference to a series,” Keynes charged that the frequentist is fatally unable to justify his choice of any particular reference class.49 Whereas Edgeworth maintained that it was possible to defend the credibility of the statistician’s initial assumptions, including the a priori uniformity of unknown distributions, Keynes argued that such justifications are either empirically unfounded, failing on the frequentist’s own criteria, or circular.50 And whereas Edgeworth continued to believe that probabilistic expectation could guide individual conduct, Keynes expressed grave concern about its relevance, arguing that it fails, among other things, to capture the actual psychology of risk taking and the relevant particulars of individual cases.51 Keynes was forceful on many of these points, particularly the applicability of standard accounts of mathematical expectation to personal choice, as even Edgeworth seemed at one point to admit.52 Nevertheless, by casting doubt on the foundations of statistics without offering new techniques of his own, Keynes consigned himself to relative obscurity within the discipline.53 This fact alone offers a window onto the practical bent of mathematical probability, which Keynes seemed eager to avoid.54 He ventured into the traditional moral territory of the field only fleetingly, when he suggested—partly in a footnote—that gambling is objectionable because it entails an individual loss in the long run and is likely to increase inequality in the short run. He immediately retreated from expanding on these claims, however, since it “would lead too far from what is relevant to the study of probability.”55 Nor did Keynes have any particular regard for insurance as a successful application of probability theory. He mildly chastised the industry for encouraging the misguided “presumption in favor of the numerical valuation” of all likelihoods, a proposition he took pains to debunk.56 On the political front, according to Karel Williams and John Williams, Keynes regarded Beveridgean social insurance as “an empty fiction” that merely “concealed a

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convenient form of taxation.”57 In a 1938 review of J. E. Meade’s Consumers’ Credits and Unemployment, Keynes considered Meade’s proposal of a “subsidy to wide classes of consumers whenever the indices of unemployment exceed a certain figure, and a tax on employment whenever they fall below a certain figure.”58 As Keynes explained it, such a scheme would calibrate contributions “in accordance with the state of unemployment,” such that they would rise as employment increased and decrease whenever it fell. As such, the plan could readily be made “part and parcel of the various contributory insurance schemes” already in existence, and perhaps expanded to cover additional risks. “Indeed the policy is obviously an extension and working out of the idea of budgeting for a deficit in depressions and a surplus in recoveries.”59 In his assessment, Keynes acknowledged that “there is a good idea behind this” scheme, already exemplified in key respects by “the existing system of benefit to the unemployed.”60 Yet he proceeded to take Meade to task for not comparing the effects of his proposed policy to the one Keynes had advocated in The General Theory of Employment, Interest and Money. Such a comparison, he argued, reveals that the “real burden of a policy of subsidising consumers is very greatly in excess of that of an investment policy.”61 While the effect of the two approaches on individual incomes may be the same, investment would increase employment directly, while subsidies would do so only secondarily, as a consequence of increased investment. As a result, the overall economic effect of the former would be much greater. “The only qualification to this” prediction, Keynes averred, “would arise if some of the recipients of investment expenditure were more likely . . . to save their increased income” than the recipients of subsidies.62 It is certainly tempting—and not only in light of this statement—to link Keynes’s stance on social insurance to his broader suspicion of saving, and perhaps the so-called bourgeois virtues more generally. Keynes regarded saving as a reflection not of individual responsibility but of interest rates and employment levels.63 As such, the moralistic and reformative account of the welfare state articulated by Beveridge and others likely held little appeal for Keynes. Similarly, although he was concerned about budgetary deficits, his review of Meade underscores his willingness to deviate from a policy of strict fiscal responsibility understood as living entirely within one’s current means. The key to workers’ welfare, on Keynes’s account, is not for government to teach financial independence or foresight, whether through social or macroeconomic policy, but to manage investment in a way that will maintain full employment. Moreover, if the traditional account of bourgeois virtue posited a certain correspondence between effort

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and reward, with benefits reliably and justly accruing to those who help themselves, Keynes saw a much larger role for luck in economic success and failure. As he put it in the Treatise, discussing the social effects of gambling, “the philosopher must draw what comfort he can from the conclusion with which his theory furnishes him, that millionaires are often fortunate fools who have thriven on unfortunate ones.”64 This last point in turn brings us to a central issue linking Keynes’s probabilistic and economic work—namely, the salience of uncertainty.65 Not all probabilities are susceptible to quantification on Keynes’s view, and even those that can be expressed in numerical terms may differ from individual to individual, given the estimator’s prior knowledge and the degree of belief she places therein. In addition, Keynes’s emphasis on the question of weight, or how much confidence one has in a probability judgment, allows for the possibility that different individuals will be guided to different degrees by their estimates depending on the completeness of the evidence available to them.66 Thus, while Keynes maintained in the Treatise that probability relations are “objective,” meaning that the logical rules by which one reasons to probabilistic conclusions are universally valid and compelling, he left quite a bit of room for individual particularities in the process of estimating and acting under uncertainty. As he put it in his critique of mathematical expectation, “I, at any rate, have not the same lively hope as Condorcet, or even as Edgeworth, ‘éclairer les Sciences morales et politiques par le flambeau de l’Algèbre’”—to enlighten the moral and political sciences with the torch of algebra.67 Keynes’s treatment of uncertainty at the epistemic level in turn sheds light on his understanding of financial markets and, perhaps, his view of social insurance. Paul Davidson argues that in contrast to many other economists and policymakers, Keynes suggested that some important economic phenomena are not subject to statistical analysis as “ergodic” processes—that is, we cannot presume that by collecting enough data about the past we will be able to make reliable predictions about the future.68 In addition, Keynes’s analysis of investor behavior in asset markets showed that individuals’ awareness of future uncertainty leads to some counterproductive tendencies, including the avoidance of action and a demand for liquidity, or more generally to keep one’s options open.69 Insofar, then, as social insurance is based on statistical probabilities for economic phenomena to which they do not pertain, or on citizens’ (often erroneous) judgments about such probabilities, it would appear on Keynes’s view to be suspect. Keynes’s stance on probabilities, although distinct from the subjective

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understanding that became prominent in statistics and decision theory in the second half of the century, reflected a deliberate turn away from the frequentist view that, I argued in the last chapter, had lent support to earlier social insurance policies. As we will now see, this trend extended beyond Keynes and had significant consequences for thinking about social welfare in the second half of the twentieth century.70 The Rise of the Subjectivist View The modern theory of subjective probability was inaugurated in earnest in 1926, with Frank Plumpton Ramsey’s essay “Truth and Probability.” There Ramsey argued that “the laws of probability are laws of consistency, an extension to partial beliefs of formal logic, the logic of consistency.”71 He was certainly not the first to try to formulate a coherent account of inductive inference with reference to the probability calculus, and he wrote this article in the wake of important contributions to the same effort by Peirce as well as Keynes. Yet while Peirce argued that the probability of an argument’s truth is a long-run empirical frequency, and while Keynes understood probabilities as logical relations, Ramsey’s account was personalistic, resting on initial degrees of belief that are set independently of any external standard. “To ask what initial degrees of belief are justified,” he wrote, “seems to me a meaningless question; and even if it had a meaning I do not see how it could be answered.”72 Instead, the subjective theory would focus on the nature of rational inference from initial beliefs or “priors” that are taken as givens.73 Ramsey based this account of rational inference on a series of hypothetical bets. To have “any definite degree of belief implies a . . . willingness to bet on a given proposition at the same odds for any stake,” as well as “a consistency between the odds acceptable on different propositions as shall prevent a book being made against you.”74 (The reference is to a so-called Dutch Book, or a set of bets that guarantees a net loss to one side.) Beliefs are thus consistent if one has a clear set of preferences that do not change depending on the order in which they are presented, or in other words if they follow the axioms of probability. If this is not the case, Ramsey showed, then the individual “could have a book made against him by a cunning better and would then stand to lose in any event.”75 This reliance on betting as the standard for rational belief “will not seem unreasonable when it is seen that all our lives we are in a sense betting. . . . The options God gives us are always conditional on our guessing whether a certain proposition is true.”76

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In contrast to both the frequentist and Keynesian accounts, then, the subjective interpretation of probability tends to hold that all likelihoods are quantifiable: Their numerical value is simply a measure of the individual’s personal belief in an event or statement given the evidence available to her at the time.77 Subjective theories also differed from earlier accounts in maintaining internal coherence as their only or main demand on an individual’s beliefs or choices, meaning that to act rationally in situations of uncertainty, it is sufficient to avoid having a distribution of degrees of belief that will entail a certain or very likely loss of utility.78 With Bruno de Finetti’s introduction in the 1930s of the concept of exchangeability, which characterizes events the estimated probability of which does not depend on the order of their appearance, it became possible to connect these subjective probability values with the procedures of Bayesian statistical inference, in which one starts with an initial probability distribution and modifies it in light of experience. De Finetti concluded that for a series of exchangeable events, a reasonable individual will arrive after sufficient observation at a probability value close to the event’s observed frequency regardless of the opinions she held at the outset. Because of its compatibility with Bayes’s theorem, the subjective interpretation of probability quickly gave rise to an entire field of analysis known as Bayesian decision theory, which applied inverse statistical methods to generate an account of rational decision making based on an individual’s subjective priors.79 The Bayesian decision maker learns from empirical observation, incorporating an objective element into the theory. Yet the foundations of her beliefs—that is, the initial probabilities from which learning begins—are entirely personal. Over the second half of the twentieth century, many mathematicians and economists embraced Bayesian decision theory as a guide to rational choice under uncertainty. Many in this tradition also came to embrace the salience of insurance in public policy. As American economist Kenneth Arrow put it in a seminal article on the economics of healthcare, “a good part of the preference for redistribution expressed in government taxation and expenditure policies and private charity can be reinterpreted as desire for insurance.”80 In noting that government support tends to go “to those who are disadvantaged in life by events the incidence of which is popularly regarded as unpredictable,” Arrow was echoing the probabilistic argument for social insurance as we have been tracing it since the late eighteenth century.81 Yet because of the subjective foundations of their approach, the “risk” entailed in such arguments for welfare was not the same “risk”

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that had inspired the earliest welfare programs or, by imperfect extension, the postwar welfare state. Let us now consider in more detail how these accounts differed. The Moral Character of Subjective Probability Like all accounts of probability, the subjective view lends itself to a normative interpretation. As applied to decisions, it posits coherence as a necessary condition of rationality, and rationality as the ability to achieve one’s desired ends or maximize personal utility.82 Unlike the classical and frequentist views, however, this particular normative approach downplayed the earlier concern of probability theory with equity and focused instead on “rational betting,” or the “avoidance of certainty of losing to a clever opponent.”83 Thus where earlier accounts took pains to distinguish the counsels of mathematically enlightened reason from gambling, the subjective view embraced the wager-like character of all decisions. This shift was in part a consequence of the behaviorist assumptions of subjective probability theory. To infer an individual’s personal probabilities and utilities, one must start with a preference ranking of acts, all of which involve uncertainty in the same way and which may therefore be considered as fundamentally alike. Although accounts of subjective probability were not the only theories of rational choice to infer psychological states or preferences from wagers, they were the first to do so and thus helped pave the way for the normalization of betting as a reflection of acceptable and even reasonable predilections.84 This shift in the normative character of probability theory had, I submit, two consequences that relate to the theory of social insurance. First, it allowed for an unlimited proliferation of risks, understood as any quantified likelihood or prediction, and with it of the conceivable range of insurance-like products to manage them. As Arrow put it, “the variety of possible risks in the world is really staggering. The relevant commodities include, in effect, bets on all possible occurrences in the world which impinge upon utilities.”85 Second, while the applicability of insurance as a commodity spread, mutual insurance as an ethical practice lost its unique significance and appeal. As we have seen, philosophers of probability had long assigned a pride of place to insurance as one of the most important applications of the calculus, opposed to gambling in its personally and collectively beneficial effects. On the subjective theory, however, probabilities lost much of their interpersonal authority and fairness became a secondary

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concern, subordinate to the demands of personal utility maximization on the basis of risk preferences taken as givens.86 Advocates of the subjective Bayesian approach clearly understood the need for a theory of “multisubjective” decisions, as de Finetti termed them, that would allow for the drawing of valid social conclusions irrespective of the parties’ different premises.87 As Arrow put it in a 1958 review article, the results of statistics “are supposed to be interpersonally valid. It follows that even if one accepts the subjective or personal probability viewpoint as a guide to an individual’s action, there is need for some method of combining the utility functions and subjective probabilities of different individuals.”88 Yet, as Arrow acknowledged, decision theorists could not agree on the best criterion for social choice under uncertainty because each available alternative involved serious flaws.89 It also proved difficult on the subjective Bayesian view to model interpersonal agreement about probabilities themselves. This problem received influential treatment in a 1976 paper by mathematician and economist Robert Aumann. In it, Aumann showed that when two people hold the same prior probability distributions and communicate their posterior probabilities to one another such that those posteriors are common knowledge (that is, each party knows that the other one knows, and both know that the other knows this, and so on), each will revise his new posterior until the two are equal.90 As a result, Aumann concluded, parties who begin with the same probability estimates and who follow the rules of Bayesian rationality “cannot agree to disagree.”91 Ongoing debates within decision theory indicate that the difficulty is far from resolved, however. For one, Aumann’s result rests on the assumption that individuals share a common prior, an idea that has been subject to serious challenge.92 Aumann explained the rationale for this assumption as follows: While “people with different information may legitimately entertain different probabilities,” there is “no rational basis for people who have always been fed precisely the same information to do so.” Although in general individuals do have different information, Aumann admitted, if we imagine that they forget what they already know, they will then be in a situation in which their information is the same. In this case, we can “conclude that then they all do have the same probability.”93 We may well ask, however, why two people in an identical state of ignorance would assign the same probabilities to an unknown event or hypothesis—a question, we recall, that has haunted probabilists at least since Laplace. As Stephen Morris puts it, there is “no reason why we would expect the endogenous

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probabilities [of individual decision makers] to be equal unless there exist exogenous probabilities,” or probabilities that are logically prior to the decision problem, “to which we expect them to be equal or at least approximately equal.”94 To do this, however, would be to recognize the need for some nonsubjective view that accounts for those exogenous probabilities.95 In practice, where the common prior assumption fails, it is not clear that individuals will converge in their posterior probabilities. Morris lists a number of circumstances in which heterogeneous prior beliefs may persist: when learning is costly, for example, or when there is insufficient experience to contradict existing beliefs (as is often the case with respect to public policies).96 Then there is the problem of unreasonable priors, which the radical subjectivist cannot rule out. As James Franklin notes, the Bayesian argument that differences in priors tend to “wash out” with experience, making their arbitrariness unimportant, works only for “reasonable” priors. “If one takes a ‘crazy’ prior, which assigns some real possibility a zero or near-zero prior probability, then no amount of experience will be able to dig one out of that commitment. The difference between a reasonable and a crazy prior will not wash out.”97 One might contend that rational individuals should agree about the probability of events for which empirical frequencies are available, and therefore for most events that are relevant for insurance, even when they do not begin with common priors. This argument certainly has intuitive appeal and receives support from de Finetti’s theorem, provided that the events in question are exchangeable. The assumption of exchangeability must be invoked with caution, however, since it rules out the possibility that the order of events is relevant to future predictions of those events. Where the order is relevant, the pattern as a whole must be generalized in such a way that its iterations are exchangeable. Yet this seems to make the agreement we are searching for more elusive since, in that case, to arrive at the same frequencies, individuals must first agree on the specific ways in which the future is likely to resemble the past.98 Finally, even if we grant the common prior assumption, doubt remains regarding whether agreement about posterior probabilities necessarily results from Bayesian updating.99 With so many opportunities for probability estimates to diverge, subjectivist decision makers may well disagree about their risks even when there is good reason not to. Unlike the frequentist view, according to which the collective experience of others must factor into the decision maker’s estimation at the outset, on the subjective Bayesian view such experience may provide data for updating but will not necessarily determine one’s final

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judgment.100 The subjective account thus undercuts the kind of probabilistically informed fellow feeling or solidarity that had inspired earlier arguments for mutual and social insurance. It does so in prioritizing internal coherence over empirical fidelity or concurrence as the mark of rational belief and in making interpersonal agreement about risks more elusive. Combined with the presumption that probabilities can be assigned to every event and the notion of subjective risk preferences, these features paint a picture of insurance not as a distinctively mutualistic or social practice but as a means of satisfying individual tastes regarding wholly personal risks. The perception of equal vulnerability and reciprocity that had been central to the earlier case for probabilistic insurance became less accessible under the subjective account and its decision-theoretic successors.101 What is more, toward the end of the twentieth century a new field known as behavioral economics, combining insights from psychology and microeconomics, brought to light the various ways in which actual decision making under uncertainty deviates from the counsels of Bayesian rationality. The empirical findings of Daniel Kahneman and Amos Tversky showed that individuals frequently base their choices on inaccurate probability assessments, inconsistent weighting of outcomes, and various other biases and misleading rules of thumb.102 The turn to libertarian paternalism, or “nudging,” to manipulate preferences and guide individual choices is one prominent response to such failures of probabilistic reasoning.103 It bears a resemblance to the atomist-statist approach we considered in chapter 3, in that both begin with individualist premises and end by turning to the state to encourage desirable conduct. Yet the increasing availability of statistical data, combined with the tendency to regard all or most probabilities as quantifiable, could in principle extend the reach of such “choice architecture” well beyond what late-classical thinkers imagined.104 This discussion of subjective probability theory has emphasized the difficulty, on that account, of justifying a mutualistic or communal response to uncertainty, particularly insofar as such a response is contingent on individuals’ agreement about risks.105 We have also seen how, over roughly the same period, theorists of the welfare state began to seek justifications for social policy beyond what they perceived to be the constraining rubric of insurance. I now wish to argue, building on both of these points, that the most influential work of political philosophy to emerge from this period, John Rawls’s A Theory of Justice, can be understood precisely as an attempt to rescue the logic of social insurance by doing without probabilities what neither economists nor welfare theorists of his time could do with them.

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The Egalitarian Welfare State without Probability Probability versus Justice We have seen that by the mid-twentieth century, the practice of probabilistic social insurance had been called into question on two fronts. On one side, the insurance rubric and its de facto actuarialism stood in tension with some of the more egalitarian aims of postwar welfare policy. On the other side, subjective probability theory had rendered decision making under uncertainty a private affair. If frequentism had encouraged a kind of prior identification with others, the subjective view began by shrinking the scope of each individual’s interest down to his own case alone. It may not be a coincidence, then, that important strands of social and political theory gave up on risk at right about the time that risk itself stopped being social. Whatever the relationship between these developments, John Rawls’s recasting of the social contract as a problem of decision making under conditions of uncertainty can be understood, in part, as a reaction to both. First, his rejection of all probabilities in the original position allowed him to distance the choice procedure from a gamble and to align it instead with a kind of insurance, wherein the individual sets out to guarantee her basic security or minimize her likely exposure to misfortune. Second, such insurance without probabilities could allow for precisely the kind of broad-based solidarity that the postwar welfare state had tried but failed to achieve. The goal that Rawls set for himself in A Theory of Justice was to determine those principles that would be agreed on by “free and rational persons concerned to further their own interests” from within “an initial position of equality.” From this hypothetical state, or original position, individuals “are to decide in advance how they are to regulate their claims against one another and what is the foundation charter of their society.”106 More specifically, Rawls stipulated that individuals make this decision behind a veil of ignorance, which prevents every one of them from knowing “his place in society, his class position or social status . . . his fortune in the distribution of natural assets and abilities, his intelligence, strength and the like,” as well as his conception of the good and his psychological propensities.107 A society satisfying the principles chosen in this scenario comes as close as possible to being a voluntary scheme, whose members are “autonomous and the obligations they recognize self-imposed.”108 Under these conditions, according to Rawls, the two principles that

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would be selected are, first, that each person has an equal right to the most extensive scheme of basic liberties compatible with a similar scheme of liberties for others; and second, that any social and economic inequalities must redound to everyone’s advantage and be attached to positions open to all. Rawls further interpreted the second principle as requiring that social and economic inequalities be arranged so as to provide the greatest benefit to the least advantaged, or what he calls the difference principle. One argument that Rawls used to support the choice and interpretation of these two principles came directly from decision theory. Rawls was not the first twentieth-century thinker to devise an account of collective choice based on a hypothetical scenario of ignorance.109 Yet he was, as far as I am aware, the first English-language writer to adopt the maximin criterion as the best choice for participants in such a scenario.110 This strategy, which derives from game theory, dictates focusing on one’s worst possible payoff and choosing the option that maximizes it. Unlike a game situation, however, in which the individual faces a calculating opponent whose goal is to outsmart him, in a decision context one’s “opponent” is nature, which may be arbitrary but is not unfailingly wicked. The choice of this strategy in a decision context had therefore been described as “a manifestation of pure cowardice,” focusing so intently on the worst-case scenario that it neglects all other possible outcomes.111 Indeed, Rawls admitted that the principles of justice representing the maximin strategy are “those a person would choose for the design of a society in which his enemy is to assign him his place.”112 In addition to securing basic liberties, then, the principles of justice show special solicitude toward the least advantaged. The difference principle in particular ensures that the benefits of cooperation are widely shared and that inequalities of fortune are not allowed to become sources of dependency or self-contempt.113 In Rawls’s words, it represents “an agreement to regard the distribution of natural talents as a common asset and to share in the benefits of this distribution whatever it turns out to be.”114 This image of a shared resource pool, the contents of which are to be distributed from the lucky to the unlucky among a set of ex ante equals, makes the parties’ agreement look quite like a mutual insurance contract. The main difference is that here, the absence of probabilities enables a much more complete assumption of equality—and, on Rawls’s view, justifies greater caution in the face of potential misfortune—than an agreement based on calculated risks would likely do. Rawls explained the choice of the maximin principle as a direct consequence of the absence of probabilities in his original position. The veil

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of  ignorance, as he set it up, ensures that the parties have “no basis for determining the probable nature of their society, or their place in it.” Because such “knowledge of likelihoods is impossible, or at best extremely insecure,” the participants have “strong reasons for being wary of probability calculations if any other course is open to them.”115 This assumption of probabilistic ignorance is necessitated perhaps above all by Rawls’s premise that “injustice exists because agreements are made too late,” after “people already know their social positions and relative strength in bargaining.”116 A contract based on empirical probabilities will therefore reflect existing morally irrelevant advantages, as participants segregate themselves by category and jockey for resources on that basis. Subjective likelihoods are unavailable as well because probability estimates should have an “objective basis . . . in knowledge of particular facts” if they are to serve as grounds for a rational decision and as public reasons.117 As Rawls was surely well aware, subjective probabilities had been shown in other accounts of social choice to have little interpersonal authority, even if they could be the basis for certain (flawed) collective decisions. Rawls and Social Insurance without Risk Despite this rejection of probabilities, however, Rawls was apparently determined to preserve the insurance-like character of the parties’ choice. The other two features of the decision procedure that justify the maximin strategy, he explained, are first that the alternatives to the guaranteed minimum are unacceptable—that is, another conception of justice could result in “serious infractions of liberty for the sake of greater social benefits”—and second that the person choosing “has a conception of the good such that he cares very little, if anything, for what he might gain above the minimum stipend that he can, in fact, be sure of by following the maximin rule.”118 Rawls denied that individuals in the original position are inherently riskaverse, but rather took it as his task to show that choosing “as if one had such an aversion is rational given the unique features of that situation.”119 Parties behaving in this way will choose not only to “protect their basic rights” but also to “insure themselves against the worst eventualities,” including the loss of their own freedom for someone else’s advantage.120 This last point in particular distinguishes justice as fairness from utilitarianism, which in adopting “for society as a whole the principle of rational choice for one man” entails what is effectively a gamble.121 As Rawls explained in a subsequent article, while a utilitarian principle may sometimes secure basic individual liberties and interests, “there is no reason

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why it will do so in general,” and “it would be pointless to run the risk of encountering circumstances when it does not.”122 This association between utilitarianism and gambling also helps to explain why Rawls rejected another social decision rule available under conditions of uncertainty: the equiprobability assumption proposed by economist John Harsanyi.123 Harsanyi had reinterpreted the classic principle of indifference (according to which one assumes equal probabilities in the absence of knowledge to the contrary) as an expression of ethical impartiality, allowing the individual to imagine herself as interchangeable with everyone else in her society. This is quite similar to Rawls’s depiction of the veil of ignorance, except that under the equiprobability assumption, Harsanyi showed, participants will choose to maximize the overall sum of utilities since each one’s expectation is an equal portion of the total pool. The rule is thus insensitive to both individual liberties and ex post individual welfare levels, and as such represents precisely the kind of wager that Rawls believed his participants would reasonably avoid.124 On Rawls’s view, then, every available account of probabilities poses a problem for the decision procedure or the justice of its outcome. He later explained that because “there is at present so much disagreement about the meaning and interpretation of probability,” arguments from the parties’ ignorance may be best used to support the “strains of commitment” case for maximin. This is the view that “no one is permitted to agree to a principle if they have reason to doubt that they will be able to honor the consequences of its consistent application.” When choosing between two possible accounts of justice, one of which would permit or require social positions that the individual could not accept, while the other results in “arrangements that everyone can honor in all circumstances,” the decision maker must agree to the latter. The two principles, which “always secure acceptable conditions for all,” are therefore preferable to any criterion that may not.125 In short, whatever account of probabilities one chooses, reasoning based on mathematical likelihoods could place one in a position that is too difficult to bear—a risk that no reasonable person should take. I therefore propose that we understand Rawls’s application of the maximin rule as a defense of the basic logic of social insurance, in particular its aim of guaranteeing security by means of a contract among those who regard themselves as equally vulnerable to harm, against the countervailing pulls of contemporary economic thought. Even in conditions of uncertainty, Rawls maintained, it is possible to make a decision that is not in essence a wager on whether a certain empirical proposition is true. Once probabilistic reasoning is ruled out, he then showed that the person-

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ally and collectively beneficial result stems from each person’s choice to guarantee for himself an acceptable minimum even under the worst-case scenario. Rawls’s argument can also be read as a commentary on the politics of postwar social policy. If the impetus for the egalitarian welfare state was, in Titmuss’s words, “connected with the demand for one society; for nondiscriminatory services for all without distinction of class, income or race; for services and relations which would deepen and enlarge self-respect; for services which would manifestly encourage social integration,” Rawls responded that the only way to achieve this in practice is by so deeply insinuating the insurance idea into the fabric of social relations that the resulting arrangement ceases to outwardly resemble insurance. When it comes to not only the basic guarantees of liberty and security but also the foundations of self-respect, Rawls argued, no one should choose to gamble.126 In this, he echoed the moralists of the probabilistic tradition, who argued for insurance as the personally responsible choice and as a commitment to the overall social order. Unlike previous accounts, however, justice as fairness maintains the liberal character of a fair contract while doing away with the particularistic distributive entitlements that had limited the scope of earlier schemes. The same extreme uncertainty that mandates caution also guarantees inclusiveness, on Rawls’s view, because it unsettles traditional distributive politics completely. The Persistence of Probability I have suggested that understanding the limitations of both postwar social insurance practice and twentieth-century probability theory sheds light on Rawls’s attempt to formulate an account of distributive justice that, while closely resembling a polity-wide insurance agreement, jettisoned probabilities even more completely and explicitly than existing welfare programs had done. If my interpretation is right, then Rawls’s theory also implies a critique of any continued reliance on actuarial or probabilistic insurance principles as the basis for welfare policies.127 Welfare states arose, in part, from a recognition that conditions had made it difficult to attribute economic hardships to the choices or failings of individuals who suffer from them.128 It was not a failure to take proper care that led factory workers to become injured, or a failure to adequately plan for the future that led the unemployed into poverty during economic depressions. Insurance offered an elegant solution to the challenge of helping individuals through bad times without denying that they were, in some

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sense, still in charge of their fates. Because they had done their part when they were able—either directly, by paying contributions for their coverage, or indirectly, through their labor and taxes—they could accept aid as their earned right, without losing self-respect, a sense of autonomy, or the motivation to continue working to improve their lot and that of their families. Rawls’s account suggests that existing social insurance arrangements have not yet recognized how thoroughly collectivized economic conditions have become. Because so much of economic success hinges on factors that have nothing to do with effort or merit, such as where one is born, the traits one inherits, and the accumulated wisdom on which every personal success builds, a theory of distributive justice should reject individualized attributions of desert in favor of a convention that reflects our interdependence.129 In this regard, probability estimates seem to represent an obstacle because they can encourage dubious claims of personal or group distinction or give individuals false confidence in their ability to plan for future contingencies on their own. Insofar as the social choice procedure and social insurance itself remain tied to probabilities, then, they will fall short of the more robust equality and solidarity that justice as fairness prescribes. Despite the continued influence of Rawls’s thought in more academic quarters, however, social insurance remains the central tool of welfare states and has lately garnered a new wave of support among philosophers, economists, and other scholars of social policy. Some have praised it as a tool for promoting efficiency, providing protection that citizens desire when markets fail to do so. Others have argued that it promotes egalitarian or communitarian aims.130 Invoking several of these rationales, Robert Goodin contends that the political virtue of understanding welfare transfers as insurance is that “redistribution, of a sort, is thus justified without any appeal to old-style and increasingly unfashionable values of equality or altruism.” Thus the “‘solidarity’ of the shared risk pool,” along with the efficiencies of public over private insurance provision, “may be quite enough to motivate support for something rather like the welfare state into the indefinite future.”131 This assessment, while likely correct, does not address the central problem we have been considering: that of defining the shared risk pool in a way that is simultaneously prudential and egalitarian. The reintroduction of means tests into many Beveridge-type systems over the second half of the twentieth century points to the limits of an approach that aspires to universality while relying on the perception of contractual fairness for support.132 Indeed, if the politics of welfare retrenchment of the 1980s are any indication, it is precisely such universal insurance programs that prove

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most susceptible to reform pressures arising from both fiscal and moral concerns.133 These programs are often insufficient for the upwardly-mobile middle classes, who frequently turn to private insurance and fringe benefits to supplement their coverage; relatively limited in their impact on the poor; and, where more generous, vulnerable to the critique that they discourage personal responsibility.134 By contrast, welfare states that offer primarily earnings-related or “Bismarckian” social insurance more closely correlate with the principle of individualized desert because those who earn more receive more in the way of benefits. Although these countries may have lower overall levels of income inequality and poverty than those that provide targeted or flat-rate payments, their policies appear to be even more removed from the kind of equality and solidarity that Rawls proposes. (They are also, as Monica Prasad notes, based to a greater extent on regressive sales and payroll taxes.135) In short, it seems that Rawls had a reasonable case that only by doing away with probabilistic insurance in welfare policy is anything like universal, egalitarian provision sound in theory and attainable in practice. Yet Rawls’s account also leaves us with the question of what exactly we give up when we exclude probability from the political theory of the welfare state. By precluding the empirically grounded solidarity of self-identified risk groups, his account seems to undercut one of the most important sources of psychological and political support for welfare policy. Perhaps such groups, which emerge from an experience of shared vulnerability yet need not be confined to strict actuarial classes, are the closest a liberal democratic state can come to the kind of friendship or uncalculating relationship that gestures beyond justice. What is more, the collective action of these groups shows that, while many economic outcomes cannot be attributed to individual effort or desert, the insured are not simply pawns of an overwhelming fate but can take steps to secure themselves in an uncertain world. If social insurance can be both individually choice-worthy and universal in scope only if it is not probabilistic, we would do well to ask whether choosing the first two features over the third does not somehow undermine the purpose and the viability of the welfare project itself. Insurance and Distributive Theory after Rawls The same question arises with respect to another account of distributive justice that emerged in Rawls’s wake and which explicitly invokes insurance as the object of rational choice under uncertainty. Known as luck egalitarianism, this account takes its bearings from Ronald Dworkin’s distinction

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between “brute” and “option” luck, or in other words between misfortune that is beyond the individual’s control and losses that result from deliberate choices or gambles. The rationale for this distinction, Dworkin explained, is that “it is unjust when some people lead their lives with less wealth available to them, or in otherwise less favorable circumstances, than others, not through some choice or gamble of their own but through brute bad luck.”136 Dworkin consequently set out to defend a distribution of resources that would be “ambition sensitive,” reflecting individual choices, but “endowment insensitive,” compensating for undeserved harms. To establish the desired distribution, Dworkin posits a choice scenario involving a hypothetical insurance market, in which participants begin with a fair distribution of resources and are given the chance to purchase reasonably priced insurance against a particular eventuality. Insurance “provides a link between brute and option luck,” he explains, “because the decision to buy or reject catastrophe insurance is a calculated gamble.”137 The average amount of insurance that participants would purchase under these conditions could then serve as the basis for a tax and redistribution scheme that would effectively provide citizens with the selected coverage.138 Dworkin makes two important assumptions about this hypothetical insurance market, which takes slightly different forms depending on the risk in question but preserves the same overall character for each. The first is that participants will regard themselves as equally likely to encounter the given eventuality. Although he admits, in the context of unemployment, that this is a “nearly impossible assumption,” it is related to the second critical feature of the market, namely that insurers will offer coverage “at community rates,” or at the same premium for the same coverage for everyone.139 Since “risks of most catastrophes are now regarded by the actual insurance market as randomly distributed,” the hypothetical market could follow “actual insurance practice, modified to remove the discrimination insurers make when they know one group is more likely . . . to suffer a particular kind of brute bad luck.”140 Dworkin argues that the choices made under these conditions and the distribution that ultimately results will be fair: Those who receive compensation “would have paid a premium reflecting the cost of that option to others,” while those who experience poor option luck thanks to their unwillingness to insure will have to acknowledge their own responsibility for their fate.141 Dworkin’s hypothetical choice scenario thus incorporates both an epistemic interpretation of probability, in participants’ assumption of their equal risks, and an aleatory one, in the form of the presumably random distribution of various hazards. This combination seems to accord with

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certain intuitions about fairness and may avoid some of the pitfalls of both Harsanyi’s utilitarian application of the principle of indifference and Rawls’s difference principle.142 Nevertheless, it is also vulnerable to objection on both epistemic and aleatory grounds. First, it is not clear why decision makers—especially those who already know their “hopes, fears, tastes, and values,” and in some cases their talents and ambitions—would assume that they are equally as susceptible to a given risk as everyone else in the population, or why they would be reasonable to do so.143 Second, it is not clear how an insurance market would work on the admittedly inaccurate assumption that the risks in question are randomly distributed across the entire population. Dworkin acknowledges the problem of adverse selection, which would induce insurers to raise rates in response to the oversubscription of higher-risk individuals, and says in the context of healthcare that the only way to prevent this is to nationalize insurance.144 Yet such insurance, to provide the same coverage to everyone, would either have to offer low benefits across the board or subsidize those with higher-risk profiles. In the first case, the scheme may offer less coverage than the average person would choose.145 In the second case, it would be susceptible to charges of unfairness since those with lower-risk profiles would pay more than their actuarially fair share, despite having purchased insurance on the premise that they are equal to their higher-risk peers. (Where the less risky also happen to be wealthier, this outcome may not be too troubling from an egalitarian point of view, but there is no reason to think that risk proneness and wealth will always coincide in such a neat way.146) It appears, then, that the epistemic and aleatory assumptions of Dworkin’s scheme are not simply congruent, as he implies. If probabilistic equality represents a moral constraint, a kind of ethical impartiality, then it need not be justified on empirical grounds.147 Yet in that case, it does not provide much guidance for individual decisions in anything resembling a realistic insurance market, where insurers must calculate their liabilities and will try to offer prices that are calibrated to actual risks.148 If, on the other hand, probabilistic equality is a statement about the world, then it permits the kind of insurance market that Dworkin has in mind, but only insofar as the risks involved are randomly distributed across the entire population, which is not always the case. Finally, in neither scenario does Dworkin allow for the type of probabilistically informed solidarities that have helped to generate and sustain social insurance schemes. While this is not a fatal flaw for a normative theory of justice, it is another piece of evidence that his approach, like that of Rawls, may undercut rather than support the politics of social provision.

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Dworkin’s idea of a distribution that is at once ambition sensitive, reflecting individual choices under uncertainty, and endowment insensitive, compensating for statistically defined harms, reflects the harmonizing impulse that has long characterized proposals for social insurance. Yet it is not clear that any form of insurance can achieve such harmony in principle. Rather, our sustained consideration of the history of probability and insurance implies that it is only possible in practice, and only approximately at that. Without this awareness, we may neglect not only the psychological sources on which social insurance depends but also the careful balancing act that it unavoidably entails.

The Fate of Social Insurance in the Twentieth Century and Beyond The Problem of Polarization In the first part of this chapter, I argued that Beveridge-style social insurance struggled to accomplish its goal of adequate universal coverage, in large part because of the probabilistic psychology on which it rested. While aspiring to universal self-respect and social cohesion, it depended critically on the participation of the middle classes, and in particular on members’ perceptions of their own similarity and of the risks that they as a group were liable to face. As a result, its generosity toward the worst off was limited, and eventually many of its programs had to be supplemented or supplanted by targeted and means-tested support for the poor—precisely the type of differentiated approach that advocates of universal welfare had sought to avoid. The failure of such social insurance to realize the inclusive aims of its early advocates became, by the middle of the twentieth century, part of a powerful critique of the idea among welfare theorists. I have interpreted Rawls’s A Theory of Justice as part of this line of critique, arguing that social insurance cannot be universal in its reach as long as it remains tied to probability estimates of any sort. Yet I have also suggested that Rawls underestimated the psychological underpinnings of the welfare state, and in particular the sense of identity and solidarity on which the political demand for social insurance rests. To be sure, such identity is shifting and contingent; its generosity is often bounded by perceptions of similarity; it can be divisive and even dangerous if unmoored by a concern for the common good. Yet it also reflects a kind of mutual concern and reciprocity that points toward friendship on a national political scale. By excluding

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probabilities from his account, Rawls also precludes the type of solidaristic reasoning on which the welfare state was built. The alternative justification for social insurance that emerged in the last century was based on its ability to satisfy preexisting consumer preferences and to correct failures of the private market to do the same. This account also differed significantly in its underlying psychology from the one that had inspired earlier welfare programs. It inserted radical subjectivity at the foundation of probability estimates; maintained that all or most eventualities can be quantified, including in the individual case; and subordinated interpersonal agreement to internal consistency. While subjective Bayesians do allow for the adjustment of personal probabilities in light of experience, the arbitrariness of each individual’s starting point and the limited extent of her experiential learning make eventual agreement uncertain.149 From the point of view of encouraging cooperative action in the face of uncertainty, then, subjective Bayesianism leaves something to be desired. In the wake of these developments, the late twentieth century witnessed the emergence of two opposing, even polarizing, intellectual tendencies with regard to social insurance and the welfare state more generally. On one side, advocates of a robust social equality sought a moral case for welfare that did away with empirical risk assessments and the particularistic claims to which they give rise. On the other side, advocates of a contractual, market-oriented approach set out to create a system that would cater directly to individual judgments and preferences. These two dispositions align for the most part with the political left and right, respectively, and their difference of principle is in some degree to be expected. Yet the heightened divide between them in contemporary politics may also reflect the difficulty, in light of the developments we have considered, of articulating an account of social insurance that can appeal to both. The Impact of Information In addition, recent technological developments seem to lend credence to critics’ concerns about the limitations of social insurance in promoting egalitarian aims.150 There is evidence that the data revolution is facilitating the expansion of private coverage by encouraging purchasers to share information with their insurers and allowing insurers to offer premiums that more closely track differentiated risks. Private insurance thus increasingly offers a substitute for social insurance, at least for those with lower risks, and may threaten political support for public systems. The standard economic analysis of insurance markets begins with the

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problem of asymmetric information: Market failures occur when individuals know their risk types but conceal this information from insurers, leaving the latter with more high-risk subscribers and higher-than-expected losses (adverse selection).151 As a result, insurers are forced to raise prices, driving lower-risk subscribers away and, on some accounts, creating a market only for the most accident-prone individuals. Social insurance arises in response to such failures, according to this view, providing citizens with the protection they want but cannot otherwise obtain. As Torben Iversen and Philipp Rehm have pointed out, however, this standard model entails several difficulties. For one, the quest for efficiency is not what generates social insurance policies; rather, in democratic states, the driving force is a political majority that supports a public system. For another, the assumption that only buyers know their risks is increasingly untenable, both because those with lower risks have an incentive to share information with insurers to obtain lower prices, and because insurers have greater access to data and sophisticated tools for analyzing it.152 There is indeed a compelling case that such enhanced information sharing will lead to greater segmentation in insurance markets, and in so doing undermine the political demand for broad risk-pooling arrangements. This prediction echoes the Rawlsian view that ignorance—including enforced ignorance about probabilities—is a precondition for egalitarian welfare policy. Yet the argument of this book suggests that information is not the only relevant variable in evaluating the demand for social insurance. As we have seen, the subjectivist view of probability also undermines the case for broad risk pooling. Since, on this view, the insured estimates her own risk independently, without having to first consider the experiences of her peers, there is a strong individualist bias built into the model. This bias could generate a demand for more segmented risk groupings even before the question of information sharing enters into the analysis. In short, if the demand for insurance is indeed a central driver of policy outcomes, then the understanding of probability on which citizens rely will meaningfully shape not only scholarly models but the real-world politics of welfare as well.153 On the supply side, there are ways to counteract the segmenting tendencies generated by this new tide of information. For example, antidiscrimination regulations prevent insurers from using the information they have about particular risks to differentiate between or exclude certain categories of people. When regulated in this way, private insurance may serve some of the same purposes as social insurance, allowing for widespread access to insurance pools and promoting “subsidizing solidarity,” in which low-

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risk individuals subsidize higher-risk ones as a result of prohibitions on differential pricing.154 The historical story that I have traced in the preceding chapters confirms the conceptual continuity between private (and in particular mutual) and social insurance arrangements. Both entail some combination of prudential and communal rationales, and both rest on contestable judgments about who should be included in the shared risk pool. Yet private insurers also have an incentive to work around antidiscrimination regulations—for instance, by finding proxies for the categories in question—and, where they succeed, the results could be even more inequitable than the original arrangements.155 As a result, whether the regulation of private markets is indeed the most effective way to promote broad access to insurance will depend on the design and long-term effects of those regulations. Returning to social insurance, perhaps the solution for those seeking to expand the scope of public arrangements beyond more limited risk pools is not simply to suppress the flow of information but to persuade would-be distributive equals of their shared vulnerability and need for mutual  protection. Such persuasion could begin with how we interpret risk itself. It would be beyond the scope of this work to propose or defend a particular theory of probability. Nevertheless, the preceding analysis does suggest a few general steps that could help to better align our theoretical conception of risk with the practical demands of social policy. The first is to question a radically subjectivist view that holds internal coherence as its only constraint and that regards all probabilities as quantifiable and all risks as insurable on an individual level. Such questioning could encourage recognition of the importance of shared probability estimates, invariably based on some type of empirical input, in the practice of mutual insurance. At the same time, it would make room for greater appreciation of the conditionality of all probabilities on a designated reference class or body of knowledge, as well as the fact that some probabilities are more uncertain or ambiguous than others because they are based on less extensive or less reliable information. Economists have acknowledged that failures in insurance markets arise not only due to information asymmetries but also because of difficulties in establishing the probability of loss. The relative uncertainty of some probability estimates, particularly in realms such as employment or healthcare, should therefore be seen as relevant to the demand for social insurance.156 Citizens will no doubt continue to face new risks arising from changing labor markets and other economic realities. The flexibility that has long

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been a hallmark of social insurance should permit its evolution beyond existing actuarial categories to new hazards and solidaristic classes.157 At the same time, it will be important to recognize that this type of solidarity is inherently somewhat constrained, both by existing knowledge about risks and by the ever-present demands for personal choice, autonomy, and distinction. Social insurance will therefore have to be supplemented by other policies, institutions, and arguments as one element of a realistic political theory of distributive justice. Nevertheless, when properly understood, it provides an appealing framework for conceptualizing and mediating distributive politics—a stable, if somewhat shifting, foundation on which many basic needs of a population can be met and, at the same time, its members’ own judgments and aspirations given reign.

Conclusion

The Long-Standing Appeal of Insurance The preceding chapters have traced a history of social insurance, from the origins of risk through the advanced welfare state. I have argued that probability theory played a central role in the development of welfare thinking and practice, proposing an account of distributive justice that has proven remarkably influential in political life. Probabilistic justice, as I have been calling it, had the potential to replace divisive claims of desert and need with an interpretation of equality that in some way encompassed both. Insurance understood as a political principle thus promised to supplant long-standing distributive disputes and their accompanying passions with impartial determinations of equality based on the rigorous counsels of mathematics. In making this case, I have advanced three principal claims about probability theory and its relationship to welfare thinking. The first is that mathematical probability is frequently, if not inherently, normative in its character. We saw that the very project of quantifying probabilities grew out of a moral and legal question, namely the need to apportion fair shares in an interrupted game of chance. Each subsequent account of probability has in turn both reflected and furthered the practical aims of its exponents. This should not be surprising, given that the discipline is at its core an attempt to guide good judgment and quantify equality, both of which are normative efforts, closely linked to views about the ends of human action and justice broadly understood. The second claim, which follows from the first, is that theorists of mathematical probability have long tried to reconcile individual choice with some account of the common good. Not long after the founding of the

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discipline, probabilists began to recognize a potential disconnect between personal prudence, or common sense, and contractual fairness as defined by their calculations. Many subsequent contributions to the theory attempted to resolve this problem in its various forms. Each account had a different character and resulted in different proposals. Yet they shared the promise of harmonizing individual judgments with aggregate regularities, which respectively correspond to the two sides of probability itself. Finally, I have argued that the answers to this problem that emerged in connection with probability theory, from roughly the end of the eighteenth century through the twentieth, played a crucial role in the development of the modern welfare state. Statistical insurance was the first practice in which philosophers of probability sought, and in their view found, the means to reconcile individual benefit with a common good. The application of insurance principles on a social scale therefore promised to extend such harmony well beyond isolated associations to the polity as a whole. Insurance would reflect the free choices of individuals while simultaneously securing social order. It would give each citizen her due while promoting the aggregate benefit. And it would distribute resources on the basis of both personal responsibility and equal vulnerability or need, accommodating the two principles without clearly favoring either one. As it turns out, the practical success of insurance in this regard far exceeded its theoretical capacity. That is, it was not by theoretically resolving discrepancies between the individual and the common good that social insurance established itself in political life and remained salient over the course of roughly two centuries. Rather, it did this by subsuming competing principles within the seemingly technical, impartial language of risk. The fact that social insurance has remained the dominant paradigm for welfare provision despite historically embodying very different assumptions and aims speaks to its flexibility and resulting political appeal. Insurance manages to reconcile competing principles by concealing, at least in part, the differences between them. Probability theory set the stage for this coup, in that it advanced an account of distributive justice based on what appear to be impartial, unassailable claims of equality. In fact, determinations of probabilistic equality are inherently relative. Statistical probabilities require the decision maker to classify events by choosing some characteristics as relevant and disregarding others. Logical probabilities require a prior body of knowledge on the basis of which an event can be judged more or less likely to occur. All probabilities require an interpretation of the concept itself, in light of which they are made. Such relativity is often hidden to the untrained eye,

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whether behind statistical regularities or in the assignment of prior probability distributions. They affect the character of public policy while remaining largely removed from the realm of open political conflict. These remarks are intended not simply as a critique but also as a reflection on the important mediating function that insurance has served in modern politics. Social insurance is the direct heir to the liberal project: a contract, frequently hypothetical, that is made among those who regard themselves as equally vulnerable to some harm and that is intended to guarantee their individual and collective security. Like liberalism itself, it has spawned countless criticisms and undergone various modifications. Its character has changed as the understanding of risk evolved from an individual entitlement attached to a social obligation, to the property of a collective, to a wholly personalized prediction. Yet throughout these evolutions, social insurance has set out to serve the same overarching purpose: to unite individuals with diverse natures and interests under a single practice of reward or recompense.

Explaining the Welfare State While it is beyond the scope of this book to explain in detail the emergence and evolution of the modern welfare state, my argument does address a puzzle in the study of welfare policy: why, among both scholars and the general public, the welfare state continues to be associated with insurance, despite the tenuous relationship between many welfare policies and traditional insurance practices. It also suggests a corrective to some recent scholarship in the field. Since roughly the middle of the twentieth century, it has been common in economics, political science, and legal studies to explain social insurance policies as correcting market failures and reducing the social cost of compensating for accidents.1 Even when it departs from actuarial principles, on this view, compulsory or publicly orchestrated insurance covers risks that are inadequately addressed by private markets and therefore likely to impose excessive costs or impede overall economic growth.2 Such explanations certainly help to explain why policymakers might opt for compulsory coverage instead of leaving certain risks to voluntary arrangements. These accounts may also explain why democratic and especially middle-class voters, who often play a crucial role in the enactment of welfare legislation, would support welfare programs even when they are not perceived as actuarially fair. Where private markets fail to provide adequate or affordable protection, as has long been the case for important economic risks, citizens

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may be prudent to support public programs that protect them even at a cost that exceeds their mathematical expectations. Explanations for welfare that focus solely on economic advantage, however, do not account for the claims of mutual concern and solidarity that have inspired so many political and philosophical accounts of the welfare state. In this regard, a class-mobilization thesis now prominent in comparative welfare-state studies comes closer to understanding social insurance as the complex political phenomenon that it is. More specifically, a recent strand of thinking that understands the preference for welfare as the demand of groups of risk-prone citizens for insurance offers a compelling account of the link between electoral politics and social policy outcomes.3 Ex ante, welfare policies provide voters with a desired sense of protection; ex post, they distribute wealth from economic winners to losers. Political scientists working in this tradition have set out to show how preferences rooted in voters’ economic positions are aggregated into social policies that in turn fill both insurance and redistributive functions. This explanation helps to account for how many welfare policies were enacted in advanced democracies, especially in the period just prior to and since the Second World War. It also indicates that efficiency- and solidaritybased arguments for welfare can be, and often have been, closely aligned. Policies that protect against the dangers of income disruption or destitution can reflect both an instrumentally rational response to insecurity and a form of solidarity, binding groups of citizens who perceive themselves as equally vulnerable to a particular harm. Accounts of social choice that rule out probabilistic reasoning therefore also deny the kind of collectivities that have generated social insurance programs in many countries for over a century now. At the same time, my argument suggests that scholars of the welfare state could pay greater attention to the understanding of probability at work in their accounts of policy formation. Arguments for risk-class mobilization would appear most naturally aligned with a frequentist view, with its case for interpersonal identity and solidarity. As a theory of probability, frequentism is problematic and has come under powerful criticism. Yet, as I argued in the previous chapter, the subjective Bayesian view also encounters serious difficulties, particularly as a basis for interpersonal judgments and collective action. If we are to understand social insurance as a product of citizens’ perceptions of risk, we need also to reflect on what exactly is meant by risk and how citizens estimate and interpret the probability values that define it. In addition, my argument suggests that accounts of the political econ-

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omy of welfare would do well to consider the nature of social insurance as a distributive regime—one that is mixed in character, at its best—and not solely as a response to the self-seeking claims of particular groups. The history of probability reveals that insurance can accommodate a variety of different answers regarding the definition of equality to which distributive claims should correspond. If the political genius of social insurance lies in its ability to accommodate more than one such answer, both at once and over time, political scientists and others would do well to analyze the mixed distributive consequences of social insurance programs as part of their design and staying power. Doing so would make clear not only the sources of political support for welfare programs but also the distinct and at times competing moral principles that animate them.

The Limits of Social Insurance Any book about social insurance must address, at least briefly, the most pressing political controversies surrounding the welfare state today: namely, the problem of finance and the question of personal responsibility. If at one point the rubric of insurance invoked an image of fiscal restraint, promising to limit what the state distributes to the amount that it collects in contributions, the welfare state has come to be identified among critics with out-of-control spending and government debt. And if mutual insurance was originally touted as a reflection of prudence and a means to propertied independence, it is now commonly associated with what economists refer to as moral hazard, meaning the encouragement of risky and expensive behaviors, as well as dependence on the state. It is true that, in most advanced welfare states, social expenditures increased over the course of the twentieth century, not only in absolute terms but also as a percentage of gross domestic product.4 Some scholars have explained this phenomenon as a product of Wagner’s Law, which predicts that the share of government spending relative to GDP will increase with rising incomes.5 As citizens grow wealthier and live longer, this argument goes, they will increasingly seek out the kind of quality-of-life improvements provided by the risk-pooling and consumption-smoothing functions of the welfare state, including healthcare, pensions, and education.6 This view recasts the welfare state as more compatible with economic efficiency, of a sort, than many partisan criticisms allow. Yet it does not appear to clearly distinguish efficient responses to market failures from less efficient efforts by powerful groups to claim resources on behalf of their own narrower interests. The difficulty is compounded by the fact that citi-

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zens tend to see benefits, once granted, as personal entitlements or rights, making it politically difficult to reduce them regardless of whether they are beneficial or fair.7 Combined with concerns about demographic changes and mounting government debt, such observations have led critics of the welfare state to propose various demutualizing and privatizing alternatives. Replacing public provision with individual savings and foresight promises, on this view, to rein in government spending and encourage personal responsibility, along with other traits of character conducive to success in a market economy. Supporters of the welfare state worry that such measures will spell the end of solidarity, increase economic inequality, and leave individuals to bear the slings of fortune alone. Indeed, some privatizing proposals have threatened to shift responsibility and risk onto individual citizens without addressing the fiscal challenges of existing programs.8 Even more important, the “hidden welfare state,” comprising the many benefits and transfers accomplished through tax policy, has financial and distributive consequences that are less publicized, less well understood, and frequently more regressive than visible welfare spending. While it may be the case that taxes are more amenable to legislative change than the “entitlements” created by social insurance, substituting tax-financed measures for other forms of welfare spending will not necessarily lead to greater fiscal discipline, efficiency, or fairness.9 While I cannot undertake a serious examination of the problem of welfare finance here, my argument suggests that partisans on both sides of this debate have correctly understood something about social insurance. Insofar as such programs grade benefits to contributions or coexist with a significant degree of self-help, they appear to reward individual effort or at least to be compatible with such rewards. At the same time, insofar as they mandate contributions from all and grant payments on the basis of qualifying events, they rest on an assumption of shared vulnerability that transcends individual distinctions. Indeed, by recognizing that outcomes in a market economy are not simply coextensive with merit, social insurance rejects the assumption that all wealth justly rests with the economically successful. Yet by also maintaining, at least in principle, that benefits be earned through some form of contribution, it sustains an image of personal responsibility and a reward for those who “do their part.” My analysis thus highlights a feature of existing practice and institutions that, while not in itself justifying them, ought to be born in mind by critics and supporters alike. For example, observers who wish to impose a greater degree of fiscal restraint on the welfare state should note the distinc-

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tion between a mixed regime and one of pure market justice or “wealthtalent,” which social insurance is not.10 They should also recall that moral hazard—the problem that insureds may take fewer precautions against the risk or incur associated costs that are excessive—is a challenge for all forms of insurance, not only state-provided ones.11 The solution is careful policy design, not necessarily the removal of risk-pooling arrangements. Meanwhile, those who wish for a greater degree of collective responsibility should keep in mind that claims of personal choice and self-sufficiency are part of the basic character of the regime; they cannot be satisfied by simply ceding more responsibility for citizens’ needs to the state. The same ambivalent, amorphous, and—at best—mediating quality that has made social insurance so appealing has simultaneously guaranteed that it will remain subject to competing interpretations and pulls. The political success and longevity of such programs will likely continue to depend on their ability to resist the extreme of each view.

A Contemporary Example Current challenges in healthcare policy help to illustrate the last point. Medical care and health insurance are among the most widely cited examples of imperfectly competitive markets.12 Economists note that the market for health insurance is plagued by information problems, in particular adverse selection, the phenomenon whereby relatively sicker people come to be overrepresented in insurance pools, leading insurers to increase prices or find ways to exclude those who are more prone to illness. Many health systems around the world try to resolve such challenges through direct government provision of insurance, a combination of public funding with privatesector delivery, or managed competition among insurance providers.13 In the United States, however, healthcare was not included among the legislative initiatives of the New Deal, and thanks to a series of subsequent developments, working Americans came to receive health insurance primarily through their employers. As a result, Medicare and Medicaid, the two programs designed to provide government-sponsored healthcare, began not with broad risk pools but with those least able to obtain private coverage.14 These precedents, combined with rising healthcare costs and a large number of uninsured Americans, have led to an ongoing policy debate that illustrates the same challenge we have been considering throughout this book: namely, how to define the shared risk pool in a way that secures the agreement of each and the benefit of all. In 2010, President Barack Obama succeeded in passing a major piece

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of legislation called the Affordable Care Act (ACA), popularly known as Obamacare. The law sharply divided the American public in the years after its passage, with roughly equal percentages of most demographic and economic groups steadily favoring and opposing it.15 A majority of Americans, including Republicans, Democrats and independents, supported some of its provisions, such as its subsidies to lower-income citizens to buy insurance on the so-called individual market and its prohibition on denying coverage to those with preexisting medical conditions. Yet one provision proved consistently unpopular, particularly among Republicans and independents: the individual mandate, which required nearly all Americans to obtain health insurance or pay a fee.16 The ACA’s architects emphasized that the mandate was necessary to cover preexisting conditions because it created a risk pool broad enough to accommodate those more likely to need care. According to some numbers, this should have been a winning argument: Over half of all adults in the United States have reported that they or someone else in their household had a preexisting condition according to the ACA’s definition.17 Add to these the many who could reasonably anticipate getting sick and struggling thereafter to find coverage, and one would seem to have a strong contingency in support of compulsory risk pooling. Nevertheless, opponents of the mandate insisted that they did not want the government dictating their choices, and in particular that the requirement to purchase insurance placed on them too heavy a financial burden. This has been especially true for many middle-income Americans who did not qualify for ACA subsidies yet found their health coverage increasingly unaffordable due to rising costs.18 Although this is not the place for anything near a thorough examination of American healthcare policy, I wish to suggest that the politics of the ACA confirm the continued salience of risk perceptions and risk groups in generating the demand for social policy, as well as some of the challenges of the insurance rationale for welfare. Public justifications for both the law and many proposed alternatives have focused on the hazard of becoming ill and being priced out of health insurance as a result. Those who face this prospect do not constitute a homogeneous actuarial class but a kind of composite that has emerged in response to economic circumstances, including the predominance of employer-sponsored coverage and the oftenprohibitive costs of care. The creation of this new cohort thus indicates the same kind of flexible aleatory solidarity that has given rise to and sustained social insurance programs in a variety of contexts. In fact, while President Donald Trump and congressional Republicans have repeatedly attempted

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to undermine or repeal the ACA, they have also insisted that their replacement plans will preserve coverage for those with preexisting conditions.19 At the same time, some of the political challenges that have haunted the ACA since its passage stem from the more prudential or individualist face of social insurance. This face shows itself in defining the risk pool, an act that includes some while excluding others (particularly those thought to impose avoidable costs on their peers), and in the fact that support for such policies hinges on their being perceived by individuals as choiceworthy or fair in light of their own particular circumstances.20 As we have seen, the key constituency in the latter respect has often been the middle class, broadly defined. In the case of the ACA, many middle-income Americans objected that those earning only slightly less than they did fared better in the individual insurance market thanks to ACA subsidies, while others who qualified for Medicaid seemed to get decent healthcare for free. The requirement to purchase ACA-approved insurance under these circumstances, particularly given its costs, struck many as unfair and stoked their opposition to the law.21 As long as welfare states remain dominated by the insurance principle, and with it some account of risk, both of these faces will remain with us. This observation is in turn an invitation to think seriously about some of our basic concepts and to look for an understanding of risk that will help to support a responsible and inclusive vision of social insurance. Such a vision would bridge the need for individual judgments, rooted in particular knowledge and aspirations, with the facts of our interdependence and the undeserved character of many hardships. This would not be the radically subjectivist view that became prominent in twentieth-century decision theory, which made risk bearing a predominantly individual affair. Nor would it be the nonprobabilistic approach of some egalitarian distributive theories, which rules out important psychological and political sources of solidarity. Rather, a more compelling account of risk and social insurance would acknowledge the salience of empirical probabilities while remembering that they are relative to a particular body of knowledge, which is liable to change as our collective experience grows. It would recognize that many risks to economic security are relatively ambiguous or uncertain, meaning that our information about them is incomplete and, therefore, that the idea of objective actuarial fairness may be inapt. Above all, it would accept the ongoing relevance of both the epistemic and the aleatory faces of probability in shaping the evolving distributive regime at the heart of the modern welfare state. Today, the idea of social insurance shows signs of returning to favor.

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Whereas mid-twentieth-century theorists on both the left and the right criticized the practice for concealing the true aims of welfare, contemporary voices from across the political spectrum now tout its advantages.22 This is most likely a salutary development, especially if its intent is to find common ground in a deeply polarized political culture. The virtue of the insurance principle lies not only in its ability to accommodate different risk groups, financing arrangements, and aims, but also in creating a rhetorical and practical arena in which those with different views about the principles animating our politics can debate and negotiate their visions while still remaining committed to the liberal democratic project. At the same time, if insurance is to remain the central tool of welfare policy, it may be necessary to modify our understanding of what the welfare state, on its own, can do. By itself, social insurance will not eliminate all poverty or rectify all unfair disadvantages, and it certainly will not reduce central government to a “night-watchman” role. Nevertheless, understood in its proper perspective, it can be instrumental in bringing about a roughly fair and stable polity: one in which the need for security is satisfied enough that citizens can concern themselves with higher pursuits, and in which the demand for independence and distinction is paid enough deference that they will be moved to do so.

AC K N OW L E D G M E N T S

This book has been several years in the making, during which I’ve acquired quite a few debts of gratitude. The first is to my academic mentors in the Government Department at Harvard. Richard Tuck offered encouragement and advice in the earliest stages of the research and continued to provide valuable guidance thereafter. Michael Sandel’s incisive queries, and his close engagement with questions of pressing public concern, helped to shape the argument in crucial ways. Finally, Harvey Mansfield, with whom I took my first course in the history of political thought as a first-year student at Harvard College, has been a source of wisdom and encouragement for as long as I have known him. I would not have ventured down this road, nor continued on it for so long, had it not been for his influence. After completing my PhD, I had the good fortune of joining a diverse and vibrant group of scholars at the Edmond J. Safra Center for Ethics at Tel Aviv University. Roy Kreitner closely read and insightfully commented on several chapters of the manuscript. Hanoch Dagan encouraged me to think about various legal and economic questions in a way that broadened the scope of my concern and enriched the project as a whole. Generally, the wide-ranging discussions I’ve had at Safra have been a source of constant intellectual fodder, and I am indebted to each and every one of my colleagues there for their curiosity, critical thinking, and engagement. Two excellent readers provided comments on the entire manuscript, and their influence extends throughout the work. I am deeply grateful to William Deringer for his many informed and constructive suggestions and to Joseph Heath for his challenges and prompts for clarification. A number of other outstanding scholars also read and commented on portions of  the text. I would like to sincerely thank Elizabeth Anderson, Peter Baldwin, David Bellhouse, Pierre Crépel, Lorraine Daston, James Franklin,

184 / Acknowledgments

Alan Hájek, Peter Hall, Ron Harris, Morton Horwitz, Penelope Ismay, Christopher Kelly, Charles McCann Jr., Stephen Stigler, Sandy Zabell, and Michael Zakim for their insightful and very helpful remarks. In so generously sharing their time and expertise, they not only made this work better but also modeled academic collegiality at its best. My editor at Chicago, Charles Myers, patiently shepherded me through the publication process and offered wise counsel along the way. Lisa Wehrle offered many valuable editorial suggestions, and Ekemini Ekpo provided able assistance in checking many of the citations. Any remaining mistakes are my responsibility alone. Portions of this work have been presented at the Center for European Studies at Harvard University; the David Berg Foundation Institute at Tel Aviv University; the Jerusalem Lecture Series on Political Thought and Intellectual History at Hebrew University; the Law and History Workshop at Tel Aviv University; and the Law and Philosophy Workshop at Hebrew University. I am grateful to the conveners of these forums, especially Yiftah Elazar, David Enoch, and David Schorr, for the opportunity to present, as well as to participants for their thoughtful questions and comments. I am also thankful for the financial support of the Faculty of Arts and Sciences at Harvard University, the Edmond J. Safra Center for Ethics at Tel Aviv University, and the Fulbright Program. Last but certainly not least, the encouragement of my family and friends has been indispensable on the long and often-solitary path of writing a book. I would especially like to thank Michael Friedman, Adriana and Jeff Rabkin, and Anna Schmidt for their companionship and steadfast support. Leah and Eitan Friedman provided plenty of pleasant distraction. I dedicate this book to my parents, Irene and Arthur Zabarkes, who have given me everything they could, and whose unending love and generosity have made everything possible.

NOTES

INTRODUCTION

1.

2.

3. 4.

5.

6. 7.

Among member countries of the Organization for Economic Cooperation and Development, public social expenditures in 2018 amounted to just over 20 percent of GDP on average, with the greatest percentage going to pensions followed by health and income support for the working-age population. See OECD, Social Expenditure Update 2019, Public Social Spending is High in Many OECD Countries (Paris: OECD, 2019), https://www.oecd.org/social/soc/OECD2019-Social-Expenditure-Update.pdf. On the meteoric rise in the scope and scale of social insurance programs in wealthy democracies since 1880, see Peter H. Lindert, Growing Public: Social Spending and Economic Growth Since the Eighteenth Century, vol. 1 (Cambridge: Cambridge University Press, 2004), esp. 171–90. A small percentage of Social Security tax revenue comes from the partial taxation of the benefits of recipients whose income exceeds a certain amount. According to Peter Diamond and Peter Orszag, this taxation of benefits will likely play a growing role in the financing of both Social Security and part of the Medicare program. See Peter A. Diamond and Peter R. Orszag, Saving Social Security: A Balanced Approach (Washington, DC: Brookings Institution Press, 2006), 25. Social Security Administration, “Social Security Beneficiary Statistics,” accessed November 29, 2019, https://www.ssa.gov/oact/STATS/OASDIbenies.html. According to Diamond and Orszag, writing in 2006, Social Security benefits then amounted to at least 90 percent of total income for around a third of elderly beneficiaries and 100 percent of income for 20 percent of elderly recipients. Diamond and Orzsag, Saving Social Security, 15. Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Insurance Trust Funds, “Projections of Future Financial Status,” in 2019 OASDI Trustees Report, https://www.ssa.gov/oact/TR/2019/II_D_project.html#10 5057. See, e.g., Martin Feldstein, “Private Accounts Can Save Social Security,” Wall Street Journal, May 2, 2011. Elizabeth Bauer, “So, Hey, Why Not Just Remove the Social Security Earnings Cap?” Forbes, April 28, 2018, https://www.forbes.com/sites/ebauer/2018/04/28/so-hey -why-not-just-remove-the-social-security-earnings-cap/#55a4566e2b23.

186 / Notes to Pages 3–4 8.

9.

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14.

15.

An annuity is a financial product in which a present sum is exchanged for some form of regular payment in the future. In the case of life annuities, the purchaser receives a fixed amount annually for the remainder of his life. Martha Derthick, Policymaking for Social Security (Washington, DC: The Brookings Institution, 1979), 226. Legislation passed in 2000 made it possible to claim benefits before retirement, although earnings over a certain limit can still reduce benefit amounts. Flemming v. Nestor, 363 U.S. 603, 610 (1960). See also Charles A. Reich, “The New Property,” Yale Law Journal 73, no. 5 (April 1964): 733–87. As Martha Derthick points out, designers of the program had clearly recognized that giving benefits in return for contributions lent the impression that coverage was a matter of right, not charity or political expedience. This “confusing mixture of purposes and benefit principles,” as well as “the widely appealing symbolism of insurance,” help to explain the popularity of the program. Derthick, Policymaking for Social Security, 227. As economist Kenneth Arrow influentially put it, it is because “the welfare case for insurance policies of all sorts is overwhelming” that the government “should undertake insurance in those cases where this market, for whatever reason, has failed to emerge.” Arrow’s argument, while acknowledging a “concern for the welfare of others” and the interdependency this creates, focuses on the advantages of social insurance to those who “wish to transfer . . . risks to others for a certain price” but are unable to do so because of the absence of a viable market. Kenneth J. Arrow, “Uncertainty and the Welfare Economics of Medical Care,” American Economic Review 53, no. 5 (December 1963): 961, 954, 946. See also Joseph Heath, “Three Normative Models of the Welfare State,” Public Reason 3, no. 2 (December 2011): 13–43. See, e.g., Michael Walzer, “Socializing the Welfare State,” in Democracy and the Welfare State, ed. Amy Gutmann (Princeton, NJ: Princeton University Press, 1988), 16– 17. An earlier articulation of this view came from the new liberals in Britain and then from their postwar successors, such as T. H. Marshall and Richard Titmuss. The former group helped to reconcile liberalism with a philosophy of welfare, while the latter group forcefully defended this view in the context of the sweeping welfare programs enacted after the Second World War. See Michael Freeden, The New Liberalism: An Ideology of Social Reform (Oxford: Clarendon Press, 1986), esp. 229–38; Andrew Vincent and Raymond Plant, Philosophy, Politics and Citizenship: The Life and Thought of the British Idealists (Oxford: Basil Blackwell, 1984). Both the power-resources theory and the more recent risk-focused account of the class bases of the welfare state articulate a version of this view. See, respectively, Gøsta Esping-Andersen, The Three Worlds of Welfare Capitalism (Princeton, NJ: Princeton University Press, 1990); Philipp Rehm, Jacob S. Hacker, and Mark Schlesinger, “Insecure Alliances: Risk, Inequality, and Support for the Welfare State,” American Political Science Review 106, no. 2 (May 2012): 386–406. The classic exemplar of this approach is Bismarck, who famously set out to use social insurance to make socialism appear less attractive to workers and to direct their loyalty toward the state instead. See, e.g., Asa Briggs, “The Welfare State in Historical Perspective,” European Journal of Sociology 2, no. 2 (1961): 246–50. The question of desert is a controversial one in contemporary theories of distributive justice. Here I use the term descriptively, to indicate that social insurance has historically been tied to conceptions of desert. At the same time, as we will see, moral desert is typically not the explicit rationale for distributive entitlement in the-

Notes to Pages 4–7 / 187

16.

17.

18.

19.

20.

21.

22.

23. 24.

25. 26.

ories of social insurance but tends to be invoked indirectly, in the form of granting benefits based on some form of contribution. A similar interpretation is also emphasized by Theodore Marmor, Jerry Mashaw, and John Pakutka, though without explicit reference to the character or history of probability. See Theodore R. Marmor, Jerry L. Mashaw, and John Pakutka, Social Insurance: America’s Neglected Heritage and Contested Future (Los Angeles: CQ Press, 2014). The term “risk” has taken on various meanings over time and across disciplines. For the most part, I use it in its broad, colloquial sense to mean a possible harm or quantified uncertainty. More technically, risk has been understood as the probability of a loss, the expected value of an adverse event, the degree of dispersion in a distribution, or the uncertainty concerning a loss. Some of the authors I discuss also offered their own, more idiosyncratic definitions. Regardless of which definition of risk one accepts, however, mathematical probability is essential to its quantification. See Plato, Republic, trans. Robin Waterfield (Oxford: Oxford University Press, 1993), 473d; Aristotle, Politics, trans. H. Rackham (Cambridge, MA: Loeb Classical Library, 2005), 1325b37–1328a21, 1330a35–1330b17. For analysis on this theme, see Martha Nussbaum, The Fragility of Goodness: Luck and Ethics in Greek Tragedy and Philosophy, 2nd ed. (Cambridge: Cambridge University Press, 2001). For an influential example, see Immanuel Kant, Perpetual Peace: A Philosophical Sketch, in Kant: Political Writings, 2nd ed., ed. Hans Reiss, trans. H. B. Nisbet (Cambridge: Cambridge University Press, 1991). The literature explicating this position in its various iterations is both large and complex, and I dedicate more space to it later in the book. For influential treatments, see Ronald Dworkin, Sovereign Virtue: The Theory and Practice of Equality (Cambridge, MA: Harvard University Press, 2000); G. A. Cohen, “Part One: Luck Egalitarianism,” in On the Currency of Egalitarian Justice, and Other Essays in Political Philosophy, ed. Michael Otsuka (Princeton, NJ: Princeton University Press, 2011), 3–143. For a discussion of this problem and a rights-based response, see Gerald F. Gaus, “Why All Welfare States (Including Laissez-Faire Ones) Are Unreasonable,” Social Philosophy and Policy 15, no. 2 (1998): 1–33. When I refer throughout this text to “mathematical probability” or “probability theory,” I mean both the interpretation of numerical likelihoods and their calculation, which are closely linked, as we will see. The seminal treatment in contemporary scholarship is Ian Hacking, The Emergence of Probability, 2nd ed. (Cambridge: Cambridge University Press, 2006). Throughout this text, I use the term “likelihood” in its colloquial sense—that is, as synonymous with probability—and not in the technical sense, proposed by R. A. Fisher, meaning the nonadditive probability of a hypothesis. See Hacking, Emergence, 12. On continuities between private and social insurance, see Jyri Liukko, “Genetic Discrimination, Insurance, and Solidarity: An Analysis of the Argumentation for Fair Risk Classification,” New Genetics and Society 29, no. 4 (December 2010): 457–75; Yves Thiery and Caroline Van Schoubroeck, “Fairness and Equality in Insurance Classification,” Geneva Papers on Risk and Insurance 31, no. 2 (April 2006): 190– 211; Ine Van Hoyweghen, Klasien Horstman, and Rita Schepers, “‘Genetics Is Not the Issue’: Insurers on Genetics and Life Insurance,” New Genetics and Society 24,

188 / Notes to Page 7

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28.

29.

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no. 1 (April 2005): 79–98; Kenneth S. Abraham, “Efficiency and Fairness in Insurance Risk Classification,” Virginia Law Review 71, no. 3 (April 1985): 403–51. In a similar vein, Jacob Hacker has shown that private welfare benefits, which are often publicly subsidized and regulated, constitute an important form of social provision. See Jacob S. Hacker, The Divided Welfare State: The Battle over Public and Private Social Benefits in the United States (Cambridge: Cambridge University Press, 2002). The duality of insurance is also brought out in Dan Bouk’s history of American life insurers, How Our Days Became Numbered: Risk and the Rise of the Statistical Individual (Chicago: University of Chicago Press, 2015). The “Janus-face of the welfare state” is noted in Torben Iversen, Capitalism, Democracy and Welfare (Cambridge: Cambridge University Press, 2005), 13. Important works in this field are Hacking, Emergence; James Franklin, The Science of Conjecture: Evidence and Probability before Pascal (Baltimore: Johns Hopkins University Press, 2001); Alain Desrosières, The Politics of Large Numbers: A History of Statistical Reasoning, trans. Camille Naish (Cambridge, MA: Harvard University Press, 1998); Ian Hacking, The Taming of Chance (Cambridge: Cambridge University Press, 1990); Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger, eds., The Probabilistic Revolution, vol. 1, Ideas in History (Cambridge, MA: MIT Press, 1990); Gerd Gigerenzer et al., The Empire of Chance: How Probability Changed Science and Everyday Life (Cambridge: Cambridge University Press, 1989); Lorraine Daston, Classical Probability in the Enlightenment (Princeton, NJ: Princeton University Press, 1988); Theodore M. Porter, The Rise of Statistical Thinking, 1820–1900 (Princeton, NJ: Princeton University Press, 1986). In addition to Bouk’s How Our Days Became Numbered, this wide-ranging literature includes Jonathan Levy, Freaks of Fortune: The Emerging World of Capitalism and Risk in America (Cambridge, MA: Harvard University Press, 2012); Geoffrey Clark et al., eds., The Appeal of Insurance (Toronto: University of Toronto Press, 2010); Richard V. Ericson and Aaron Doyle, eds., Risk and Morality (Toronto: University of Toronto Press, 2003); Tom Baker and Jonathan Simon, eds., Embracing Risk: The Changing Culture of Insurance and Responsibility (Chicago: University of Chicago Press, 2002); François Ewald, L’État providence (Paris: Grasset, 1986); Viviana A. Rotman Zelizer, Morals and Markets: The Development of Life Insurance in the United States (New York: Columbia University Press, 1979). Contributions in this vein include Iversen, Capitalism, Democracy and Welfare; Michael J. Graetz and Jerry L. Mashaw, True Security: Rethinking American Social Insurance (New Haven, CT: Yale University Press, 1999); Peter Baldwin, The Politics of Social Solidarity: Class Bases of the European Welfare States, 1875–1975 (Cambridge: Cambridge University Press, 1990). François Ewald’s L’État providence is a noteworthy exception in having paid sustained attention to social insurance and to the social character of risk. Yet while Ewald offers an incisive discussion of the dual appeal of social insurance and the salience of risk in its early development, specifically in nineteenth-century France, he does not explicitly trace this character to the dualism of probability itself, as I do here. Nor does he explore how shifting interpretations of risk have influenced social policy design. More recently, Emily Nacol has made a lucid contribution in analyzing ideas about risk in early modern political thought in Britain, though her focus is at once historically narrower and conceptually somewhat broader than that of this work. Emily C. Nacol, An Age of Risk: Politics and Economy in Early Modern Britain (Princeton, NJ: Princeton University Press, 2016). Other political theorists and philoso-

Notes to Pages 8–9 / 189

32.

33.

34.

35.

36. 37.

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phers who have explored the role of risk in political theory or welfare policy and to whom I am indebted include Joseph Heath, “The Benefits of Cooperation,” Philosophy and Public Affairs 34, no. 4 (Autumn 2006): 313–51; Michael Freeden, “The Coming of the Welfare State,” in The Cambridge History of Twentieth-Century Political Thought, ed. Terence Ball and Richard Bellamy (Cambridge: Cambridge University Press, 2003), 5–44; Robert E. Goodin, “The End of the Welfare State?” in Ball and Bellamy, Twentieth-Century Political Thought, 202–16; Pierre Rosanvallon, La nouvelle question sociale: Repenser l’État providence (Paris: Éditions du Seuil, 1995); Philippe van Parijs, “Assurance, solidarité, équité: Les fondements éthiques de l’État providence,” Cahiers de l’École des sciences philosophiques et religieuses 12 (1992): 49–72. None has addressed this particular issue from a historical perspective or in booklength form, however. In placing considerable weight on how participants are likely to understand social insurance programs, my approach is similar to the “internal” perspective advocated by J. Donald Moon in his perceptive critique of both rights-based and equalitybased arguments for the welfare state. J. Donald Moon, “The Moral Basis of the Democratic Welfare State,” in Gutmann, Democracy and the Welfare State, 27–52. The perspective of this study is not exclusively internal, however, since I offer a theoretical explanation for the ambiguous character of social insurance that goes beyond the day-to-day experiences of its operation. Of great influence for my own research and thinking have been the work of Hacking, Ewald, and Lorraine Daston, all of whom have written seminal treatments of topics that I take up. Daston’s Classical Probability in the Enlightenment has been particularly important in highlighting various ways in which early ideas about probability reflected ethical ideals and interacted with social practices, including insurance. Another illuminating and relevant genealogy is Tom Baker, “On the Genealogy of Moral Hazard,” Texas Law Review 75, no. 2 (December 1996): 237–92. As Hacking puts it about the concept of probability, “perhaps an understanding of our [conceptual] space and its preconditions can liberate us from the cycle of probability theories that has trapped us for so long.” Hacking, Emergence, 16. In the nineteenth century, for example, some French liberal economists took this view quite literally, interpreting taxes as an insurance premium that ought to be proportional to the value of the goods protected by the state. For several references and further discussion, see Nathalie Sigot, “Utility and Justice: French Liberal Economists in the Nineteenth Century,” European Journal of the History of Economic Thought 17, no. 4 (October 2010): 782. On the relationship between insurance and liberalism, see also Liz McFall, “‘The Rules of Prudence’: Political Liberalism and Life Insurance,” in Clark et al., Appeal of Insurance, 127–50. See also Otto Gierke, Natural Law and the Theory of Society, 1500–1800, trans. Ernest Barker (Boston: Beacon Press, 1957), 112–13, incl. n. 110. As discussed by Aristotle in Book IV of the Politics, the mixed regime is characterized by a mixture of oligarchy and democracy and more broadly as mediating popular passions and claims. Aristotle, Politics, 1293b22–1294b40. For a good discussion of the role of competing distributive principles in Aristotle’s political science, see Bernard Yack, “Community and Conflict in Aristotle’s Political Philosophy,” Review of Politics 46, no. 1 (January 1985): 92–112. See Ulrich Beck, Risk Society: Towards a New Modernity, trans. Mark Ritter (London: Sage, 1992); Mary Douglas and Aaron Wildavsky, Risk and Culture: An Essay on the Selection of Technical and Environmental Dangers (Berkeley: University of California

190 / Notes to Pages 9–11

39.

40.

41.

42.

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Press, 1983). Beck catalogs the emergence of an advanced modernity characterized by the production of risks, specifically pervasive, often global threats resulting from technological and economic development itself. These new risks are more systemic, less visible, and more likely to be mediated through scientific expertise than those that had their origin in earlier processes of industrialization. For their part, Douglas and Wildavsky argue that risks appear more or less salient to citizens and experts depending on their moral and political commitments. On their interpretation, understandings of risk are both collective and contestable, fought over by those with different visions about the best way to organize social life. Another illuminating contribution in this vein is Arwen P. Mohun, Risk: Negotiating Safety in American Society (Baltimore: Johns Hopkins University Press, 2013). This point is also emphasized in Marmor, Mashaw, and Pakutka, Social Insurance, 6–9. The authors list birth into a poor family, early death of a family member, ill health, involuntary unemployment, disability, and outliving one’s savings as the risks protected by social insurance schemes in virtually all advanced industrial societies. See ibid., 17–33. Abram De Swaan identifies disability, old age, disease, and unemployment, as well as in some cases the financial burden of children, as the “risks that threatened to disrupt the wage-earner’s life” and that have therefore been “considered to be a collective concern,” as expressed in welfare policy. Abram De Swaan, In the Care of the State: Health Care, Education, and Welfare in Europe and the USA in the Modern Era (Cambridge: Polity Press, 1988), 177. I also note here Hacking’s suggestive idea of an “economic history of probability,” based on his observation that many of the most important thinkers in this tradition were motivated by problems surrounding the means of production and the organization of the state. Hacking, Emergence, 5. In the same vein, while I consider arguments for and against various interpretations of probability, it is not my intention to rigorously defend any particular view. This is not the same as endorsing relativism with respect to probability. Rather, the purpose of this book is to illuminate how different interpretations of this concept have interacted with political thinking and practice. While this exercise does shed valuable light on the interpretations that I consider, it would exceed the scope of this work to propose or defend a coherent account. Instead, I hope to make scholars of politics aware of the need to think seriously about probability, and to suggest a few of the criteria that a compelling theory would fulfill. Peter A. Hall, “Policy Paradigms, Social Learning, and the State: The Case of Economic Policymaking in Britain,” Comparative Politics 25, no. 3 (April 1993): 275– 96. Over the past several decades, political scientists have debated how exactly it is that ideas influence policymaking. For reviews of the recent literature and interesting applications, see the contributions to Ideas and Politics in Social Science Research, ed. Daniel Béland and Robert Henry Cox (Oxford: Oxford University Press, 2010). Hall, “Policy Paradigms,” 279. A critique of the concept and subsequent uses may be found in Pierre-Marc Daigneault, “Reassessing the Concept of Policy Paradigm: Aligning Ontology and Methodology in Policy Studies,” Journal of European Public Policy 21, no. 3 (March 2014): 453–69. Daigneault, “Reassessing,” 461–62. See also John Hogan and Michael Howlett, “Reflections on Our Understanding of Policy Paradigms and Policy Change,” in Policy Paradigms in Theory and Practice: Discourses, Ideas and Anomalies in Public Policy Dynamics, ed. John Hogan and Michael Howlett (New York: Palgrave Macmillan, 2015), 5–11.

Notes to Pages 11–18 / 191 44. For the view that a paradigm may comprise “contradictory but relatively enduring normative patterns and institutional settlements” that hold “general sway over a society for a period of time,” see Daniel Wincott, “Ideas, Policy Change, and the Welfare State,” in Béland and Cox, Ideas and Politics, 149, citing Jane Jenson, “Paradigms and Political Discourse: Protective Legislation in France and the United States before 1914,” Canadian Journal of Political Science/Revue Canadienne de science politique 22, no. 2 (June 1989): 235–58. 45. Hall, “Policy Paradigms,” 289. 46. It may be helpful to clarify the difference between a “paradigm” and a “regime.” In this book, the notion of a paradigm serves an explanatory purpose, highlighting in rough terms the interface between the philosophical developments I trace and real-world policy outcomes. The notion of a regime serves a more fundamental theoretical purpose. A regime, or constitution, refers to the character of a political order, and in particular to the claims about justice that define it. My designation of social insurance as a mixed regime is thus meant to convey its character as a kind of political order (more limited than the Aristotelian conception, to be sure) that blends different distributive principles. 47. This distinction is also made in Briggs, “Welfare State,” 228. Briggs, however, identifies the welfare state more narrowly as advancing the second vision. 48. A number of important works have analyzed the legal background of early mathematical probability theory, including Rüdiger Campe, The Game of Probability: Literature and Calculation from Pascal to Kleist, trans. Ellwood H. Wiggins Jr. (Stanford, CA: Stanford University Press, 2012); Franklin, Science of Conjecture; Daston, Classical Probability; and Ernest Coumet, “La théorie du hasard est-elle née par hasard?,” Annales: Economies, Sociétés, Civilisations, 25, no. 3 (May–June 1970): 574–98. 49. As I use the term, “probabilistic justice” includes what is commonly known as actuarial fairness, or the idea that individuals should pay insurance premiums that directly reflect their own risks. Probabilistic justice is broader than actuarial fairness, however, in referring to the idea that the equality to which distributive claims should correspond is a function of individuals’ equal vulnerability to uncertain events. It can therefore be applied to justify insurance practices even when probability values refer to a class rather than individual instances or, although with greater difficulty, when they are understood as primarily epistemic in character. I will have more to say about this term and its relationship to actuarial fairness further on, particularly in chapter 1. 50. See, e.g., Rehm, Hacker, and Schlesinger, “Insecure Alliances”; Torben Iversen and David Soskice, “Democratic Limits to Redistribution: Inclusionary versus Exclusionary Coalitions in the Knowledge Economy,” World Politics 67, no. 2 (April 2015): 185–225. 51. For an account of justice that invokes and defends a plurality of distributive principles, see David Miller, Principles of Social Justice (Cambridge, MA: Harvard University Press, 1999). CHAPTER ONE

1. 2.

For an articulation and defense of the distinction, see Heath, “Benefits of Cooperation,” 323–24. It, too, can therefore be understood as a tool for cooperation and mutual aid, particularly for merchants who would not be able to conduct their businesses without it. Indeed, this was one element of early juridical defenses of insurance as licit under

192 / Notes to Pages 19–20 canon law. For examples and discussion, see Giovanni Ceccarelli, “Risky Business: Theological and Canonical Thought on Insurance from the Thirteenth to the Seventeenth Century,” Journal of Medieval and Early Modern Studies 31, no. 3 (Fall 2001): 611, 629. 3. For a relatively late example of a discussion that moves freely between the two rationales, see Allan H. Willett, The Economic Theory of Risk and Insurance (New York: Columbia University Press, 1901), esp. 116–24. Similar distinctions have surfaced throughout the history of thinking about insurance, as we will see in the chapters that follow. Condorcet, for example, writing in the late eighteenth century, distinguished between voluntary and involuntary exchanges of risk, the former being the province of the market and the latter of the law. Others, writing in the midnineteenth and early twentieth centuries, distinguished between fixed premium and mutual insurance, the former entailing set prices for the transfer of risk and the latter involving payments that could fluctuate depending on the expenses of the association. 4. Daniel Bernoulli, “Exposition of a New Theory on the Measurement of Risk,” trans. Louise Sommer, Econometrica 22, no. 1 (January 1954): 24–25. 5. See, e.g., Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, no. 2 (March 1979): 264; and, more recently, David A. Moss, When All Else Fails: Government as the Ultimate Risk Manager (Cambridge, MA: Harvard University Press, 2002), 26. 6. An important articulation of the view that utility curves are not always concave came from Milton Friedman and L. J. Savage, “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56, no. 4 (August 1948): 279–304. Friedman and Savage continued to relate risk preferences to initial levels of wealth, however. For a more recent discussion that treats risk aversion as a preference for certainty over uncertainty, analytically distinct from diminishing marginal utility, see Ronen Avraham, “The Law and Economics of Insurance—A Primer,” Connecticut Insurance Law Journal 19, no. 1 (Fall 2012): 37. 7. Even if most people are risk averse, as many economists maintain, this does not preclude the existence of different risk preferences in principle. See Tom Baker and Peter Siegelman, “Behavioral Economics and Insurance Law: The Importance of Equilibrium Analysis,” in The Oxford Handbook of Behavioral Economics and the Law, ed. Eyal Zamir and Doron Teichman (New York: Oxford University Press, 2013), 494. For a recent philosophical analysis that helpfully distinguishes between the two concepts, see Lara Buchak, Risk and Rationality (Oxford: Oxford University Press, 2013). 8. For a relatively late example of this tendency, see Alfred Marshall, Principles of Economics, 8th ed. (London: Macmillan, 1920; Hampshire, UK: Palgrave Macmillan, 2013), 693–94. 9. As a result of such preferences, the agreement to pool risks will depend in principle not only on individuals’ probability estimates—which, as we will see, are often a matter of dispute—but also on features of their personalities that have nothing to do with probability. On a related note, Xavier Landes points out the practice among insurers of adjusting premiums based on the kind of coverage that policyholders select, or in other words based on their risk preferences. Xavier Landes, “How Fair Is Actuarial Fairness?,” Journal of Business Ethics 128, no. 3 (May 2015): 530. 10. For an excellent philosophical discussion of the classification problem in probabil-

Notes to Pages 20–23 / 193

11. 12.

13.

14.

15.

16.

17. 18. 19. 20. 21. 22.

23.

ity, see Alan Hájek, “The Reference Class Problem Is Your Problem Too,” Synthese 156, no. 3 (June 2007): 563–85. See also Landes, “How Fair,” 530. Karl H. Van D’Elden, “The Development of the Insurance Concept and Insurance Law in the Middle Ages,” in The Medieval Tradition of Natural Law, ed. Harold J. Johnson (Kalamazoo: Medieval Institute, Western Michigan University, 1987), 192–95. For examples, see Charles Farley Trennery, The Origin and Early History of Insurance (London: P. S. King, 1926), 107. In the case of the various efforts by the Roman government to indemnify traders, the merchants paid by simply rendering their services. In exchange, they received a fixed payment and a promise that the emperor would cover losses once incurred. Ibid., 119–20. Many medieval guilds seem to have operated by collecting fixed fees in advance and/or an equal assessment from each member after any one was struck with misfortune. Van D’Elden, “Development,” 194–95. The Greek slave policies tied the amount of benefits to the premiums paid in, but it is not clear whether they made any effort to grade those contributions in accordance with the chances of the loss. Ibid., 192. For example, historian Geoffrey Clark includes early reversionary annuity societies and redistributive insurance schemes in his consideration of the early life insurance market, despite the fact that unlike premium insurance they did not involve explicit attempts to quantify risks. See Geoffrey Clark, Betting on Lives: The Culture of Life Insurance in England, 1695–1775 (Manchester, UK: Manchester University Press, 1999), 4–7, 72. See Christopher Ebert, “Early Modern Atlantic Trade and the Development of Maritime Insurance to 1630,” Past and Present 213, no. 1 (November 2011): 87–114; Florence Edler De Roover, “Early Examples of Marine Insurance,” Journal of Economic History 5, no. 2 (November 1945): 173. In addition to the loan-type arrangements discussed here, merchants and shipowners reduced their exposure to sea risks by owning stakes in a number of different ships, sending their goods on a number of different voyages, and entering into agreements to share one another’s losses. See Ebert, “Early Modern Atlantic Trade,” 102 (which describes “diversifying portfolios” as one of the most common risk-reduction strategies); Violet Barbour, “Marine Risks and Insurance in the Seventeenth Century,” Journal of Economic and Business History 1, no. 4 (1929): 570. The Digest of Justinian, 18.1.35.7, 18.6.1, 19.2.13.5, and 22.2.4, all cited in Franklin, Science of Conjecture, 260. De Roover, “Early Examples,” 178. Ibid., 178–79. Violet Barbour also distinguishes insurance by its involvement of “persons not otherwise interested in the ventures.” Barbour, “Marine Risks,” 571. De Roover, “Early Examples,” 185. For example, the fourteenth-century account book of a Florentine firm refers to an 8.75 percent rischio charged by a shipping company that had agreed to deliver goods at its own peril but at the buyer’s expense. Ibid., 181–82. Both Roman and late medieval maritime loans operated with the understanding, implicit or explicit, that a lender could assume the possible losses of a venture in exchange for compensation in the form of interest. Franklin concludes from such evidence that Romans understood risk as “almost a detachable entity in

194 / Notes to Pages 23–24

24.

25.

26.

27. 28.

29.

30.

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itself,” and notes their conceptual advance in seeing “hopes and perils as quantities that can have a price.” Franklin, Science of Conjecture, 260. See also Sylvain Piron, “L’apparition du resicum en Méditerranée occidentale aux XIIème-XIIIème siècles,” in Pour une histoire culturelle du risque. Genèse, évolution, actualité du concept dans les sociétés occidentales, ed. Emmanuelle Collas-Heddeland et al. (Strasbourg: Éditions Histoire et Anthropologie, 2004), 59–76. According to historian John Noonan, early usury theory rested on the view that risk was a mark of ownership, not a claim to further profit. A capitalist’s earnings therefore derived from the use of his money rather than from his acceptance of risk. Yet beginning in the early fifteenth century—that is, shortly after the birth of insurance—commentators began to disregard this doctrine and allow that risk could be exchanged independent of title. See John T. Noonan Jr., The Scholastic Analysis of Usury (Cambridge, MA: Harvard University Press, 1957), 202–4. De Roover notes that once insurance was established as a business, it typically involved multiple independent underwriters insuring each venture. De Roover, “Early Examples,” 180, 187–88. For evidence that alternative forms of risk management in maritime trade involved parties to the business agreement who simply subdivided the potential dangers among themselves, see A. D. M. Forte, “Marine Insurance and Risk Distribution in Scotland before 1800,” Law and History Review 5, no. 2 (1987): 406. Some early juridical and theological contributions on insurance emphasized this point, arguing that the insurer is entitled to the premium for having received or assumed the risk, even without a concomitant transfer of the property being insured. See Ceccarelli, “Risky Business,” 618–19. Franklin, Science of Conjecture, 274. As a result, many loan agreements avoided mentioning the interest payment, although scholars assume that some form of compensation was given to the insurer before the voyage. See Humbert O. Nelli, “The Earliest Insurance Contract: A New Discovery,” Journal of Risk and Insurance 39, no. 2 (June 1972): 215–20. For a survey of scholastic treatments of usury in sea loans, see Noonan, Scholastic Analysis, 145–51. Beginning at the turn of the fifteenth century, several leading moralists declared insurance licit because selling risk involves the assumption of a burden in exchange for compensation. Noonan, Scholastic Analysis, 203. Ceccarelli provides an extended discussion of several of these. One of them, Spanish Dominican jurist Domingo de Soto, in what Ceccarelli calls an “exemplary sixteenth-century contribution,” defended insurance as licit precisely because the assumption of the risk could be evaluated in terms of a price. Ceccarelli, “Risky Business,” 610–11. One obscure fifteenth-century scholar objected to insurance on the grounds that one could not transfer a risk without transferring ownership, but his view was quickly drowned out by the chorus of jurists who accepted that the assumption of risk in itself entitled the capitalist or insurer to a reward. Noonan, Scholastic Analysis, 203–5. Franklin, Science of Conjecture, 274–78. Juristic writings defending the sale of risk also played a role in this outcome: The fifteenth-century Portuguese clergyman João Sobrinho, for example, listed insurance contracts as an exception to the general rule in his comprehensive treatment of commercial practices that could be considered usurious. Later authors followed his ideas in light of ongoing developments in international commerce. António Almodovar and José Luís Cardoso, A History of Portuguese Economic Thought (London: Routledge, 1998), 14–15. According to the

Notes to Pages 24–26 / 195

32. 33.

34.

35. 36.

37. 38.

39. 40. 41. 42. 43.

44. 45.

authors, Portuguese jurists’ subsequent acceptance of risk, and its compensation, in business practices indicated “a new ethical attitude towards the legitimacy of earnings arising from acts and contracts of purchase and sale.” Ibid., 17. Ibid.; Daston, Classical Probability, 210–23. Franklin, Science of Conjecture, 262–69; Noonan, Scholastic Analysis, 281–83, 289. For further discussion of conceptions of the just price in scholastic thought, see Joel Kaye, Economy and Nature in the Fourteenth Century: Money, Market Exchange, and the Emergence of Scientific Thought (New York: Cambridge University Press, 1998), 87–101. Noonan, Scholastic Analysis, 147. Franklin quotes the Portuguese jurist Santerna, who explained in his 1488 On Insurance and Merchants’ Bets that “the insurer sells only the hope of a future outcome. . . . From the fact that this hope is uncertain, it might not seem capable of estimation.” Yet it is possible to estimate the just price, not “at how much the thing or goods would be worth in case the peril was realized, but at how much the doubtful event should likely be estimated. In which case the price seems to be constituted with respect to that hope.” Santerna, Assecurationibus et sponsionibus mercatorum, pt. 5, sec. 3 and 4, quoted in Franklin, Science of Conjecture, 277. Barbour, “Marine Risks,” 571. A. B. Leonard, “Introduction: the Nature and Study of Marine Insurance,” in Marine Insurance: Origins and Institutions, 1300–1850, ed. A. B. Leonard (Hampshire, UK: Palgrave Macmillan, 2016), 6. Andrea Addobbati, “Italy 1500–1800: Cooperation and Competition,” in Leonard, Marine Insurance, 60. Franklin notes that in sixteenth-century Antwerp, the center of commercial developments at the time, little distinction was drawn in general between entrepreneurship and speculation, and that in particular insurance contracts were “used as much for speculation as for the reduction of risks.” Franklin, Science of Conjecture, 279. For more on the blurry line between prudence and speculation in the practice of insurance, see Clark, Betting on Lives, esp. 21–27; Barbour, “Marine Risks,” 591. Herman van der Wee, The Growth of the Antwerp Market and the European Economy (The Hague: Martinus Nijhoff, 1963), 365. Addobbati, “Italy 1500–1800,” 60–61. Clark, Betting on Lives, 3–4, 13–21, 40–53. Piron, “L’apparition du resicum,” 62. Translations are mine unless otherwise noted. In a similar vein, Ceccarelli suggests that “chance, before being conceived in probabilistic and statistical terms,” had to become tradable. Ceccarelli, “Risky Business,” 633. Whereas Ceccarelli emphasizes the influence of the earlier “moral economy” on subsequent Catholic theologians, however, I am interested in its influence on subsequent accounts of probability and corresponding justifications of insurance. This point has been brought out thoroughly by Daston, Classical Probability, 6–30, drawing on Coumet’s “La théorie du hasard.” For a survey of treatises on commercial arithmetic in fifteenth- and sixteenth-century France, including their treatment of the Rule of Fellowship, see David Murray, Chapters in the History of Bookkeeping, Accountancy, and Commercial Arithmetic (New York: Arno Press, 1978), 423–45. For further discussion and citations, see Daston, Classical Probability, 20. For an overview of canon law and later scholastic treatments of this issue, see Franklin, Science of Conjecture, 263–69, 285–88. See also Coumet, “La théorie du hasard,” 591.

196 / Notes to Pages 26–28 46. See Edith Dudley Sylla, “Introduction,” in Jacob Bernoulli, The Art of Conjecturing, trans. Edith Dudley Sylla (Baltimore: Johns Hopkins University Press, 2006), 63– 70. Some theologians had also defended the legality of gambling in cases where there was “equality of uncertainty, peril or chance.” Daston, Classical Probability, 23. 47. Antoine Arnauld and Pierre Nicole, La logique, ou l’Art de penser: Contenant, outre les Regles communes, plusieurs observations nouvelles propres à former le jugement (Paris: Charles Savreux, 1662), 467–68. 48. Jean Domat, Les Loix civiles dans leur ordre naturel; le droit public et Legum delectus (1689–94), nouvelle édition, vol. 1 (Paris: Le Clerc, 1777), 29–30. 49. Coumet points to the similarity between this statement and Pascal’s arithmetic triangle, which provided the mathematical foundation for combinatorial probability. Coumet, “La théorie du hasard,” 591. 50. According to Ceccarelli, by the end of the sixteenth century, scholastic thinkers had begun to debate this issue as related to the assumption of risk, and the idea emerged that the just price of an insurance premium depends on both cargo value and the voyage risk. By the middle of the seventeenth century, he finds one thinker insisting that the equity of such contracts must be considered from a geometrical or distributive rather than proportional or commutative perspective. This is precisely the distinction and the emphasis that I also find in mathematical probability. Ceccarelli, “Risky Business,” 627–28. 51. As Hacking explains, the popular legend that this correspondence marked the birth of probability is wrong in its fine details, but “encapsulates the truth.” In the decade around 1660, he shows, a number of people arrived independently at the idea of probability. See Hacking, Emergence, 11. 52. My understanding of the correspondence is indebted to Franklin, Science of Conjecture, 306–13. 53. Sylla, “Introduction,” 71. 54. Several commentators have pointed out that the concept of expectation used in these early probabilistic writings differs substantially from that employed later in frequentist probability theory. Unlike later probabilists, who explicitly distinguished probability as a relative frequency from outcome value, the early probabilists tended to treat expectation as the fundamental unit of analysis, a distinct entity with its own economic worth. See Daston, Classical Probability, 26; Sylla, “Introduction,” 71. 55. Bernoulli, Art of Conjecturing, 133. 56. For example, in a game involving an equal chance of winning either seven or three coins, the player’s expectation is five. One can then prove that five is the fair price of this wager by imagining another fair wager in which the player would pay the same price for an equivalent lot. Huygens’s equivalent wager in this case entails two players, each of whom puts up five coins with the stipulation that whoever wins the total sum will give the loser three. With five coins, then, “I could again arrive at a situation in which I had an equal expectation of getting three or seven coins, contending on equal terms” with another person. Ibid. See also Hacking, Emergence, 96. 57. This point is indebted to Daston, Classical Probability, 25–26. 58. Thanks to the rules of the game, each has an equal likelihood of winning, and even if each player ends up with different individual chances, their sum will always equal the total pool.

Notes to Pages 28–31 / 197 59. Bernoulli, Art of Conjecturing, 134. 60. On the salience of games among the aristocracy and their appeal for mathematicians, see Sylla, “Introduction,” 14–17. 61. Bernoulli, Art of Conjecturing, 134. 62. See ibid., 141. 63. Sylla points out that both Huygens and Bernoulli use the Latin sors as a synonym for the Latin expectatio, although sors means both capital and expected payoff. Thus “sors, which means the capital for a loan or investment, can also be used for the expectation in a game of chance because in a fair game one should always pay as much to play as one expects to receive in prizes.” This amount has an economic value and is not only a relative frequency. Sylla, “Introduction,” 71 (all italics original, unless otherwise noted). Sylla also notes that in medieval Venetian commercial law, sors was a person’s share in a partnership, as when a ship traveled to the East and investors had an agreement regarding how to divide the earnings once the cargo was sold. Ibid., 121. 64. See ibid., 51. 65. For these thinkers, as Hacking so well explains, probability was simultaneously epistemic and aleatory, and therefore a reflection both of our knowledge and of the physical world. Possibility was similarly dualistic. As a result, it was not necessarily circular to conceive that one probability value could be objectively equal to another because the two cases are equally possible. Hacking, Emergence, 122–23. On Leibniz’s contribution, see ibid., 125; Wolfgang David Cirilo de Melo and James Cussens, “Leibniz on Estimating the Uncertain: An English Translation of De incerti aestimatione with Commentary,” Leibniz Review 14 (December 2004): 31–32. 66. Gottfried Wilhelm Leibniz, “On Estimating the Uncertain” (1678), trans. Wolfgang David Cirilo de Melo, Leibniz Review 14 (December 2004): 43. 67. In other words, Leibniz is not saying here that we assign equal probabilities to the players because we do not know who will win but that the game is set up in such a way that their odds of winning are considered to be physically equal. See Cirilo de Melo and Cussens, “Leibniz on Estimating the Uncertain,” 33. 68. Leibniz, “On Estimating the Uncertain,” 46. 69. Ibid., 44. 70. Ibid., 45. 71. Aristotle, Nicomachean Ethics, trans. Robert C. Bartlett and Susan D. Collins (Chicago: University of Chicago Press, 2011), 1132a30. 72. Ibid., 1132a1–6. 73. Ibid., 1133a10–20. 74. Ibid., 1130b30–1131a5. 75. Ibid., 1131b30–31, cf. 1131b12–14. 76. Ibid., 1131a28–29. 77. See Kaye, Economy and Nature, 80, 133–37, 158–62. 78. Ceccarelli, “Risky Business,” 627–28. 79. Aristotle speaks of proportionality in the context of reciprocity as well, which concerns exchange and does not fit simply with either type of justice. In “communities concerned with exchange, the just in this sense—reciprocity in accord with proportion and not in accord with equality—holds them together.” Aristotle, Nicomachean Ethics, 1132b32–34. According to Kaye, the shift from an arithmetic to a geometric model in the early fourteenth century reflected a shift in ideas about what consti-

198 / Notes to Pages 32–36

80. 81. 82.

83. 84. 85.

86. 87. 88. 89.

90. 91. 92. 93.

94. 95. 96. 97. 98. 99.

tuted equality: from a model based on knowable values to one based on approximate values; from an emphasis on individual judgment to the idea of a suprapersonal system of valuation. Kaye, Economy and Nature, 80, 111–15. Pierre Rémond de Montmort, Essay d’analyse sur les jeux de hazard (Paris: Jacque Quillau, 1708), 2. Ibid., 3. For another example of the importance of both commutative and distributive justice in scholastic analyses of contracts, see the discussion of the mons pietatis in Noonan, Scholastic Analysis, 296–99. See Franklin, Science of Conjecture, 288. Coumet, “La théorie du hasard,” 591–92. While Leibniz at times speaks the language of commutative justice—for example, in explaining at the beginning of his article that each player “buys his hope with . . . a fair price”—his normative argument concerns equity or proportion in divvying up a common resource. Leibniz, “On Estimating the Uncertain,” 43. The priority he thereby places on distributive justice may be a result of the fact that he regarded it as more authoritative than “strict” or commutative justice. See his “Meditation on the Common Concept of Justice,” in Leibniz: Political Writings, 2nd ed., ed. Patrick Riley (Cambridge: Cambridge University Press, 1988), 60. Aristotle, Nicomachean Ethics, 1131a24. Bernoulli, Art of Conjecturing, 140. Ibid. Daston argues that the “seemingly neutral techniques and applications” pertaining to mortality statistics thus altered the theory itself, giving rise to a new interpretation of probability. Daston, Classical Probability, 135. I do not intend to dispute this claim as a matter of historical development. Nevertheless, my argument emphasizes the conceptual continuity between the a priori and a posteriori accounts, insofar as both take the equally likely case as their unit of distributive concern. Bernoulli, Art of Conjecturing, 327. Ibid. Ibid., 328. Thus, for example, Edmond Halley’s discussion of his table provided a means of calculating both the pricing of life insurance and the valuation of annuities. See E. Halley, “An Estimate of the Degrees of the Mortality of Mankind, Drawn from Curious Tables of the Births and Funerals at the City of Breslaw; With an Attempt to Ascertain the Price of Annuities upon Lives,” Philosophical Transactions 17 (1693): 602. Daston argues, however, that by the second quarter of the eighteenth century, Abraham de Moivre’s Treatise of Annuities on Lives was typical in excluding insurance from the possible kinds of aleatory contracts that had been discussed by earlier thinkers. Daston, Classical Probability, 137. See Daston, Classical Probability, 136–37. See Hacking, Emergence, 111–21. John De Witt, Treatise on Life Annuities (1671), in Robert Gibbes Barnwell, A Sketch of the Life and Times of John De Witt (New York: Pudney and Russell, 1856), 86–88. Ibid., 98–99. Ibid., 99. What may be accidental is that the model succeeded, as Ian Hacking notes. Hacking locates the coincidence in the fact that the statistics available at the time, which concerned mortality, confirmed the model of equal chances. Hacking, Emergence,

Notes to Pages 36–38 / 199

100.

101.

102.

103.

104. 105. 106.

107.

108.

109. 110.

121. Yet the shared model appears less accidental when one considers that the first examples of life insurance mathematics emerged directly out of probabilistic treatments of games of chance and were therefore heavily influenced by the latter’s normative concerns and analytic framework. De Witt, Treatise, 96–102. For analysis, see Anders Hald, A History of Probability and Statistics and Their Applications before 1750 (Hoboken, NJ: John Wiley, 2003), 124–31. For discussion of the two approaches, see Hald, History of Probability and Statistics, 128–41. As Hald notes, Halley’s calculation of the expectation of payments made to the living became a fundamental quantity in life insurance, known as a pure endowment. Ibid., 141. On Halley’s proposed uses, including the significance of reversionary annuities as a means of supporting the families of those who had movable property but no land, see David R. Bellhouse, Leases for Lives: Life Contingent Contracts and the Emergence of Actuarial Science in Eighteenth-Century England (Cambridge: Cambridge University Press, 2017), 36–47. A further clue to Halley’s concerns is found in a letter containing a brief additional commentary on his analysis of the Breslaw bills. Discussing the question of population and in particular the reluctance of some people to marry and have children, Halley noted the need for “effectual care to provide for the subsistence of the poor,” whose “difficulty of subsisting is occasioned by the unequal distribution of possessions, all being necessarily fed from the earth, of which yet so few are masters.” Edmond Halley, “Further Considerations on the Breslaw Bills of Mortality,” Philosophical Transactions 17 (1693): 655–56. He was thus clearly aware of the potential of life insurance mathematics for addressing the difficulties of subsistence among the poorer classes. On some important differences between Halley’s political aims and those of later thinkers such as Richard Price, however, see Peter Buck, “People Who Counted: Political Arithmetic in the Eighteenth Century,” Isis 73, no. 1 (March 1982): 28–45. Halley, “Estimate,” 602. Ibid., 603. Abraham de Moivre, The Doctrine of Chances: or, A Method of Calculating the Probabilities of Events in Play, 2nd ed. (London: H. Woodfall, 1738), 212. Halley’s calculation was different: He considered the odds of survival to be the ratio of survivors at a given age to those who had passed away during the previous year. This generates slightly divergent results from de Moivre’s formula, which takes the original number of members in the group as its denominator. Richard Price, “Observations on the Expectations of Lives, the Increase of Mankind, the Influence of Great Towns on Population, and Particularly the State of London with Respect to Healthfulness and Number of Inhabitants. In a Letter from Mr. Richard Price, F. R. S. to Benjamin Franklin, Esq; LL.D. and F. R. S.,” Philosophical Transactions 59 (1769): 90–92. Daston notes the same difference in purpose in commenting on the correspondence between Christiaan Huygens and his brother on how to calculate life expectancy. Daston, Classical Probability, 135. I am grateful to David Bellhouse for pointing out that the difference is important for calculating both single-life and joint-life annuities. Price, “Observations on the Expectations of Lives,” 91. Ibid., 92.

200 / Notes to Pages 39–40 111. Ibid., 91. 112. The most sophisticated of these was probably the Scottish Widows’ fund, discussed and in later editions praised by Richard Price in his Observations on Reversionary Payments, 6th ed. (London: T. Cadell and W. Davies, 1803), 108–15. 113. Clark, Betting on Lives, 122–23. 114. For example, the Royal Exchange and London Assurance offered a flat rate but limited their coverage to short-term policies. They also charged a higher premium to those undertaking very long journeys and excluded customers with smallpox. Daston, Classical Probability, 170–71. The Amicable Society offered long-term life insurance, but its model of fixed payments and equal dividends required it to limit admission to men in good health between ages twelve and forty-five and to cap its membership at 2,000. Most of the later widows’ funds did scale members’ payments to age, but they fixed those payments primarily by guesswork and did not consider that claims on the fund would increase as their member population aged. As a result, they failed at an alarming rate. Ibid., 169. Clark contrasts the “spectacularly disastrous results” of Assheton’s Annuity Scheme under Mercers’ Company management with the Church of Scotland’s scheme, which carefully traced the habits and mortality experience of its members and was consequently able to anticipate the cost of its reversionary annuities and change its fees accordingly. Clark, Betting on Lives, 134, 144–46. 115. Daston, Classical Probability, esp. 163–82. 116. See Bellhouse, Leases for Lives, 3–7, for an overview of this argument. 117. Daston, Classical Probability, 174–75. See also A. Fingland Jack, An Introduction to the History of Life Assurance (London: P.S. King, 1912), 233. 118. See Augustus De Morgan, “Some Account of James Dodson, F.R.S.,” Journal of the Institute of Actuaries and Assurance Magazine 14, no. 5 (October 1868): 346. 119. Society for Equitable Assurances, A Short Account of the Society for Equitable Assurances on Lives and Survivorships (London, 1762), 6, 20. 120. Richard Price, who served as advisor to the Equitable, critiqued the plan of London’s Amicable Society as inequitable for a variety of reasons, among them its “requiring the same payments from all persons under 45, without regarding the differences of their ages; whereas, the annual payments of a person admitted at 45, ought to be double the annual payment of a person admitted at 12.” Richard Price, Observations on Reversionary Payments; on Schemes for Providing Annuities for Widows, and for Persons in Old Age; on the Method of Calculating the Values of Assurances on Lives; and on the National Debt, in Two Volumes, 7th ed., vol. 1 (London: T. Cadell and W. Davies, 1812), 164. The Equitable, by contrast, “assures any sums or reversionary annuities on any lives, for any number of years as well as for the whole continuance of the lives, at rates settled by particular calculation; and in any manner that may be best adapted to the views of the person assured. That is, either by making the assured sums payable certainly at the failure of any given lives, or on condition of survivorship: and also either by taking the price of the assurance in one present payment, or in annual payments during any single or joint lives, or any terms less than the whole continuance of the lives.” Ibid., 176. William Morgan, another of the Equitable’s early advisors, noted of the Amicable’s approach that “nothing could exceed the injustice and improvidence of such a plan, which made no distinction between the old and the young in its premiums.” William Morgan, A View of the Rise and Progress of the Equitable Society (London: Longman, Rees, Orme, Brown, and Green, 1828), 13.

Notes to Pages 40–43 / 201 121. According to Morgan’s account, however, it took several years before the Equitable attempted to manage its finances with any mathematical rigor. See Morgan, Equitable Society, 16–19. 122. William Morgan, The Principles and Doctrine of Assurances, Annuities on Lives, and Contingent Reversions, Stated and Explained (London: Longman, Hurst, Rees, Orme, and Brown, 1821), 2. 123. On this point, see also Price, “Observations on the Expectations of Lives,” 90–93. 124. See Morgan, Equitable Society, 53–60. Morgan noted, however, that doing so with “perfect justice” was impossible, as it would have required significant feats of information gathering and calculation each time a division took place. 125. Society for Equitable Assurances, Short Account, 3. 126. While fire insurance had existed in England since the 1680s, companies did not analyze their underwriting data or share extensive data among themselves until the 1820s. As a result, they could not precisely measure the differential rates of fire in different buildings or, indeed, place their pricing on any kind of rigorous empirical footing. Robin Pearson, “Fire, Property Insurance, and Perceptions of Risk in Eighteenth-Century Britain,” in Clark et al., Appeal of Insurance, 97–98. Clark notes that marine insurers did raise or lower premiums depending on certain distinguishing factors, but their attention to the particular risks of each voyage directed them away from a statistical approach. Clark, Betting on Lives, 7. Ultimately, it was the financial success of the Equitable and its successors that fully established the idea that aggregate regularities are the key to individual security. Daston, Classical Probability, 174–75. 127. See Timothy L. Alborn, Regulated Lives: Life Insurance and British Society, 1800–1914 (Toronto: University of Toronto Press, 2009), 116–21. Alborn relates that English insurers ignored nearly all other distinguishing features, including occupation, health, and even sex, in setting their premiums, through a significant part of the nineteenth century. 128. See P. H. J. H. Gosden, The Friendly Societies in England, 1815–1875 (Manchester, UK: Manchester University Press, 1961), 7–8, 17. 129. Charles Ansell, A Treatise on Friendly Societies (London: Baldwin and Cradock, 1835), 9, 10. 130. See Simon Cordery, British Friendly Societies, 1750–1914 (Hampshire, UK: Palgrave Macmillan, 2003), 25–26; Geoffrey Finlayson, Citizen, State, and Social Welfare in Britain 1830–1990 (Oxford: Clarendon Press, 1994), 41–42. 131. See Frederick Morton Eden, Observations on Friendly Societies: for the Maintenance of the Industrious Classes during Sickness, Infirmity, Old Age, and other Exigencies (London: J. White and J. Wright, 1801), 14–15; Daniel Gottlieb, “Asymmetric Information in Late Nineteenth Century Cooperative Insurance Societies,” Explorations in Economic History 44 (2007): 271. 132. See also Penelope Ismay, “Between Providence and Risk: Odd Fellows, Benevolence and the Social Limits of Actuarial Science, 1820s–1880s,” Past and Present 226, no. 1 (February 2015): 115–47. 133. Bernard Harris notes that this statement is primarily true when one focuses on ordinary friendly societies (those providing a sickness benefit) and the affiliated orders. If one expands the definition to include collecting societies, then “total membership extended much further down the social hierarchy,” although the latter tended to offer only small, one-time benefits to cover funeral expenses. Bernard Harris, The Origins of the British Welfare State: Society, State and Social Welfare in England and

202 / Notes to Pages 43–50 Wales, 1800–1945 (Hampshire, UK: Palgrave Macmillan, 2004), 84. Cordery disputes the claim that only well-paid and skilled workers joined friendly societies, but also emphasizes that friendlies consciously excluded workers in dangerous or unhealthy occupations and tightened their membership qualifications as actuarial science improved. He also notes that while people in low-status and poorly paid jobs joined various societies, mid-Victorian friendly society members “did mentally divide themselves into two segments, an upper echelon of affiliated orders with relatively high subscription rates and a subordinate group of neighbourhood clubs and burial societies,” which provided only funeral benefits. Cordery, British Friendly Societies, 72; cf. 26. Both accounts confirm that the reach of friendly societies’ coverage was limited relative to the aspirations of some of their later reformers. 134. Ismay discusses some of the successes and limitations of one society’s efforts to expand its network of sociability in the early nineteenth century. Ismay, “Between Providence and Risk,” esp. 126–32. C H A P T E R T WO

1. 2. 3. 4. 5. 6. 7.

8.

9. 10.

11. 12. 13.

14.

See Daston, Classical Probability, 177–79. Society for Equitable Assurances, Short Account, 18. The most exhaustive and influential of these is Ewald’s L’État providence, to which my own owes a considerable debt. See W. Morgan, “Introduction,” in Price, Observations on Reversionary Payments, 7th ed., 1:vi. Hall, “Policy Paradigms,” 279. Ibid., 289–90. Such evolution therefore reflects what Hall refers to as first- and second-order change—that is, adjustments in policy that do not alter the overall terms of the paradigm—rather than a paradigm shift. Ibid., 279. For an insightful commentary on the role of mathematics in Hobbes’s politics, see Mary Poovey, A History of the Modern Fact: Problems of Knowledge in the Sciences of Wealth and Society (Chicago: University of Chicago Press, 1998), 104–8. Locke, on several occasions in his Essay Concerning Human Understanding, repeats his view that morality is like mathematics in that both are capable of certain demonstration. See John Locke, An Essay Concerning Human Understanding, vol. 2 (1690; London, 1725), 114, 174, 263. On the centrality of the problem of individual judgment in Locke’s political philosophy, see Douglas John Casson, Liberating Judgment: Fanatics, Skeptics, and John Locke’s Politics of Probability (Princeton, NJ: Princeton University Press, 2011). Nacol, Age of Risk, 21–33, on Hobbes, and 45–47, on Locke. Daniel Defoe, An Essay Upon Projects (London: Tho. Cockerill, 1697), 143–44, 147– 49. If everyone, “old and young, rich and poor, were to pay into one common bank” a modest fee, the “overplus paid by those who die off, and by those who never come to want,” would “in all probability maintain all that should be poor” and abolish “beggary and poverty out of the kingdom.” Ibid., 171. Ibid., 145. Ibid., 125–28, 132–34. Ibid., 119. Should a society be formed on such unequal terms, “the seamens executors would most certainly have an advantage, and receive more than they pay.” Ibid., 120. Ibid., 118

Notes to Pages 50–54 / 203 15. 16. 17. 18. 19.

20.

21. 22. 23.

24. 25. 26. 27. 28.

29. 30. 31. 32. 33. 34.

35. 36.

Ibid., 122. Ibid., 116; cf. 171. Ibid., 8–9. Ibid. According to Penelope Ismay, however, Defoe’s contribution did give “added meaning to the term friendly society; it became understood as a method for securing against a particular social risk” and encouraged the creation of societies designed to secure against a variety of different contingencies. She also notes that by bringing together strangers who shared the same risk, Defoe’s conception made common interests rather than familiarity or a “shared spiritual fate” the glue binding individuals together. See Penelope Ismay, Trust Among Strangers: Friendly Societies in Modern Britain (New York: Cambridge University Press, 2018), 44–45. See, e.g., William Harral Johnson, The Past, Present, and Future of Friendly Societies (London: F. Farrah, 1867), 8. Defoe’s insistence that the projects he had in mind would align “public good and private advantage” confirms that the animating spirit of Defoe’s tract was indeed closely aligned with the later writings I describe in what follows. See Defoe, Essay, 28 and for discussion Poovey, History of the Modern Fact, 158–62. Daston, Classical Probability, esp. 182–83; Clark, Betting on Lives, esp. 144–46. Ismay, Trust Among Strangers, 58–59. My understanding of the significance of property ownership for Price, as well as the relationship between social and political equality in his thought, is indebted to Yiftah Elazar, “The Liberty Debate: Richard Price and His Critics on Civil Liberty, Free Government, and Democratic Participation” (PhD diss., Princeton University, 2012), esp. 249–54. Bellhouse, Leases for Lives, 9–12, 18–19. Halley, “Estimate,” 606. For discussion, see Bellhouse, Leases for Lives, 36–38. Society for Equitable Assurances, Short Account, 7. Ismay, Trust Among Strangers, 110–11. Peter Buck, “People Who Counted: Political Arithmetic in the Eighteenth Century,” Isis 73, no. 1 (March 1982): 38–43. See also William Deringer, Calculated Values: Finance, Politics, and the Quantitative Age (Cambridge, MA: Harvard University Press, 2018), 291–92. See Price, Observations on Reversionary Payments, 7th ed., 1:293–94. Ibid., 294. Buck, “People Who Counted,” 38–43. Price, Observations on Reversionary Payments, 7th ed., 2:158. See also Richard Price, An Essay on the Population of England, From the Revolution to the Present Time, 2nd ed. (London: T. Cadell, 1780), 25–27. R. Merkin, “Gambling by Insurance—A Study of the Life Assurance Act 1774,” Anglo-American Law Review 9, no. 4 (1980): 337. See also Daston, Classical Probability, 174–75. Timothy Alborn, “A License to Bet: Life Insurance and the Gambling Act in the British Courts,” Connecticut Insurance Law Journal 14, no. 1 (2007): 2. For example, the first chapter of the first volume of Observations on Reversionary Payments is devoted to “Questions relating to Schemes for granting Reversionary Annuities, and the Value of Assurances on Lives.” Similarly, Price presents both the Hamburgh annuity society and the Equitable, which offered life insurance as well, as models of successful schemes. Price, Observations on Reversionary Payments, 7th ed.,

204 / Notes to Pages 54–56

37.

38.

39.

40.

41. 42. 43. 44. 45. 46.

47.

48.

49.

50. 51.

52.

53.

1:181–91. Laplace similarly blurs the distinction between the two practices, describing the possibility of purchasing for one’s heirs, “by means of a life annuity, an amount payable at the end of the year of his death.” He then goes on to speak of maritime and fire insurance as operating on the same principles. See Pierre-Simon Laplace, Philosophical Essay on Probabilities, 5th ed. (1825), trans. Andrew I. Dale (New York: Springer-Verlag, 1994), 88. This claim is consistent with Buck’s argument, which distinguishes political arithmetic in Price’s era from earlier iterations, such as Halley’s, that set out to strengthen the state. Buck, “People Who Counted,” 29–35. See Emma Rothschild, Economic Sentiments: Adam Smith, Condorcet, and the Enlightenment (Cambridge, MA: Harvard University Press, 2001), 71, 150, on Adam Smith, and 251–52, on Condorcet. Richard Price, Additional Observations on the Nature and Value of Civil Liberty, and the War with America: also Observations on Schemes for Raising Money by Public Loans; an Historical Deduction and Analysis of the National Debt; and a Brief Account of the Debts and Resources of France, 2nd ed. (London: T. Cadell, 1777), 20–21. In this vein, Price blames the “landed interest” in England for undermining the operation of the previous sinking fund. Price, Observations on Reversionary Payments, 7th ed., 1:305. Richard Price, Observations on the Importance of the American Revolution, and the Means of Making It a Benefit to the World (London, 1784), 71. Ibid., 69. Ibid., 71–73. Ibid., 72. Price, Observations on Reversionary Payments, 7th ed., 1:149. For a lucid discussion of Bayes’s argument, including how his argument for a uniform prior distribution differs from that of Laplace, which we consider further on, see Stephen M. Stigler, “Thomas Bayes’s Bayesian Inference,” Journal of the Royal Statistical Society. Series A 145, no. 2 (1982): 250–54. On Bayes’s reception within the development of probability see ibid., 255; on his concentration on theory rather than application, see Stephen M. Stigler, “Richard Price, the First Bayesian,” Statistical Science 33, no. 1 (2018): 118. On Price’s adoption of Bayes’s method, including the significance of Hume, see Stigler, “Richard Price,” 120–22. Another exposition is found in Anders Hald, A History of Mathematical Statistics from 1750–1930 (New York: Wiley, 1998), 138–47. Richard Price, Letter to John Canton, in Thomas Bayes, “An Essay Towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes. Communicated by Mr. Price in a Letter to John Canton,” Philosophical Transactions 53 (1763), reprinted in Biometrika 45, no. 3–4 (December 1958): 296. Ibid., 297. As William Deringer puts it, “Price looked forward to a polity in which mathematical reforms could make both more rational government and more rational citizens.” Deringer, Calculated Values, 295. These points are persuasively argued in ibid., 288–96. Richard Price, The Evidence for a Future Period of Improvement in the State of Mankind, with the Means and Duty of Promoting It (London: T. Cadell and J. Johnson, 1787), 14. I am grateful to Yiftah Elazar for calling my attention to this text and to the issue of providence in Price’s thought more broadly. Ibid., 11.

Notes to Pages 56–59 / 205 54. Price, Observations on Reversionary Payments, 7th ed., 1:xvi. For a recent discussion of annuity societies around this time, including their workings and their financial difficulties, see Bellhouse, Leases for Lives, 125–30, 138, 148–49. 55. See Price, Observations on Reversionary Payments, 7th ed., 1:29, 47, 127. 56. Ibid., 160, 155. 57. See ibid., xxx. See also William Morgan’s Preface to the Sixth Edition in ibid., esp. xl–xliii. Morgan noted that Price’s proposals would have replaced those “many wretched schemes which have so often risen up to delude” the poor, and that with proper mathematical guidance “the indigent labourer and his family might then look forward without anxiety to seasons of sickness and old age, and the more wealthy enjoy the advantage of a reduction in the enormous expense with which the parishes are loaded for the maintenance of the poor.” Ibid., xli–xlii. 58. Ibid., 149–50. Price’s tables, which took their data from parish records at Northampton, were not superseded until nearly a century later, based on information from a number of English insurers. 59. See Maurice Edward Ogborn, Equitable Assurances (London: George Allen and Unwin, 1962), 96; Cordery, British Friendly Societies, 130. 60. See Ismay, Trust Among Strangers, 65–66; James Stephen Taylor, “The Impact of Pauper Settlement 1691–1834,” Past and Present 73, no. 1 (November 1976): 42–74. 61. Cordery, British Friendly Societies, 85. 62. Ibid., 146. Advocates of savings banks argued that affording societies this privilege would ensure their success by, among other things, providing relatively high rates of interest and security on their capital. See Rev. John Thomas Becher, Observations upon the Report from the Select Committee of the House of Commons, on the Laws Respecting Friendly Societies (Newark: S. & J. Ridge, 1826), 106. 63. Harris, Origins of the British Welfare State, 81. See also “Report of the Select Committee of the House of Commons,” 1825, reproduced in Ansell, Treatise on Friendly Societies, 17. These sources do not give the number of societies in 1815. 64. Émile de Girardin, La politique universelle. Décrets de l’avenir, 3rd ed. (Paris: Librairie Nouvelle, 1855), 369. 65. Ibid. Ismay notes that legislators did not place much faith in actuarial science, especially given the limited amount of data available concerning sickness and mortality among the working classes. Ismay, Trust Among Strangers, 109. By stating that only contingencies susceptible to calculation were the proper objects of friendly relief, however, the 1819 act did endorse the probabilistic vision, at least in principle. 66. Cordery, British Friendly Societies, 86. 67. Harris, Origins of the British Welfare State, 81. 68. See Eden, Observations on Friendly Societies, 10; Ansell, Treatise on Friendly Societies, 1–2; and the discussion in Daston, Classical Probability, 174–78. 69. See John Thomas Becher, The Constitution of Friendly Societies upon Legal and Scientific Principles, Exemplified by the Rules & Tables of Calculations, 2nd ed. (London: W. Simpkin and R. Marshall, 1824), 12–19, and the discussion in Ismay, Trust Among Strangers, 110–12. 70. This point is emphasized in Ismay, Trust Among Strangers, 11–14. 71. Eden, Observations on Friendly Societies, 14–15. 72. Ansell, Treatise on Friendly Societies, 106–7. 73. Ibid., 48. On the movement to introduce actuarial calculations for sickness, see James C. Riley, “Disease without Death: New Sources for a History of Sickness,” Journal of Interdisciplinary History 17, no. 3 (Winter 1987): 554.

206 / Notes to Pages 60–63 74. “Report of the Select Committee of the House of Commons,” 1825, reproduced in Ansell, Treatise on Friendly Societies, 21. 75. J. W. Cunningham, A Few Observations on Friendly Societies and their Influence on Public Morals (London: Ellerton and Henderson, 1817), 14. 76. Joseph-Marie  de Gérando, De la bienfaisance publique (Brussels, 1839), quoted in Émile Thomas, “Caisses de Retraites—Sociétés de Secours Mutuels,” in Dictionnaire de l’économie politique, vol. 1 (Paris: Guillaumin, 1854), 257. 77. For instance, one early nineteenth-century parliamentarian, John Christian Curwen, advocated a National Benefit Society that would be administered by vestries with equal funding from taxpayers, workers, and employers on the same principles that guided his strong support for friendly societies. Such institutions would create “respectable members of society,” who take responsibility for their own welfare, and would end reliance on the poor laws. J. C. Curwen, Hints on Agricultural Subjects (London: J. Johnson, 1809), 286, 357–59, quoted in Cordery, British Friendly Societies, 48–49. By mid-nineteenth century, the same view found expression in the United States. See Tom Baker, “Embracing Risk, Sharing Responsibility,” Drake Law Review 56, no. 2 (Winter 2008): 565. 78. Price, Observations on Reversionary Payments, 2nd ed., 43, quoted in Francis Maseres, A Proposal for Establishing Life-Annuities in Parishes for the Benefit of the Industrious Poor (London: B. White, 1772), 27. 79. Maseres, Proposal, 35. 80. Ismay, Trust Among Strangers, 60. 81. According to B. Keith-Lucas, the earlier program, which was voluntary, provided subscribers benefits upon marriage and childbirth. As a result, those who subscribed disproportionately did so with the knowledge they would soon marry or have a child, and the liabilities of the parishes quickly exceeded their assets. The act was subsequently repealed. B. Keith-Lucas, “A Local Act for Social Insurance in the Eighteenth Century,” Cambridge Law Journal 11, no. 2 (1952): 195. 82. John Acland, A Plan for Rendering the Poor Independent on Public Contribution; Founded on the Basis of the Friendly Societies, Commonly Called Clubs. To Which Is Added, a Letter from Dr. Price, Containing His Sentiments and Calculations on the Subject (Exeter: R. Thorn, 1786), 10. 83. Ibid., 11–12. 84. Ibid., 11. 85. Ibid., 28. 86. Gareth Stedman Jones, An End to Poverty? A Historical Debate (New York: Columbia University Press, 2004), 34. 87. See Keith Michael Baker, Condorcet: From Natural Philosophy to Social Mathematics (Chicago: University of Chicago Press, 1975), 280–81; Stedman Jones, An End to Poverty?, 34–36. 88. Emmanuel-Étienne Duvillard de Durand, Plan d’une association de prévoyance (Paris: 1790), 4. 89. Ibid., 25. 90. See also Ismay, Trust Among Strangers, 43–46. 91. Jean-Antoine-Nicolas de Caritat, Marquis de Condorcet, “The Sketch,” in Condorcet: Political Writings, ed. Steven Lukes and Nadia Urbinati (Cambridge: Cambridge University Press, 2012), 102. Emma Rothschild notes that the “fragments” of the tenth and final period covered in this work were published in the 1840s. Rothschild, Economic Sentiments, 159.

Notes to Pages 63–67 / 207 92. Condorcet, “The Sketch,” 126. 93. Ibid., 132. Condorcet almost certainly had in mind life insurance mathematics in citing the demonstrated success of probability theory as the inspiration for his own plans. He was well aware of the work of the Equitable, having cited it in his works on probability theory, and had written an extensive essay on the mathematics of calculating insurance rates based on probabilities. See Condorcet, “Assurances (maritimes)” in Arithmétique politique: textes rares ou inédits (1767–1789), ed. Bernard Bru and Pierre Crépel (Paris: Institut National D’études Démographiques, Presses Universitaires de France, 1994), 485–94. 94. Condorcet, “The Sketch,” 131–32. 95. Ibid., 131. 96. Ibid., 130, 132. 97. Ibid., 132. 98. Ibid., 126. 99. On Condorcet’s economic liberalism, grounded in the natural rights of personal liberty and the secure enjoyment of property, see Baker, Condorcet, 218–19. 100. Stedman Jones, An End to Poverty?, 42. For Paine’s views on commerce, see Thomas Paine, Rights of Man (1792), in Rights of Man, Common Sense, and Other Political Writings, ed. Mark Philp (Oxford: Oxford University Press, 2008), 265–70. 101. Paine, Rights of Man, 296, 300. 102. Ibid., 296. 103. See C. C. Heyde and E. Seneta, I. J. Bienaymé: Statistical Theory Anticipated (New York: Springer-Verlag, 1977), 24. 104. While in principle tontines are a form of annuity with payments distributed among survivors, tontine income rises more quickly at older ages while annuity income is constant. Tontines are therefore riskier than annuities insofar as only the longestlived investors, a relatively small percentage of the mortality distribution, receive a better return from a tontine than they would from an annuity. This fact may have contributed to the association between tontines and gambling. David R. Weir, “Tontines, Public Finance, and Revolution in France and England, 1688–1789,” Journal of Economic History 48, no. 1 (March 1989): 110–12. 105. Ibid., 112. 106. Thomas Paine, Agrarian Justice (Paris, 1797), in The Writings of Thomas Paine, ed. Moncure Daniel Conway, vol. 3 (New York: G. P. Putnam’s Sons, 1894), 331–32. Elizabeth Anderson has called this “the first realistic plan to abolish poverty on a nationwide scale” and a precursor of modern social insurance. Elizabeth Anderson, “Thomas Paine’s ‘Agrarian Justice’ and the Origins of Social Insurance,” in Ten Neglected Classics of Philosophy, ed. Eric Schliesser (New York: Oxford University Press, 2016), 55. A discussion of Paine’s scheme, as well as the general idea of a basic endowment and its close cousin the basic income, is found in Philippe van Parijs and Yannick Vanderborght, Basic Income: A Radical Proposal for a Free Society and a Sane Economy (Cambridge, MA: Harvard University Press, 2017), 29–31, 70–73. 107. Paine, Agrarian Justice, 337. 108. Paine, Rights of Man (1791), in Philp, Rights of Man, 91–92. 109. A version of this problem is also discussed in Iversen, Capitalism, Democracy and Welfare, 124–29. For an extended account of the challenges that social insurance poses in this regard, see Alan M. Jacobs, Governing for the Long Term: Democracy and the Politics of Investment (Cambridge: Cambridge University Press, 2011).

208 / Notes to Pages 67–73 110. See Eric M. Patashnik, Putting Trust in the U.S. Budget: Federal Trust Funds and the Politics of Commitment (Cambridge: Cambridge University Press, 2000), 2–3, 8–10. 111. Philippe van Parijs discusses Paine’s proposal, in distinction to both Bismarckian and Beveridgean social insurance, as one of the three models of the welfare state. Van Parijs, “Assurance, solidarité, équité.” 112. For a helpful discussion of some of the problems with class rating in insurance underwriting, see Xavier Landes, “Insurance Underwriting,” in Encyclopedia of Corporate Social Responsibility, ed. Samuel Idowu et al. (Heidelberg: Springer, 2013), 1444–45. For several concrete, and troubling, historical examples of this phenomenon in the context of commercial insurance in the United States, see Bouk, How Our Days Became Numbered, 34–54. CHAPTER THREE

1.

The first of these terms reflects the claim that these thinkers were part of an ongoing tradition that employed many of the assumptions and techniques of classical probability while also beginning the transition away from it. For more on the terminology, see infra n. 13. 2. For a helpful overview of these and related developments, see Heyde and Seneta, Bienaymé, 19–20. 3. Condorcet, “Histoire abregée de ce calcul,” in Bru and Crépel, Arithmétique politique, 285. The editors suggest that this manuscript, together with a similar one, was first composed in 1773–74 and subsequently updated. Ibid., 283. 4. For an accessible account of Bernoulli’s result, see Stephen M. Stigler, “Soft Questions, Hard Answers: Jacob Bernoulli’s Probability in Historical Context,” International Statistical Review (April 2014): 1–16. 5. Abraham de Moivre, Doctrine of Chances, 3rd ed. (London: A. Millar, 1756), 251. See also Karl Pearson, “James Bernoulli’s Theorem,” Biometrika 17, no. 3/4 (December 1925): 205–6. 6. See David R. Bellhouse, “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birthday,” Statistical Science 19, no. 1 (February 2004): 16–18. 7. Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge, MA: Belknap Press of Harvard University Press, 1986), 94–95. 8. Ibid., 100. 9. Stigler points out that debates about inverse probability through the nineteenth century centered on Laplace’s work and not Bayes’s. Major contributors to the field such as Boole, Venn, Jevons, and Edgeworth all took pains to discuss Laplace, but none made substantive references to Bayes. Stigler, “Thomas Bayes’s Bayesian Inference,” 255. Laplace’s memoir also had a profound effect on Condorcet, inspiring him to regard probabilities as the foundation for a new mathematically informed science of conduct. See Baker, Condorcet, 171. Given the largely technical character of Laplace’s earliest contributions to probability theory, Charles Coulston Gillispie suggests that it was an interaction with Condorcet that prompted Laplace’s turn toward a more philosophical approach in his treatment of the probability of causes, and with it his increased interest in matters of civic and social import. Charles Coulston Gillispie, “Probability and Politics: Laplace, Condorcet, and Turgot,” Proceedings of the American Philosophical Society 116, no. 1 (February 1972): 4. 10. Roger Hahn, Pierre Simon Laplace, 1749–1827: A Determined Scientist (Cambridge, MA: Harvard University Press, 2005), 120, 106, 127–28.

Notes to Pages 73–75 / 209 11. Ibid., 190–92. 12. Hahn notes that these works were initially spurred during Laplace’s tenure as an elector of the Institut National des Sciences et des Arts, and in particular by his interactions with a group of so-called idéologues, who around the turn of the century aspired to create a science of human affairs on the model of the physical and mathematical sciences. Ibid., 170–71. 13. Daston similarly characterizes Laplace as a transitional figure in the history of probability theory, concluding that his work, “particularly his enthusiasm for statistics, marked the beginning of the end for the classical interpretation that had dominated eighteenth-century probability theory.” Daston, Classical Probability, 284. According to Hacking, however, the so-called classical theory was in fact a set of competing theories that shared a single classical feature, namely the definition of probability in terms of a fundamental probability set, or a set of mutually exclusive, equally probable alternatives, which Laplace maintained. Ian Hacking, “Jacques Bernoulli’s Art of Conjecturing,” British Journal for the Philosophy of Science 22, no. 3 (August 1971): 210. For a similar definition of the classical interpretation, see Hájek, “Reference Class Problem,” 569. 14. Laplace, “Memoir on the Probability of the Causes of Events,” trans. Stephen M. Stigler, Statistical Science 1, no. 3 (August 1986): 364–78. The following account focuses on Laplace’s discussion on 364–70. 15. A. I. Dale, “Bayes or Laplace? An Examination of the Origin and Early Applications of Bayes’ Theorem,” Archive for History of Exact Sciences 27, no. 1 (1982): 30. 16. As subsequent commentators pointed out, and as Condorcet recognized as well, Laplace’s formula in this memoir considers only the probability for a drawing of m white and n black balls from the urn in that particular order. To account for the probability without regard to the order in which the m + n balls are drawn, one must add another term, the binomial coefficient, before the expression that Laplace derives here. See Andrew I. Dale, A History of Inverse Probability from Thomas Bayes to Karl Pearson, 2nd ed. (New York: Springer-Verlag, 1999), 172. 17. Laplace, “Memoir,” 370. 18. See Stigler, History of Statistics, 100–109. 19. For example, in the years prior to the 1801 institution of a census in France, these techniques together allowed for a determination of how many observations had to be taken to reduce the probable error in a population estimate to specified limits. Gillispie, “Laplace, Condorcet, Turgot,” 11. 20. As Dale points out, whereas Bayes began with the idea of a single urn, Laplace “entertained the idea of a population of urns, and hence could ask which of them was the ‘cause’ of the sample.” Dale, “Bayes or Laplace?,” 30. 21. Unlike Bayes, who had provided a fairly extensive argument for his assumption of equal prior probabilities, Laplace treats it as an intuitive axiom. This is one point that has prompted scholars to disassociate their two accounts. See Stephen  M. Stigler, “Laplace’s 1774 Memoir on Inverse Probability,” Statistical Science 1, no. 3 (August 1986): 359, and “Thomas Bayes’s Bayesian Inference.” For discussion of Laplace’s uses of the principle of indifference with regard to the inclinations of cometary orbits, see Gillispie, “Laplace, Condorcet, Turgot,” 7. 22. Long known as the principle of nonsufficient reason, it was Keynes who designated it as the principle of indifference, a term I also prefer for its economy of expression. See John Maynard Keynes, A Treatise on Probability (London: Macmillan, 1921), 44. 23. Laplace, “Memoir,” 378.

210 / Notes to Pages 75–77 24. According to Anders Hald, Jacob Bernoulli offered an early version of the principle of indifference, arguing that causes must be assumed equally possible to avoid the need for discretion in determining the true probability of events. See Hald, History of Probability and Statistics, 249–52. Whether Bernoulli in fact intended to describe a situation in which one is truly indifferent among possible alternatives because ignorant of their respective likelihoods, or whether on the contrary he considered the alternatives to be equally probable in an objective, physical sense, is taken up in Hacking, “Jacques Bernoulli’s Art of Conjecturing,” 219. 25. See Daston, Classical Probability, 274. 26. See, e.g., David Hume, “Of Probability,” in An Enquiry Concerning Human Understanding (1772), ed. Tom L. Beauchamp (Oxford: Oxford University Press, 1999), 131–33. See also the discussions in Casson, Liberating Judgment, esp. 103–14; Daston, Classical Probability, 193–208. 27. Laplace, Philosophical Essay on Probabilities, 3. Hence also Laplace’s assertion that mathematical probability is “basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.” Ibid., 124. 28. This claim would later be echoed by Francis Ysidro Edgeworth, who noted that “the principle of Utility is at the root of even the more objective portions of the Theory of Observations. The founders of the science, Gauss and Laplace, distinctly teach that, in measuring physical quantity, the question is not so much that value which is most probably right, as that which may most advantageously be assigned—taking into account the frequency and seriousness of the error incurred . . . by proposed method of reduction.” Francis Ysidro Edgeworth, “The Method of Measuring Probability and Utility,” Mind 12, no. 47 (July 1887): 485. Stephen Stigler notes that Laplace’s frequent use of uniform prior probabilities was “not a blind metaphysical assumption that whatever was unknown was necessarily equally likely to be any of its possible values,” but an “implicit assumption that for ease of analysis the problem had been specified” such that it was reasonable to apply the principle of indifference. Stigler, History of Statistics, 135. 29. Condorcet, Mémoire sur le calcul des probabilités, pt. 4 (1786), in Bru and Crépel, Arithmétique politique, 420. 30. My understanding of this point is heavily indebted to Stigler, “Thomas Bayes’s Bayesian Inference,” esp. 252–53. 31. In the case of such an event, before any trials have been observed, “I can have no reason to think it should rather happen one possible number of times than another,” and I must therefore expect that any possible outcome is as likely to occur as any other. Bayes, “Essay Towards Solving a Problem,” 306. 32. Richard Price, Appendix, in Bayes, “Essay Towards Solving a Problem,” 312. 33. In his 1774 essay, Laplace had emphasized that to calculate the probability of more than one event occurring, empirical rather than a priori probability values must be used. Yet for single events, one could still make use of an a priori value—specifically, the equal probabilities enabled by the principle of indifference. Laplace, “Memoir,” 378. 34. See generally Condorcet, Cinq mémoires sur l’instruction publique (1791; Paris: GarnierFlammarion, 1994). 35. On the last point, see also Rothschild, Economic Sentiments, 180–85. On Turgot’s similar view of the importance of popular enlightenment in enabling social decisions to reflect the truth, see Gillispie, “Laplace, Condorcet, Turgot,” 18.

Notes to Pages 77–81 / 211 36. For discussions of Laplace and Poisson on the probability of testimony and judgments, see Daston, Classical Probability, 335–39 and 356–69. 37. See, e.g., Augustus De Morgan, An Essay on Probabilities, and on Their Application to Life Contingencies and Insurance Offices (London, 1838), 253, for a discussion of both points. 38. In his seminal 1738 article, Daniel Bernoulli had discussed the virtue of distributing losses over several trials, for example by placing portions of cargo on several ships rather than just one. D. Bernoulli, “Exposition of a New Theory,” 30–31. 39. Although the term “pooling” is anachronistic in this context, for reasons we will see as the argument progresses, I will often use it alongside “spreading” to designate the experience of the insured as opposed to the insurer. 40. Condorcet, Tableau général de la science qui a pour objet l’application du calcul aux sciences politiques et morales (1795), in Mathématique et Société, ed. Roshdi Rashed (Paris: Hermann Éditeurs, 2011), 205–6. 41. Ibid., 198. 42. Condorcet, “The Sketch,” 140. 43. This point is forcefully brought out in the discussion in Rothschild, Economic Sentiments, 158–63. 44. Condorcet, “Assurances (maritimes),” in Bru and Crépel, Arithmétique politique, 488. The editors of this volume suggest that the work was drafted around 1783. Ibid., 485. 45. Ibid., 488. 46. See also the discussion in Daston, Classical Probability, 98–99. 47. Condorcet, “Probabilité,” in Bru and Crépel, Arithmétique politique, 501. The editors date this essay to the period between 1784 and 1789. See also Condorcet, Essai sur l’application de l’analyse à la probabilité des décisions rendus à la pluralité des voix (Paris: L’Imprimerie Royale, 1785), lxxv. According to Pierre Crépel, CharlesFrançois Bicquilley articulated a version of the same view in works from around this time. See Pierre Crépel, “Mathematical Economics and Probability Theory: CharlesFrançois Bicquilley’s Daring Contribution,” in Studies in the History of French Political Economy: From Bodin to Walras, ed. Gilbert Faccarello (London: Routledge, 1998), esp. 98–99; on Condorcet, see 87, 102–8. 48. Rothschild, Economic Sentiments, 181. Condorcet rejected the use of average expectations in the context of judicial decisions since no individual has the opportunity to “play” the game of justice enough times for the average to meaningfully apply to him. For comparison of Condorcet and Poisson on this point, see Daston, Classical Probability, 362. 49. See also Rothschild, Economic Sentiments, 160–62. 50. Condorcet, Réflexions sur le commerce des blés (1776), in Œuvres de Condorcet, ed. A. Condorcet O’Connor and M. F. Arago, vol. 11 (Paris: Firmin Didot, 1847), 148. 51. Ibid., 149. 52. Writing in 1843, Antoine Augustin Cournot explicitly distinguished between premium and mutual insurance along the lines just mentioned. He noted that premium insurance allows the “prudent speculator” to take on economically beneficial activities that he would not venture into if he could not offload some of the risk, whereas mutual insurance involves a situation in which a group of individuals “associate to support in common the losses that any one among them” could accidentally sustain. Antoine Augustin Cournot, Exposition de la théorie des chances et des probabilités (Paris: L. Hachette, 1843), 339–40.

212 / Notes to Pages 81–86 53. Condorcet, Mémoire sur le calcul des probabilités, pt. 1 (1784), in Bru and Crépel, Arithmétique politique, 387–88. See also Lorraine J. Daston, “Probabilistic Expectation and Rationality in Classical Probability Theory,” Historia Mathematica 7, no. 3 (August 1980): 251, which notes that Condorcet’s interest in probability theory was apparently sparked by d’Alembert’s critique. 54. Condorcet, Mémoire sur le calcul des probabilités, pt. 1, in Bru and Crépel, Arithmétique politique, 389. 55. Ibid. 56. Ibid., 391. 57. Although I have opted not to enter into a detailed account of Condorcet’s mathematical analysis, my understanding of this work is indebted to personal correspondence with Pierre Crépel, who has lucidly explicated the probability calculations and helped to account for an error in Condorcet’s argument. This mathematical error does not, however, affect the essential point that Condorcet is trying to make or my presentation of it here. 58. D. Bernoulli, “Exposition of a New Theory,” 31. 59. Ibid., 32. 60. Ibid., 28. Although he acknowledged the difficulty of generalizing with regard to moral expectation, because “the utility of an item may change with circumstances,” he devised his formula on the assumption that, in general, human beings appreciate less each additional unit of wealth the greater their initial fortune. Ibid., 24–25. 61. Ibid., 29. See also Laplace, Philosophical Essay on Probabilities, 13–14. 62. See Daston, Classical Probability, 70–76. Although Bernoulli is usually credited with first introducing this idea, he notes in his article that French mathematician Gabriel Cramer described a very similar idea in a 1728 letter to Nicolas Bernoulli. Cramer may have also helped to spur the probabilistic works of George-Louis Leclerc de Buffon. See Thierry Martin, “La logique probabiliste de Gabriel Cramer,” Mathématiques et sciences humaines, no. 176 (Winter 2006): 44. Buffon proposed a slightly different idea, however, now known as loss aversion, which holds that losses are considerably more painful than equivalent gains. See Georges-Louis Leclerc de Buffon, Essai d’arithmétique morale (1777), in Oeuvres complètes de Buffon, mises en ordre et précédées d’une notice historique par M. A. Richard, vol. 13 (Paris: Baudouin Frères, 1827), 27–29. For the claim that Buffon was the first to propose loss aversion within an account based on utility, see Tibor Neugebauer, “Moral Impossibility in the Petersburg Paradox: A Literature Survey and Experimental Evidence,” IDEAS Working Paper Series from RePEc (2010): 6, http://ideas.repec.org/p/crf/wpaper/ 10–06.html. On the relationship between Buffon’s approach and that of Daniel Bernoulli, see Daston, “Probabilistic Expectation and Rationality,” 249–50. 63. D. Bernoulli, “Exposition of a New Theory,” 24. 64. Jean le Rond d’Alembert, “Sur la durée de la vie,” in Opuscules mathématiques, vol. 4 (Paris: Briasson, 1768), 94. Richard Price laid out the different methods of calculating life expectancies in a letter to Benjamin Franklin. Price, “Observations on the Expectations of Lives,” 89–125. 65. D’Alembert, “Sur l’application du Calcul des Probabilités a l’inoculation de la petite Vérole,” in Opuscules mathématiques, vol. 2 (Paris: David, 1761), 37–38. 66. Ibid., 37. Many subsequent thinkers were harshly critical of d’Alembert’s analyses. For some references to those reactions, see Lorraine J. Daston, “D’Alembert’s Critique of Probability Theory,” Historia Mathematica 6, no. 3 (August 1979): 276. 67. Laplace, Philosophical Essay on Probabilities, 89.

Notes to Pages 86–89 / 213 68. S. F. Lacroix, Traité élémentaire du calcul des probabilités (Paris: Vve Courcier, 1816), 219. 69. De Morgan, Essay on Probabilities, 101. 70. Ibid., 103. Stigler notes that while Laplace’s Théorie was far from easy reading, De Morgan had “digested and re-presented almost the whole of it” in his own works. Stigler, History of Statistics, 157–58. Citations to uses of this rationale in commercial insurance literature of the mid-nineteenth century may be found in Baker, “Genealogy of Moral Hazard,” esp. 247–48. 71. Condorcet, “Arithmétique politique. Morand” (1771), in Bru and Crépel, Arithmétique politique, 86. 72. In his Essai, Condorcet gives a striking example of finding “the limit at which the danger of convicting an innocent and that of freeing someone culpable, will be the same.” But while in this case “society, if one will, would play an equal game, because it repeats an indefinite number of times,” this will not be the same for the individual, who “can only play but a number of times, far too small for equality to be had for him.” Condorcet, Essai sur l’application, lxxix. 73. D. Bernoulli, “Exposition of a New Theory,” 31. 74. See Buffon, Essai d’arithmétique morale, 27–29. Bentham repeated a similar claim in his own condemnation of gambling. “The fact is [that] it is impossible for two men to play upon equal terms: terms numerically equal are in fact disadvantageous to both. For the ratio of what a man loses, if he loses, to the remainder of his fortune, is greater than that of what he gains, if he gains, is to the whole. Suppose the stake 1/3 of each man’s fortune: if he loses, he loses a third, if he gains, he gains but a fourth.” Jeremy Bentham, A Plan for the Augmentation of the Revenue (1794–95), in Jeremy Bentham’s Economic Writings, vol. 2, ed. W. Stark (London: Allen & Unwin, 1952), 132–33n. 75. Buffon, Essai d’arithmétique morale, 54. 76. Laplace, Théorie analytique des probabilités (Paris: Vve Courcier, 1812), 444–45. Several decades later, Adolphe Quetelet reiterated the same line of reasoning in noting that because the pain of loss outweighs the pleasure of gain, the “insured is generally guided by motives of prudence and economy; the gambler, by contrast, by improvidence and dissipation.” Adolphe Quetelet, Lettres sur la théorie des probabilités appliquée aux sciences morales et politiques (Brussels, 1846), 43. See also SiméonDenis Poisson, Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilités (Paris: Bachelier, 1837), 8–9. 77. Laplace, Philosophical Essay on Probabilities, 88. 78. Ibid., 89. See also Laplace, Théorie analytique des probabilités, 437–39. 79. J. B. J. Fourier, “Extrait d’un Mémoire sur la Théorie analytique des assurances,” in Annales de chimie et de physique, vol. 10 (Paris: Crochard, 1819), 179–80. 80. Ibid., 181–82. 81. Ibid., 178, 183. 82. See Ewald, L’État providence, 183–85. 83. Quetelet, Lettres, 47. On the connection between Fourier and Quetelet, see Stephen E. Feinberg, “A Brief History of Statistics in Three and One-Half Chapters: A Review Essay,” Statistical Science 7, no. 2 (May 1992): 215. 84. Ewald, L’État providence, 185. This view therefore seems to resonate with the school of midcentury French political economy that emphasized duty for the sake of social cohesion, particularly in response to the uprisings of 1848. See Giovanna Procacci,

214 / Notes to Pages 89–93

85.

86.

87.

88.

89. 90.

91. 92. 93. 94.

95. 96. 97.

“Sociology and Its Poor,” Politics and Society 17, no. 2 (June 1989): 180–83. Yet while positivists such as Comte and Saint-Simon emphasized social sympathy as against self-interest, and while political economists such as Adolphe Blanqui sought a moral transformation that would educate citizens to sociability, the argument for social insurance rested on methodological individualism bequeathed by probability theory. For several examples from the political realm, see T. H. Marshall, “The Welfare State—A Comparative Study,” in Sociology at the Crossroads and Other Essays (London: Heinemann Educational Books, 1963), 303–4. For example, in 1837 Poisson defined mathematical expectation as the individual’s due portion of a sum that can be imagined as shared between parties to an aleatory contract. He continued, “If the gain is 60,000 francs, for example, and 1/3 is the chance of the event to which it is attached, the person who is to receive that sum eventually could consider a third of 60,000 francs as a good that he possesses, and which ought to be included in the list of his actual fortune.” Poisson, Recherches sur la probabilité des jugements en matière criminelle, 71. This example comes from James Franklin, “Resurrecting Logical Probability,” Erkenntnis 55, no. 2 (September 2001): 279. For an earlier critique of the principle, see George Boole, An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities (London: Walton and Maberly, 1854), 368–75; and for discussion, see John V. Strong, “The Infinite Ballot Box of Nature: De Morgan, Boole, and Jevons on Probability and the Logic of Induction,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association (1976): 201– 3. Robert Leslie Ellis criticized Laplace’s Rule of Succession on similar grounds. See R. L. Ellis, “On the Foundations of the Theory of Probabilities,” Transactions of the Cambridge Philosophical Society 8, no. 1 (January 1849) [read February 14, 1842]: 4. Even if, as Gillispie points out, Laplace was far less interested in social concerns than Condorcet, the latter inspired him to regard probability as useful to political life and in turn to devise his analysis of the probability of causes. See Gillispie, “Probability and Politics,” 2–4. Ismay, Trust Among Strangers, 183. According to John Macnicol, this was the case well into the 1890s, despite alarmist concern about insolvency. See John Macnicol, The Politics of Retirement in Britain: 1878–1948 (Cambridge: Cambridge University Press, 1998), 122–23. Ismay, Trust Among Strangers, 169, 179–185. See ibid., 169. Ibid. Ismay points out that by the 1840s, the composition of lodges had shifted increasingly toward unskilled rather than skilled workers. Ibid., 187. The Equitable had pioneered these types of distributions, which formed an important part of its mutualistic image. It modified its policy in 1816, after a dramatic increase in membership left William Morgan, its actuary, concerned that new members would vote themselves extravagant bonuses. Morgan convinced a majority of existing members to restrict bonuses to the 5,000 members who had been with the society longest. Timothy Alborn, “The First Fund Managers: Life Insurance Bonuses in Victorian Britain,” Victorian Studies 45, no. 1 (Autumn 2002): 70–71. See ibid., esp. 73–74. See Alborn, “License to Bet,” esp. 9–17. Timothy L. Alborn, “A Calculating Profession: Victorian Actuaries among the Stat-

Notes to Pages 93–98 / 215

98.

99. 100. 101. 102.

103. 104. 105. 106.

107. 108. 109. 110.

111. 112. 113.

isticians,” in Accounting and Science: Natural Inquiry and Commercial Reason, ed. Michael Power (Cambridge: Cambridge University Press, 1996), 89–90. See James Franklin, “Risk-Driven Global Compliance Regimes in Banking and Accounting: The New Law Merchant,” Law, Probability and Risk 4, no. 4 (December 2005): 240–42. Ibid., 242. On the first point, see Macnicol, Politics of Retirement, 116; on the second, see Baker, “Genealogy of Moral Hazard,” esp. 250–55. Adolphe Quetelet, A Treatise on Man and the Development of His Faculties, trans. R. Knox (Edinburgh: William and Robert Chambers, 1842), 6–7. Poisson, Recherches, 9. Heyde and Seneta note that while Bernoulli’s theorem expresses the stability of a frequency as the number of trials increases, Poisson’s law expresses the loss of variability of the frequency. Heyde and Seneta, Bienaymé, 40. Poisson has also been credited as the first to explicitly distinguish between objective and subjective probabilities, or between the chance of events independent of our knowledge and individuals’ estimations of those events, which may differ for different people. See Poisson, Recherches, 30–31. Poisson, Recherches, 18. See also Daston, Classical Probability, 359–60. Daston, Classical Probability, 362. Quetelet, Treatise, 78. In this respect, Quetelet parted ways with Condorcet, who, as Keith Baker points out, prioritized individual choice over social engineering. Yet Condorcet was also a progenitor of Quetelet’s statistical approach, one that effectively reduced the social sphere to the state and a mass of individuals, understood as “quantifiable and interchangeable units.” Baker, Condorcet, 262. For discussion of Quetelet and the idea of a statistical law that governs the features of a population, see Hacking, Taming of Chance, esp. 115–21. Quetelet, Treatise, 6. Ibid., 108. Porter, Rise of Statistical Thinking, 56–63. In this light, social insurance looks not entirely unlike compensation-based policies designed to recognize military service and other contributions to public life. For examples of seventeenth- and eighteenth-century pension schemes in this vein, see Robin Blackburn, Banking on Death, or Investing in Life: The History and Future of Pensions (London: Verso, 2002), 36–39; in the American context, see Theda Skocpol, Protecting Soldiers and Mothers: The Political Origins of Social Policy in the United States (Cambridge, MA: Belknap Press of Harvard University Press, 1992). See, for example, Thomas, “Caisses de Retraites,” 258. Ewald avers that these two laws may be seen, “without too much anachronism, as the first two French laws of social insurance.” Ewald, L’État providence, 208. On the laws, see Anne Reimat, “Old Age Pensions, Demography, and Economic Growth in the Long Run: The French Case Revisited,” Historical and Social Research/ Historische Sozialforschung 37, no. 4 (2012): 329; Yves Saint-Jours, “France,” in The Evolution of Social Insurance 1881–1981, ed. Peter A. Köhler and Hans F. Zacher (London: Frances Pinter, 1982), 112; and Ewald, L’État providence, 208–13. Stedman Jones notes that before becoming emperor, Napoleon advocated turning workers into proprietors to remove the political threat of poverty, and that during the Second Empire he took an interest in supporting mutual societies, “but never without

216 / Notes to Pages 98–100

114.

115. 116.

117. 118.

119. 120. 121. 122. 123.

124.

125.

126. 127.

the heavy hand of administrative and political surveillance.” Stedman Jones, An End to Poverty?, 202. Ferrouillat, Rapport au nom du Comité du travail, Assemblée nationale, February 19, 1849, impression no. 896, 56, quoted in Ewald, L’État providence, 212–13 (emphasis in Ewald). Ewald, L’État providence, 219. Quetelet, Treatise, 100. Dana Simmons points out that social reformers of this period made use of statistical data to standardize everything from wages to prison diets with the aim of improving average outcomes. See Dana Simmons, Vital Minimum: Need, Science & Politics in Modern France (Chicago: University of Chicago Press, 2015), 47–52. On Napoleon III’s politics, see Roger Price, Napoleon III and the Second Empire (London: Routledge, 1997), 25. The article on pensions in the Dictionnaire de l’économie politique, an outlet of liberal economic thought, expressed support for the idea of a national pension fund administered and secured by the state. Thomas, “Caisses de Retraites,” 255–63. One of the figures quoted to this effect is Joseph-Marie de Gérando, who was a foremost advocate of the use of social surveys for philanthropic ends. On Sismondi, see Simmons, Vital Minimum, 76. Stedman Jones, An End to Poverty?, 170. See Procacci, “Sociology and Its Poor,” esp. 168–69. See Simmons, Vital Minimum, 56–78. For an introductory account of this school of thought, see Stefano Solari, “Catholic Perspectives on Poverty and Misery: From Nineteenth Century French Catholic Social Economists to the Contribution of Jesuits,” Cahiers d’économie Politique/Papers in Political Economy 59, no. 2 (2010): 185–203. Le vicomte Alban de Villeneuve-Bargemot, Économie politique Chrétienne, ou, Recherches sur la nature et les causes du paupérisme, en France et en Europe, et sur les moyens de le soulager et de le prévenir, vol. 2 (Paris: 1834), 313. Philip Manow and Bruno Palier emphasize the salience of religion, and of the political cleavages it generated, to the development of the French welfare state. See Philip Manow and Bruno Palier, “A Conservative Welfare State Regime without Christian Democracy? The French ÉtatProvidence, 1880–1960,” in Religion, Class Coalitions, and Welfare State Regimes, ed. Kees van Kersbergen and Philip Manow (Cambridge: Cambridge University Press, 2009), 147–75. According to Stedman Jones, the French political economist Jérôme-Adolphe Blanqui placed Condorcet among the bygone generation who believed that political reform could put an end to human suffering. Stedman Jones, An End to Poverty?, 193. Yet Blanqui also credited Condorcet and his generation for having been the first to realize that “there is a physiology of the social body as there is of the human body, and that there are laws according to which nations prosper or waste away, like individuals.” Jérôme-Adolphe Blanqui, History of Political Economy in Europe (1837), 4th  ed., trans. Emily J. Leonard (New York: G. P. Putnam’s Sons, 1885), 378. On the role of associations in promoting moral education for the working classes, see the discussion in Blanqui, History of Political Economy, 477–90. In this respect, while I agree with Simmons that “the politics of human need were central to the rise of the European welfare state,” my argument shows that need was only partially definitive and had to coexist in liberal regimes with a politics of choice, responsibility, and merit. Simmons, Vital Minimum, 1.

Notes to Pages 100–104 / 217 128. Freeden, “Coming of the Welfare State,” 15. 129. Ian Hacking has written that whereas “Laplace made the subjective probability idea officially preeminent,” Fourier inaugurated the “reversal of fortunes” that brought the objective idea into favor, with Quetelet and other statistical enthusiasts following suit. Hacking, Taming of Chance, 97. I have been arguing that thinking about insurance straddled the epistemic and aleatory understandings of risk and, in so doing, mirrored the uneasy coexistence of the two within probability theory throughout this period. In this respect, there is an important continuity between Laplace and Quetelet, in that both can be understood as part of single tradition in which probabilities and the practices that employed them, especially insurance, were seen to offer a bridge between the individual and the common good. 130. G. S. Boyer, Projet d’assurance générale de bienfaisance nationale et de secours mutuel dans les 86 départemens, 2nd ed. (La Ferté-sous-Jouarre: Guldon, 1842); Raoul Boudon, Organisation unitaire et nationale de l’assurance (Paris: Librairie phalanstérienne, 1848); Girardin, La politique universelle. These three tracts are also the focus of the discussion in Ewald, L’État providence, 214–19. For a discussion of several additional French enthusiasts of mutual insurance in the second half of the nineteenth century, see Rosanvallon, La nouvelle question sociale, 24–26. 131. On Girardin, see Christopher Guyver, The Second French Republic, 1848–1852: A Political Reinterpretation (London: Palgrave Macmillan, 2016), 5. 132. Boyer, Projet d’assurance générale, 7. 133. Boudon, Organisation unitaire, 21. Boudon took pains to distinguish mutual insurance, which he associated with the social principle, from fixed-premium insurance, which he associated with speculation. Ibid., 9. 134. Ibid., 22. 135. Ibid., 14, 19, and 43. 136. Ibid., 47; cf. 40. 137. Ibid., 24. See also the discussion of this issue in Thomas, “Caisses de Retraites,” 258. 138. Boudon, Organisation unitaire, 24. 139. Ibid., 36. 140. Ibid., 61–62. 141. Maurice Reclus, Émile de Girardin: le créateur de la presse moderne (Paris: Librairie Hachette, 1934), 234, 200. 142. See Émile de Girardin, Le socialism et l’impot, in Œuvres Completes d’Émile de Girardin (Paris: M. Lévy Frères, 1849), and L’abolition de la misère par l’élévation des salaires. Lettres a M. Thiers (Paris: Imprimerie Gerdès, 1850), 34–35, 40. 143. Girardin, La politique universelle, 23. 144. Ibid., 19. 145. Girardin, L’abolition de la misère, 50–51. 146. Ewald, L’État providence, 219. 147. Girardin, L’abolition de la misère, 51. Tom Baker points out that midcentury insurance underwriters also linked insurance to self-reliance and thrift, and castigated as immoral those who failed to exercise the prudence required to pay for insurance. See Baker, “Genealogy of Moral Hazard,” 255. 148. This was a central critique of the principle in mid-nineteenth-century probabilistic thinking. Keynes would later assert that the “enunciation of this principle, as it is ordinarily expressed, cloaks, but does not avoid,” the “element of direct judgment” on the part of the calculator. Keynes, Treatise, 58. 149. Despite Napoleon’s decision to preserve and even support French mutualism, many

218 / Notes to Pages 105–108 societies were openly politicized in opposition to him, particularly during the electoral campaigns of 1869–70. Price, Napoleon III, 47. As Bernard Gibaud explains, Napoleon and his administration saw mutual societies as an opportunity for social engineering, not for the exercise of individual liberty (although this task proved more difficult than anticipated). Bernard Gibaud, De la mutualité à la sécurité sociale: conflits and convergences (Paris: Les Éditions ouvrières, 1986), 37–38. CHAPTER FOUR

1.

2. 3.

4. 5.

6. 7.

8. 9.

Cournot, who was among the first frequentists, famously distinguished between objective and subjective probabilities, and those terms have remained prominent in subsequent philosophical treatments of the subject. I have followed Hacking in preferring the terms “aleatory” and “epistemic,” which are less anachronistic in the context of the earliest accounts. In the case of frequentism, “ontic” may be more appropriate than either “objective” or “aleatory.” See Thierry Martin, “Cournot’s Probabilistic Epistemology,” in Augustin Cournot: Modelling Economics, ed. Jean-Philippe Touffut (Cheltenham, UK: Edward Elgar, 2007), 23n7. Nevertheless, I use the more standard terms throughout my discussion here. Quetelet, Treatise, 7. Porter, Rise of Statistical Thinking, 77. My understanding is indebted to Porter’s account, particularly in ibid., 71–88. Ian Hacking rightly argues that there are important continuities between the frequentist interpretation and prior views as well. For example, Fourier, writing before the rise of frequentism, noted stable frequencies emerging from statistical data, while Cournot, often classified as a frequentist, held that probabilities can be both subjective and objective. Ian Hacking, “Comment: In Praise of the Diversity of Probabilities,” Statistical Science 5, no. 4 (November 1990): 451–52. Laplace, Philosophical Essay on Probabilities, 3. John Stuart Mill, A System of Logic, Ratiocinative and Inductive, bk. 3, ch. 18 (MS and 1st ed. [1843]), in Collected Works of John Stuart Mill, vol. 8, ed. J. M. Robson (Indianapolis: Liberty Fund, 2006), 1142. Ellis, “Foundations,” 1. Ellis saw his project as aligning probability with the “a priori truth, supplied by the mind itself, which is ever endeavouring to introduce order and regularity among the objects of its perceptions.” Ellis, “Foundations,” 3. Venn, meanwhile, set out to undermine “the conception of the science of Probability as a science of the laws of belief,” which he proclaimed “seems to break down at every point.” John Venn, The Logic of Chance, 4th ed., 138, quoted in Philip Mirowski, “Marshalling the Unruly Atoms: Understanding Edgeworth’s Career,” in Edgeworth on Chance, Economic Hazard, and Statistics, ed. Philip Mirowski (Lanham, MD: Rowman and Littlefield, 1994), 46. For further analysis of the differences between Ellis and Venn, see Lukas M. Verburgt, “Remarks on the Idealist and Empiricist Interpretation of Frequentism: Robert Leslie Ellis versus John Venn,” BSHM Bulletin: Journal of the British Society for the History of Mathematics 29, no. 3 (2014): 184–95. Ellis, “Foundations,” 3. John Venn, The Logic of Chance, 3rd ed. (1888) (New York: Dover, 2006), 3. While Cournot maintained that statistics should seek to “penetrate as much as possible into the knowledge of the thing in itself,” Venn and others insisted that statistics evaded the need for causal knowledge. Cournot, Exposition de la théorie des chances, 185.

Notes to Pages 109–113 / 219 10. 11. 12. 13.

14. 15. 16. 17.

18. 19. 20. 21. 22.

23. 24.

25. 26. 27. 28. 29.

30. 31. 32. 33. 34.

Mill, System of Logic, in Robson, Collected Works, 8:1141. Ibid., 138. Ellis, “Foundations,” 2. R. L. Ellis, “Remarks on the Fundamental Principle of the Theory of Probability,” Transactions of the Cambridge Philosophical Society, vol. 9 (1856) [read Nov. 13, 1854]: 605, reprinted in The Mathematical and Other Writings of Robert Leslie Ellis, M. A., ed. William Walton (Cambridge: Deighton, Bell, 1863), 50. Venn, Logic of Chance, 3rd ed., 142. Ibid., 151. Ibid., 55. For a discussion of this view in Venn, see Verburgt, “Remarks,” 191–93. On the “surprisingly rich ontology” entailed by frequentism, see also Alan Hájek, “‘Mises Redux’—Redux: Fifteen Arguments Against Finite Frequentism,” Erkenntnis 45, no. 2/3 (November 1996): 218–19. Venn, Logic of Chance, 3rd ed., 100. C. S. Peirce, “A Theory of Probable Inference,” in Studies in Logic, ed. C. S. Peirce (Boston: Little, Brown, 1883), 152. See also Keynes, Treatise on Probability, 331–32. See Mill, System of Logic (1843–72), in Robson, Collected Works, 7:534–47; and compare the first (1843) edition, in ibid., 8:1140–50. Venn, Logic of Chance, 3rd ed., 148. Cournot, Exposition de la théorie des chances, 438; cf. 160. Similarly, Boole, although not a frequentist, insisted that the “rules which we employ in life-assurance, and in the other statistical applications of the theory of probabilities, are altogether independent of the mental phaenomena of expectation. They are founded upon the assumption that the future will bear a resemblance to the past; that under the same circumstances the same event will tend to recur with a definite numerical frequency; not upon any attempt to submit to calculation the strength of human hopes and fears.” Boole, Investigation, 244–45. Mill, System of Logic, in Robson, Collected Works, 8:538. Venn, Logic of Chance, 3rd ed., 148. This argument is reminiscent of Condorcet’s suggestion, which we encountered in the last chapter, that a concurrence value or average market price could be substituted for a personal mathematical expectation in voluntary transactions. Whereas Condorcet had set out to save the classical definition of expectation, however, Venn did not insist on the direct relevance of probability values to individual instances. Ibid., 7. Ibid., 149. Ibid. See ibid., 224–31. As Venn put it, whatever uniformity one observes today “has varied, and, under the influence of future eddies in opinion and practice, may vary still; and this to any extent, and with any degree of irregularity.” Ibid., 15. Ibid., 45–46. Cournot, Exposition de la théorie des chances, 334–35. Ibid., 337. Ibid., 347. Ibid., 342–45. Cournot noted that while increasing the size of the mutual association usually allows for the stabilization of premiums, this will not be the case if new members “commit the common fund for properties or risks that are too great in

220 / Notes to Pages 113–115

35.

36. 37. 38.

39.

40.

41.

42.

comparison to” those previously insured. Ibid., 342. To my knowledge, the thinkers under consideration in this chapter did not explicitly discuss, in the context of insurance, the fact that increasing the number of observations will also increase the variance of those observations, or in other words the extent of their fluctuations around the population mean, even as the sample average approaches closer to that mean. Edgeworth did discuss this general phenomenon in an 1888 article on the banking industry. See Francis Ysidro Edgeworth, “The Mathematical Theory of Banking,” Journal of the Royal Statistical Society 51, no. 1 (March 1888): 113–27, esp. 123. American professor Allan Willett also treated it in his 1901 economic treatise on insurance. Willett noted that, “According to the well-known statistical law, the figure denoting the probable variation increases only as the square root of the number of cases. Increasing the number of similar risks [i.e., observations] a hundredfold increases the probable variation by only tenfold.” Willett, Economic Theory, 32. Willett defined risk as “the objectified uncertainty as to the occurrence of an undesired event,” which “varies with the uncertainty,” or the extent of fluctuation around the mean, “and not with the degree of probability.” Ibid., 33. As a result, the relationship between sample size and fluctuation around the mean was central to his theory of insurance. I am grateful to Sandy Zabell for bringing both the issue of increasing fluctuation and the Edgeworth article to my attention in a private correspondence. See S. L. Zabell, Symmetry and Its Discontents: Essays on the History of Inductive Probability (Cambridge: Cambridge University Press, 2005), 18–27, for a brief but illuminating survey of views about equiprobability and chance from John Arbuthnot to Frank Ramsey. On randomness and causation, see Venn, Logic of Chance, 3rd ed., 98–111; Cournot, Exposition de la théorie des chances, esp. 82–84. Venn, Peirce, and Edgeworth all affirmed this account of randomness. For a summary and critique of their views, see Keynes, Treatise on Probability, 331–32. According to Keynes, writing in 1921, frequentism had a “large measure of . . . acceptance in England at the present time,” thanks to the fact that most English writers had approached probability “from the statistical side.” Ibid., 121. On the partial rejection of Venn’s critiques by the giants of statistics at the time, Edgeworth and Pearson, and his limited influence outside of England, see Zabell, Symmetry, 121–23; cf. Francis Ysidro Edgeworth, “The Philosophy of Chance,” Mind, n.s., 31, no. 123 (January 1922): 261 (hereinafter “Philosophy of Chance (II)”). Dana Simmons recounts that in the first third of the nineteenth century, the French hygienic reformer Louis René Villermé “famously used statistical methods to link public health and social inequality,” treating the poor “as a collective entity, with a collective fate.” Simmons, Vital Minimum, 34. Simmons further notes that “workers’ efforts to aggregate wage and budget data suggest that already in the 1840s, some workers sought to establish class identity and power through statistics.” Ibid., 56. A frequentist understanding of probabilities could have provided legitimation to this incipient working-class tendency, which grew stronger in France as the nineteenth century progressed. Ibid., 95–96. See Vincent and Plant, Philosophy, Politics and Citizenship, 47–48; Freeden, New Liberalism, 18; and Baldwin, Politics of Social Solidarity, 34–35. On the role of idealism in limiting Venn’s immediate influence, see Zabell, Symmetry, 123. It is important to note that “solidarity” in this context does not exclude considerations of self-interest. Rather, the claim is that to act rationally on the frequentist

Notes to Pages 115–118 / 221

43. 44. 45. 46.

47.

48. 49.

50. 51. 52. 53. 54. 55.

56. 57. 58. 59. 60.

61. 62. 63.

view, the individual must first identify herself with others in the relevant series or group; otherwise, she cannot logically attribute a probability value to her own case at all. Such identification rests on a kind of rational sympathy, which is not equivalent to deeply or holistically caring about someone else, but is also not the same as narrow self-interest or indifference to others’ fates. Venn, Logic of Chance, 392–93. On Venn’s change of heart about utilitarianism, and Edgeworth’s reaction, see Mirowski, “Marshalling the Unruly Atoms,” 46–47. Venn, Logic of Chance, 390. Ibid., 391, 392. An extended discussion of their relationship and points of dispute is found in Mirowski, “Marshalling the Unruly Atoms,” 46–47. Here Mirowski writes that Edgeworth was particularly provoked by Venn’s invocation of him as an authority against the practical relevance of moral expectation. It was Keynes who explicitly situated Edgeworth along with Ellis, Venn, and others in the frequentist camp, as part of a strategy to replace their views with his own account of probability as a logical relation. See ibid., 51; cf. 40. Yet Keynes also had good reason for this designation, and Edgeworth continued to indicate even later in life that the probability calculus is grounded in physical law. See Francis Ysidro Edgeworth, “On the Use of the Theory of Probabilities in Statistics Relating to Society,” Journal of the Royal Statistical Society 76, no. 2 (1913): 174. Porter characterizes Edgeworth’s view as allowing for a compromise between subjectivism and frequentism. Porter, Rise of Statistical Thinking, 259. Francis Ysidro Edgeworth, “The Philosophy of Chance,” Mind 9, no. 34 (April 1884): 235 (hereinafter “Philosophy of Chance (I)”). Francis Ysidro Edgeworth, “The Method of Measuring Probability and Utility,” Mind 12, no. 47 (July 1887): 484; cf. his “Applications of Probabilities to Economics,” Economic Journal 20, no. 78 (June 1910): 284–304. Edgeworth, “Probability and Utility,” 484. Edgeworth, “Philosophy of Chance (I),” 234–35. See also Francis Ysidro Edgeworth, “A priori Probabilities,” Philosophical Magazine 18, no. 112 (1884): 204–10. Edgeworth, “Probability and Utility,” 484. Sidgwick states this explicitly in his The Methods of Ethics (London: Macmillan, 1874), 387. Edgeworth, “Philosophy of Chance (I),” 234. Ibid., 233. Francis Ysidro Edgeworth, Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (London: C. Kegan Paul, 1881), 81. See also Mirowski, “Marshalling the Unruly Atoms,” 34–46. Edgeworth, Mathematical Psychics, 51. Mirowski, “Marshalling the Unruly Atoms,” 28–29. Edgeworth, Mathematical Psychics, 56. Ibid., 104. As Mirowski also notes, quoting Edgeworth’s 1877 New and Old Methods of Ethics, its young author was “most anxious to reconcile his reverence for demonstrable innate superiority with his utilitarianism,” which in this instance he set out to do using the “language of thresholds and sensitivities” borrowed from German physicist and mystic Gustav Fechner. Mirowski, “Marshalling the Unruly Atoms,” 15. Edgeworth, Mathematical Psychics, 80; cf. 102. Ibid., 129. See Francis Ysidro Edgeworth, “The Labour Party’s Aim: A Criticism and Restatement.

222 / Notes to Pages 118–121

64. 65. 66.

67. 68. 69. 70.

71. 72. 73.

74.

75. 76.

77.

78.

By seven members of the Labour Party,” Economic Journal 33, no. 132 (December 1923): 541. On the potential of probability calculations to undermine hierarchical distinctions, see the discussion in Porter, Rise of Statistical Thinking, 267. See Edgeworth, “Theory of Probabilities,” 184. Mirowski, “Marshalling the Unruly Atoms,” 43. See Edgeworth, “Theory of Probabilities,” 186; Francis Ysidro Edgeworth, “Methods of Statistics,” Journal of the Statistical Society of London Jubilee vol. (June 1885): 194. As Porter puts it, Edgeworth’s contributions within the philosophy of probability were generally inspired by the problem of finding the relationship between subjective beliefs and objective frequencies. Porter, Rise of Statistical Thinking, 265. Francis Ysidro Edgeworth, “The Theory of Distribution,” Quarterly Journal of Economics 18, no. 2 (February 1904): 218. Ibid., 219. Ellis, “Foundations,” 5. Charles Sanders Peirce, “On the Doctrine of Chances, with Later Reflections” (1878), in Philosophical Writings of Peirce, ed. Justus Buchler (New York: Dover, 1955), 159 Ibid., 162. Ibid., 161, 163. This is true for both Edgeworth and Venn. See, e.g., Edgeworth, “Theory of Distribution,” 219, referring to “Intellectual sympathy.” A remark by Edgeworth’s utilitarian authority, Henry Sidgwick, is also illuminating on this point: “I find it very difficult to distinguish the sympathetic and the properly moral feelings in introspective analysis of my own consciousness: it seems clear that these two elements are continually combined, but it is hard to say precisely in what proportion.” Sidgwick, Methods of Ethics, 463. Mirowski calls this “one of the more seductive analogies for Ysidro” in linking probability theory to utilitarianism. See Mirowski, “Marshalling the Unruly Atoms,” 25– 27, 40. Edgeworth, “Philosophy of Chance (II),” 260. Sidgwick noted the case for social welfare provision as a form of “fairly cheap insurance against the danger of crime” by those rendered desperate due to poverty, and observed that this view has “probably had considerable effect in enabling humane adherents of the system of natural liberty to shut their eyes to the socialistic aspects of these measures.” Yet this argument, which interprets welfare provision as the selfinsurance of the wealthy or of society against the risk of crime or revolution, is not the same as one that advocates the mutual insurance of groups of risk-prone individuals, assisted or orchestrated by the state. Henry Sidgwick, The Principles of Political Economy (London: Macmillan, 1883), 425. Arthur Pigou, Wealth and Welfare (London: Macmillan, 1912), 366. See also F. Y. Edgeworth, “Wealth and Welfare, by A. C. Pigou,” Economic Journal 23, no. 89 (March 1913): 62–70. Pigou, Wealth and Welfare, 367. In the case of unemployment benefits provided by unions, for example, Pigou noted that standard practices excluding “inferior workmen” ensure some uniformity of risk but are also exercised in a “strikingly lenient manner,” since the more desirable workers have an interest in preventing their less skilled peers from “cutting the standard rate.” They are therefore willing to accept insurance on actuarially unfair terms in light of the indirect economic benefit it provides. Ibid., 368.

Notes to Pages 121–123 / 223 79. For a fairly exhaustive list of explanations and an effort to empirically test each one, see David M. Cutler and Richard Johnson, “The Birth and Growth of the Social Insurance State: Explaining Old Age and Medical Insurance across Countries,” Public Choice 120, no. 1 (July 2004): 87–121. 80. The recent literature in this vein, beginning with Francois Ewald’s L’État providence, is fairly large and rather diverse. Other noteworthy contributions include Baldwin, Politics of Social Solidarity; Heath, “Benefits of Cooperation”; Rosanvallon, La nouvelle question sociale; van Parijs, “Assurance, solidarité, équité”; and Paul Johnson, “Risk, Redistribution and Social Welfare in Britain from the Poor Law to Beveridge,” in Charity, Self-Interest, and Welfare in the English Past, ed. Martin Daunton (London: UCL Press, 1996), 225–48. 81. Hacking, “In Praise of Diversity,” 452. 82. See Philipp Rehm, Risk Inequality and Welfare States: Social Policy Preferences, Development, and Dynamics (Cambridge: Cambridge University Press, 2016); Rehm, Hacker, and Schlesinger, “Insecure Alliances”; Iversen and Soskice, “Democratic Limits to Redistribution.” 83. The following account remains agnostic about the precise causal mechanisms by which this set of ideas influenced policy outcomes. But cf. Daigneault, “Reassessing,” 464. 84. In this respect, my argument derives support from Ann Shola Orloff’s observation that “intellectuals, politicians, labor leaders, and charity workers interested in questions of social policy were, in [Canada, the United States, and Britain,] as in Europe and Australasia, a part of an international community of policy discourse which diffused ideas and specific proposals relating to the social question and workingmen’s insurance far beyond the areas in which they were initially formulated.” Ann Shola Orloff, The Politics of Pensions: A Comparative Analysis of Britain, Canada, and the United States, 1880–1940 (Madison: University of Wisconsin Press, 1993), 162. 85. This distinction—and my overall interpretation of the intersection between probability theory and public policy at this time—differs from Hacking’s emphasis on the divide between the “atomistic, individualistic and liberal” view that prevailed in France and England, grounded in a kind of statistical fatalism, and the “holistic, collectivist and conservative” view found Germany, where such fatalism was rejected. Noting that “the conservative East created the welfare state,” Hacking suggests that this view emphasized the role of the state in creating the conditions in which individuals can become good. Hacking, Taming of Chance, 36; see also 125–30. In contrast to Hacking, I have found elements of atomistic and holistic tendencies in both theories of social insurance, as well as in both geographical areas: Bismarck’s vision had atomistic aspects, for example, while mutualism in late nineteenth-century France took on a more holistic hue. Moreover, Venn, on whom I have focused as an expositor of frequentism, did not endorse statistical fatalism yet did propose what I have described as a collectivist approach to risk. Instead, the primary distinction I wish to draw is between an account that sees the state as the primary agent of reform and individuals as its primary targets, and one that emphasizes risk groups as both the subjects and the objects of social protection. In this respect, the following analysis focuses somewhat less on national differences than on the manifestation of certain ideal types or models in a variety of contexts. 86. This point is also emphasized in Moss, When All Else Fails, 157–58. 87. Detlev Zöllner, “Germany,” in The Evolution of Social Insurance, ed. Peter A. Köhler and Hans F. Zacher (London: Frances Pinter, 1982), 19, 25–26.

224 / Notes to Pages 123–125 88. Yves Saint-Jours, “France,” in ibid., 112, 114. 89. See A. I. Ogus, “Great Britain,” in ibid., 151. A very good analysis of the 1897 act and its impact is found in P. W. J. Bartrip and S. B. Burman, The Wounded Soldiers of Industry: Industrial Compensation Policy, 1833–1897 (Oxford: Clarendon Press, 1983), esp. 214–21. 90. Oliver Wendell Holmes Jr., “The Path of the Law,” Harvard Law Review 10, no. 8 (March 1897): 467. See also Morton Horwitz, The Transformation of American Law, 1870–1960 (Oxford: Oxford University Press, 1992), 54–63. 91. Theda Skocpol points out that these were the only reforms that succeeded out of the entire Progressive-era social agenda. Skocpol, Protecting Soldiers and Mothers, 8. 92. David Moss emphasizes the distinction between these two approaches, with risk spreading as a form of cooperative association and risk shifting as a transfer of costs, often as a means to reduce risk by placing its burden on the party most able to prevent it. See Moss, If All Else Fails, 1–2, 170–71. 93. Prior to this time, pensions did exist in France, specifically for military personnel and civil servants. The former dated to the post-Revolutionary period, when Napoleon honored his promise to pay pensions to veterans. The restored Bourbons preserved these, along with pensions for other civil servants. Blackburn, Banking on Death, 43. 94. Roy Lubove, “Economic Security and Social Conflict in America: The Early Twentieth Century, Part II,” Journal of Social History 1, no. 4 (Summer 1968): 327. Lubove points out the limited success of all three programs. By the early 1890s, he writes, fewer than 200,000 pensioners were on the government rolls and the life insurance institution had sold only a few thousand policies. Ibid., 327n6. 95. Under these laws, the state would be granted responsibility for administering pensions, while sickness was to remain the province of the mutuals, under the protection and statistical tutelage of the government. Ewald, L’État providence, 209–10. 96. Baldwin, Politics of Social Solidarity, 102; Zöllner, “Germany,” 13. 97. Michael Stolleis, History of Social Law in Germany, trans. Thomas Dunlap (Berlin: Springer-Verlag, 2014), 21–24, 35, 41. The mining industry was the exception, and its associations would provide an exemplar for compulsory insurance. Ibid., 36. 98. See Blackburn, Banking on Death, 46. 99. Stolleis, History of Social Law in Germany, 41. 100. Bismarck to his confidant Moritz Busch, quoted in Blackburn, Banking on Death, 46. 101. Zöllner, “Germany,” 24–25. 102. E. P. Hennock, The Origin of the Welfare State in England and Germany, 1850–1914: Social Policies Compared (Cambridge: Cambridge University Press, 2007), 160. Nevertheless, as George Steinmetz points out, the viability of the occupationally based “free funds” was damaged in 1892 by a revision to an earlier provision that had allowed them to pay cash benefits to members instead of medical care. Since they could not set up their own medical centers, this change led to the demise of many funds. George Steinmetz, Regulating the Social: The Welfare State and Local Politics in Imperial Germany (Princeton, NJ: Princeton University Press, 1993), 126. 103. See Hennock, Origin of the Welfare State, 183–87. 104. Baldwin points out that in Germany the contractual nature of this right replaced the socialist argument for a right to aid from surplus economic value. Baldwin, Politics of Social Solidarity, 71. On the singling out of particular groups, see Steinmetz, Regulating the Social, 124. 105. On differentiation, see Hennock, Origin of the Welfare State, 195, 198. Steinmetz

Notes to Pages 125–128 / 225

106. 107. 108. 109.

110.

111. 112. 113.

114. 115.

116. 117.

118.

emphasizes the disciplinary character of insurance in this respect, in that it required workers to remain stably employed and make steady payments into the system to receive benefits, and also provided an incentive for contributors to monitor one another to ward against fraud. Steinmetz, Regulating the Social, 124–25. Baldwin, Politics of Social Solidarity, 97–98. On Bismarck’s intention, see Steinmetz, Regulating the Social, 124; on the law itself, see Hennock, Origin of the Welfare State, 157–60. See Jacobs, Governing for the Long Term, 86–87. See also Stolleis, History of Social Law in Germany, 41. Jacobs notes the importance of temporal separation between payment and receipt in his discussion of old-age and disability benefits. Jacobs, Governing for the Long Term, 87. Bismarck, “Speech of June 18, 1889,” quoted in Gerhard A. Ritter, Social Welfare in Germany and Britain: Origins and Development, trans. Kim Traynor (Warwickshire, UK: Berg, 1986), 35. Baldwin, Politics of Social Solidarity, 102–4. De Swaan, In the Care of the State, 198–202. In the years leading up to its passage, many mutualists had reluctantly concluded that some form of compulsory insurance was inevitable given the relatively limited scope of voluntary schemes, and they agreed to accept a compulsory plan in exchange for a central role in its administration. See Janet R. Horne, A Social Laboratory for Modern France: The Musée Social and the Rise of the Welfare State (Durham, NC: Duke University Press, 2001), 217–22. De Swaan, In the Care of the State, 201–2. See also Saint-Jours, “France,” 120–27. During the mid-nineteenth-century debates over the national pension scheme, legislative reporter Benoist D’Azy argued against national insurance on the ground that mutual “societies are above all destined to propagate the spirit of family; they are true families, in which everyone must know each other, so that common respect will maintain reciprocal concern and the spirit of duty.” An insurance scheme based on too expansive a pool, as in compulsory state insurance, “will lose a large part of these advantages.” Benoist D’Azy, “Rapport au nom de la Commission chargée d’examiner les propositions de MM Dufournel et Lestiboudois  .  .  .  ,” Assemblée législative, October 6, 1849, quoted in Ewald, L’État providence, 211. The continued strength of French mutualism may be attributable in part to the persistence of localism in French politics more generally. According to Timothy Smith, following Eugen Weber, it was only between roughly 1880 and 1914 that Frenchmen began to shift their allegiance from their localities to the nation as a whole. See Timothy B. Smith, Creating the Welfare State in France, 1880–1940 (Montreal: McGill-Queen’s University Press, 2003), 19. Horne, Social Laboratory, 213. Léon Bourgeois, Solidarité, 1st ed. (Paris: A. Colin, 1896), 89–90. On Bourgeois’s middle way between liberalism and socialism, see Daniel Béland, “État-providence, libéralisme et lien social. L’expérience française: du solidarisme au ‘retour’ de la solidarité,” Cahiers de recherche sociologique, no. 31 (1998): 145–64. Peter Baldwin calls Bourgeois’s thought “a Gallic version of the liberal idealist theories of citizenship spoken for across the Channel by T. H. Green, Alfred Marshall, R. H. Tawney and others that would later be given concrete substance in Beveridge’s reforms.” Baldwin, Politics of Social Solidarity, 35. Léon Bourgeois, “Rapport de M. Léon Bourgeois au Congrès d’Éducation Sociale en 1900,” reprinted in Solidarité, 3rd ed. (Paris: A. Colin, 1902), 180.

226 / Notes to Pages 128–131 119. Bourgeois, Solidarité, 3rd ed., 101. 120. See Léon Bourgeois, “Extrait du compte rendu de la séance du Congrès d’Éducation Sociale du jeudi soir 27 septembre 1900,” reprinted in Solidarité, 3rd ed., esp. 190–208. 121. Ibid., 201–2. 122. Bourgeois, Solidarité, 1st ed., 94–95. See also ibid., 113–14: “For the determination of the rights and obligations of each in the solidaristic association that exists between men, for the calculation of profits and costs to be divided among all, one must be in possession of a coefficient common to all, a value of equal rights for all. Among innumerable elements of the calculation, drawn from the natural inequalities that separate and differentiate men, it is necessary always, to determine the equitable situation for each, to take into consideration this value and to admit it as equal for all.” 123. Béland, “État-providence, libéralisme et lien social,” 155. 124. Douglas Ashford notes that French politicians at this time were more concerned than their contemporaries in Britain and the United States about the effects of privileging certain categories of beneficiaries in public insurance schemes, which they worried would divide rather than unite the nation. Douglas Ashford, The Emergence of the Welfare States (Oxford: Basil Blackwell, 1986), 153–54. 125. For a detailed analysis of the relationship between postwar welfare reforms and the mutualist movement in France, see Bernard Gibaud, “Mutualité/Sécurité sociale (1945–1950): la convergence conflictuelle,” Vie sociale 4, no. 4 (December 2008): 39–52. 126. Baldwin, Politics of Social Solidarity, 65, 74–75. 127. See ibid., 81–82. 128. Preamble to the first draft of the 1881 accident insurance law, quoted in Ritter, Social Welfare, 34. 129. According to Peter Lindert, extending political voice to the full adult population was among the greatest sources, if not the greatest source, of the rise of social spending between 1880 and 1930. See Lindert, Growing Public, 179–82, 188–89. 130. This account of early welfare’s flexible actuarialism both echoes and departs from Karl Polanyi’s account of the rise of economic interventionism in the later nineteenth century. Polanyi argues that the replacement of a liberal principle in economic life with a collectivist one did not arise from a “change either in the type of interests involved, or in the tendency of the opinions brought to bear on the matter,” but from “the evolving conditions under which” the problems of a selfregulating market system “arose and a solution was sought.” Karl Polanyi, The Great Transformation: The Political and Economic Origins of Our Time, 2nd ed. (Boston: Beacon Press, 2001), 153. The discussion here accords with Polanyi’s in emphasizing the pragmatic nature of this early approach to welfare and its close connection with the demands generated by a market economy. It diverges insofar as it sees such pragmatism as also reflecting, at least in some instances, a philosophical stance. In addition, in emphasizing the class-oriented character of early social legislation, I depart somewhat from Pierre Rosanvallon’s view that the type of solidarity that historically defined the welfare state hinges on ignorance of specific actuarial differences. While this may have been true of the post–World War II welfare states, at least in principle, it was not quite true of the earliest social insurance programs. See Rosanvallon, La nouvelle question sociale, esp. 27–36. 131. As in the other countries we are considering, in Britain several laws on employer

Notes to Page 131 / 227

132.

133.

134.

135.

136.

liability and workers’ compensation had gradually extended laborers’ rights of recovery for industrial accidents between 1880 and 1906. In 1905, a legislative resolution allowing local authorities to give food to hungry schoolchildren officially established the principle of state concern for the lives of adult laborers (via their offspring), and was followed a few years later by the institution of school medical inspections. See Bentley Gilbert, The Evolution of National Insurance in Great Britain: The Origins of the Welfare State (London: Michael Joseph, 1966), 102–54. Despite these earlier developments, however, many historians seem to agree that the new era of social reform did not begin in Great Britain until the introduction of old-age pensions in 1908. Applicants had to prove they were mentally healthy, had held habitual employment in the trade of their choice, had not been in prison within the past ten years (later amended to two), and had not previously received poor relief. Ibid., 222. According to Hennock, the last condition in particular was so starkly at odds with the goal of the pension law that Parliament removed it in 1911. Hennock, Origin of the Welfare State, 224. The introduction of a means test was also starkly at odds with the aims of the labor movement. Nevertheless, at least some leaders regarded the law as a partial success. See Pat Thane, “The Working Class and State ‘Welfare’ in Britain,” Historical Journal 27, no. 4 (December 1984): 896. Bentley Gilbert, “The Decay of Nineteenth-Century Provident Institutions and the Coming of Old Age Pensions in Great Britain,” Economic History Review 17, no. 3 (1965); cf. Baldwin, Politics of Social Solidarity, 99–100; Harris, Origins of the British Welfare State, 164; and Hugh Heclo, Modern Social Politics in Britain and Sweden: From Relief to Income Maintenance (New Haven, CT: Yale University Press, 1974), 175. Remarks by Winston Churchill provide evidence that the noncontributory character of the pension scheme did not remove it from the social insurance paradigm as it was understood at the time. “There is no inconsistency or contradiction,” he explained, “between a non-contributory system of old-age pensions and a contributory system of insurance against unemployment, sickness, invalidity, and widowhood.” The reason is that the possibility of attaining old age “seems so doubtful and remote to the ordinary man, when in the full strength of manhood, that it has been found in practice almost impossible to secure from any very great number of people the regular sacrifices” to provide for that eventuality. “But unemployment, accident, sickness, and the death of the breadwinner are catastrophes which may reach any household at any moment,” making contributions more palatable. Winston Churchill, “The Budget and National Insurance,” The Free Trade Hall, Manchester, May 23, 1909, in Liberalism and the Social Problem (New York: Haskell House, 1973), 311–12. On the nature of the Liberal welfare reforms as a “major watershed in British welfare policy,” see George R. Boyer, The Winding Road to the Welfare State (Princeton, NJ: Princeton University Press, 2018), 25; on the pension law specifically, see ibid., 195. For an extended discussion of why the poor law was an unacceptable response to the problem of elderly poverty at the time that it became a political issue, see Hennock, Origin of the Welfare State, 213–19. See E. P. Hennock, “The Origins of British National Insurance and the German Precedent, 1880–1914,” in The Emergence of the Welfare State in Britain and Germany, 1850–1950, ed. W. J. Mommsen (London: Croom Helm, 1981), 84–106. See also Boyer, Winding Road, 214–15. Orloff, Politics of Pensions, 153.

228 / Notes to Pages 131–134 137. Macnicol, Politics of Retirement, 138–39. Macnicol’s analysis and the argument of this paragraph might seem to be in tension with Hennock’s conclusion that the 1908 act is “best understood as Poor Law reform.” Yet Hennock’s claim that pensions emerged out of a “determination to provide an income-support that would be a full substitute for poor relief and remove their recipients from all contact with the Poor Law authorities” supports the view that the law amounted to a deliberate shift in paradigm with lasting implications for welfare policy, even if it did not fully realize these intentions in practice. Hennock, Origin of the Welfare State, 225. 138. See Macnicol, Politics of Retirement, 144; Blackburn, Banking on Death, 47. 139. Orloff, Politics of Pensions, 157. See also Macnicol, Politics of Retirement, esp. 143– 44, which argues that the labor movement regarded pensions as part of an effort to replace the poor law with universal measures such as work or support for the unemployed and expanded public education. 140. De Swaan, In the Care of the State, 183–84, 196. The perception that unemployment could not be insured against was not uncommon: On Germany, see Isabela Mares, “Is Unemployment Insurable? Employers and the Development of Unemployment Insurance,” Journal of Public Policy 17, no. 3 (September–December 1997): 300–1; on France, see Ewald, L’État providence, 209. 141. Winston S. Churchill, “Unemployment,” Kinnaird Hall, Dundee, October 10, 1908, in Liberalism and the Social Problem (New York: Haskell House, 1973), 196. 142. Ibid., 198. 143. Ibid., 201–2. 144. Winston Churchill, “Labour Exchanges and Unemployment Insurance,” House of Commons, May 19, 1909, in ibid., 267. 145. Ibid., 266. 146. Gilbert, Evolution of National Insurance, 281. 147. William Beveridge, “Unemployment Insurance, Objections and Answers,” quoted in José Harris, William Beveridge: A Biography, rev. paperback ed. (Oxford: Oxford University Press, 1997), 181. 148. Churchill praised friendly societies and trade unions for providing workers with insurance, and emphasized that state policy should “benefit and encourage” rather than undermine existing voluntary institutions. Winston Churchill, “The Budget and National Insurance,” The Free Trade Hall, Manchester, May 23, 1909, in Liberalism and the Social Problem, 314–15. This point makes for another contrast with Bismarck’s vision. 149. John Fabian Witt, “Toward a New History of American Accident Law: Classical Tort Law and the Cooperative First-Party Insurance Movement,” Harvard Law Review 114, no. 3 (January 2001): 781, 778–79. 150. See ibid., 811. 151. Ibid., 828–32, 837. 152. See I. M. Rubinow, “Labor Insurance,” Journal of Political Economy 12, no. 3 (June 1904): 362–63. This view of the friendlies as offering charity is historically inaccurate, at least as a matter of the self-understanding of society members themselves. Cordery argues that as early as 1800, friendlies were widespread precisely because “members could claim [insurance] as a right rather than request [it] as a gift.” Cordery, British Friendly Societies, 18. 153. I. M. Rubinow, “Compulsory State Insurance of Workingmen,” Annals of the American Academy of Political and Social Science 24 (September 1904): 47. 154. See Michelle Landis Dauber, The Sympathetic State: Disaster Relief and the Origins of

Notes to Pages 134–136 / 229

155. 156.

157. 158.

159. 160.

161.

162.

163.

164.

165.

the American Welfare State (Chicago: University of Chicago Press, 2012), 12; Walter I. Trattner, From Poor Law to Welfare State: A History of Social Welfare in America, 6th ed. (New York: Free Press, 1999), 277–79. On the role played by employers in the passage of the Social Security Act, see Hacker, Divided Welfare State, 98–104. See Edward Berkowitz and Kim McQuaid, Creating the Welfare State: The Political Economy of Twentieth-Century Reform, rev. ed. (Lawrence: University Press of Kansas, 1992), 43–49. Hacker, Divided Welfare State, 106–8. Berkowitz and McQuaid, Creating the Welfare State, 126, 156. Business leaders did not succeed in achieving all of their aims, however. For example, the Clark Amendment to the Social Security Act would have allowed employers and employees who already had pension plans to opt out of the federal law. Planners objected that this would leave the federal government with the worst risks and saddle the public sector with prohibitive costs. Although the measure passed the Senate, it was tabled by Roosevelt and ultimately abandoned. See ibid., 125. Hacker, Divided Welfare State, 104. For a detailed account of the role of interest-group preferences, including and particularly business interests, in the emergence of welfare benefits in the United States, see Frank R. Dobbin, “The Origins of Private Social Insurance: Public Policy and Fringe Benefits in America, 1920–1950,” American Journal of Sociology 97, no. 5 (March 1992): 1416–50. A. V. Dicey, Lectures on the Relation between Law and Public Opinion in England during the Nineteenth Century, 2nd ed. (1914), ed. Richard VandeWetering (Indianapolis: Liberty Fund, 2008), 188. Some contemporary economists use the term “ambiguous” to refer to probabilities that are in some sense more uncertain than frequencies calculated from extensive and reliable data. This use stems from a 1961 article by Daniel Ellsberg, defining ambiguity as “a quality depending on the amount, type, reliability and ‘unanimity’ of information, and giving rise to one’s degree of ‘confidence’ in an estimate of relative likelihoods.” Daniel Ellsberg, “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, no. 4 (November 1961): 657. For example, in his discussion of early Danish social insurance, Baldwin notes that whereas work accident insurance dealt with risks the incidence of which differed clearly among social and occupational groups, pensions covered a “universally probable eventuality whose variation according to class was little understood.” As a result, universal coverage was politically feasible for pensions in a way that it was not for accident insurance. Baldwin, Politics of Social Solidarity, 81. At the same time, new observation and experience could reveal shared vulnerabilities that had not been widely noted before. For instance, as Arwen Mohun points out, in the first decades of the twentieth century new statistical data showed that “the risks of living in an industrial society were not restricted to or even primarily rooted in riding railroads or working in factories,” but extended to other areas of everyday life. Mohun, Risk: Negotiating Safety, 140. This realization spawned a public-safety movement based on the collective experience captured by those statistics. Ibid., 141–46. Hájek, “‘Mises Redux’—Redux”; Alan Hájek, “Fifteen Arguments Against Hypothetical Frequentism,” Erkenntnis 70, no. 2 (March 2009): 211–35. Venn was a finite frequentist, for example, while Peirce took a hypothetical view. Hájek, “‘Mises Redux’—Redux,” 217–18.

230 / Notes to Pages 136–140 166. Ibid., 220–21. 167. The same cannot clearly be said about hypothetical frequentism, which faces philosophical challenges no less severe and which has no discernable answer to Hájek’s “argument from concern.” 168. Furthermore, to the extent that one sees such relativity as a problem, it is not unique to frequentism; frequentists may just be the most explicit in acknowledging it. See Hájek, “Reference Class Problem,” 563–85. 169. As American actuary Miles Dawson put it, in insurance “persons who, so far as they can themselves see or so far as the managers can discriminate, are equally liable to a given peril, contribute equally in proportion to the indemnity desired by each, small sums to a common fund” from which anyone who suffers the loss will draw. Miles Menander Dawson, The Business of Life Insurance (New York: A. S. Barnes, 1905), 3. Similarly, the 1913 work by economics professor William Gephart notes that all one needs for the application of the “insurance principle” is “a relatively homogenous group exposed to a risk, the probability of which can be calculated with some reasonable degree of accuracy.” W. F. Gephart, Principles of Insurance (New York: Macmillan, 1913), 37. 170. In a market setting, a risk pool comprising only high-risk individuals will result in prices that are prohibitive to those with lower risks. As a result, one might conclude that the purpose of risk pooling is not to promote banding together within one’s own group but to enable mutually beneficial cooperation beyond it. As stated, however, this argument does not account for the distinction between the perspective of the insured and that of the insurer. If probability estimates for the various risk classes are known, then the desirability of insurance from the perspective of a lowerrisk individual cannot rest on the fact that her premiums subsidize others. It might be shown that such subsidization is necessary or beneficial—for example, if increasing the size of the pool will reduce the uncertainty for all. Yet such a claim still does not tell us how much subsidization should take place or why those with lower risks would not be better off forming a pool of their own. CHAPTER FIVE

1.

2.

3.

4.

It is important to reiterate here that throughout this text I use the term “likelihood” in its nontechnical sense, as interchangeable with probability. Contemporary Bayesians distinguish likelihoods from probabilities, defining the former in the context of Bayes’s rule as the probability of the observed data given the choice of a parameter value and model. Because the parameter value can and does change in Bayesian inference, likelihoods on this definition do not necessarily integrate to the value of one and are therefore technically distinct from probabilities. The authoritative articulation of this view came from Richard Titmuss, “War and Social Policy” in his Essays on “the Welfare State,” 3rd ed. (London: George Allen & Unwin, 1976), 75–87. See also Briggs, “Welfare State,” 223. These statutes were the Family Allowances Act of 1945, the National Insurance and National Health Service Acts of 1946, and the National Assistance Act of 1948. See Sir William Beveridge, Social Insurance and Allied Services, American ed. (New York: Macmillan, 1942). For a full account of Beveridge’s report and its implementation see Harris, William Beveridge, esp. 377–450. Baldwin, Politics of Social Solidarity, 135, 140–44, 152–53. A flat-rate pension was also created in the Netherlands in the postwar period, while in Canada, as in Swe-

Notes to Pages 140–141 / 231 den and Britain, means testing was abandoned as part of the push for a more universal, Beveridge-style old-age assistance system. See Cutler and Johnson, “Birth and Growth,” 98–99. 5. Baldwin, Politics of Social Solidarity, 279–86; Hacker, Divided Welfare State, 21. In focusing on universality as the principal aim of many policies during this period, I do not rely on the distinctions influentially proposed by Gøsta Esping-Andersen between liberal, conservative, and social-democratic welfare regimes. See EspingAndersen, Three Worlds, 26–29. One reason for this is my narrower focus on social insurance, which reveals commonalities among countries from different categories, rather than on the broader constellation of factors that defines each regime. Without denying the importance of his typology, then, I believe my account of the challenges of universal coverage, as well as the mixed character of social insurance in general, is relevant to all welfare states. 6. See Robert E. Goodin, “The End of the Welfare State?,” in Ball and Bellamy, Twentieth-Century Political Thought, 203–4. On the totalizing ambitions of Beveridgestyle social insurance compared to its predecessors, see Peter Baldwin, “Beveridge in the Longue Durée,” in Beveridge and Social Security: An International Retrospective, ed. John Hills, John Ditch, and Howard Glennerster (Oxford: Clarendon Press, 1994), 42–45. 7. Alan T. Peacock, The Economics of National Insurance (London: William Hodge, 1952), 41–42. 8. Douglas Ashford has chronicled the ways in which the interwar period, while lacking in significant policy innovations, helped lay the institutional and political foundations for postwar social legislation. For example, during those years the advanced democracies of Europe and the United States experienced significant bureaucratic expansion, the ongoing substitution of national for local welfare provision, and the waning of mutual insurance societies. Ashford, Emergence of the Welfare States, 106–85. 9. One such distinction is between the earlier social assistance state, the insurancedominated “social security” state, and the noncontributory “social welfare” state. See Robert E. Goodin, Reasons for Welfare: The Political Theory of the Welfare State (Princeton, NJ: Princeton University Press, 1988), 3–4. 10. For example, Eveline Burns, writing in 1949, noted that workers were only rarely required to make contributions under American unemployment laws, and never under workers’ compensation, yet such programs were still widely understood as offering “insurance.” Eveline M. Burns, The American Social Security System (Boston: Houghton Mifflin, 1949), 29. Similarly, as Beatrice and Sidney Webb had admitted a few decades earlier, in discussing compulsory invalidity insurance, the issue of how precisely to finance such schemes “is, in reality, one as to what is the most equitable and most convenient incidence of taxation,” without regard for proportionality between contributions and benefits. Sidney and Beatrice Webb, The Prevention of Destitution (London: Longmans, Green, 1911), 186. 11. Eveline M. Burns, “Social Insurance in Evolution,” American Economic Review 34, no. 1 (March 1944): 201. 12. An early version of this claim was made by Burns, who pointed out that existing social insurance programs exert a “dynamic influence,” broadening public perceptions of the aims of welfare and legitimating insurance as the means for achieving those aims. Ibid., 199–211.

232 / Notes to Pages 141–145 13. Hacker’s argument, for example, is that in the American case path dependence frequently encouraged the continuation of private over public welfare provision. Hacker, Divided Welfare State, 55–58. 14. Desrosières, Politics of Large Numbers, 164. 15. Ibid., 204–9. 16. Ibid., 165–66; Briggs, “Welfare State,” 229. 17. On Beveridge’s opposition to means testing in all but extreme cases, see Harris, William Beveridge, 377, 381–86, 410. More generally, see Eveline M. Burns, “Priorities for Public Welfare,” Social Work 3, no. 4 (October 1958): 38–39. 18. See also Burns, “Social Insurance in Evolution,” 207. 19. William Beveridge, “Insurance for All and Everything” (London: Daily News, 1924), 31. Harris argues that during the interwar years, Beveridge opposed the kind of liberal-collectivist, mixed-economy principles that later became associated with his proposals and instead believed that policymakers had to choose between a free market softened by a limited safety net and a completely planned economy on the model of the Soviet Union. He changed his position during the Second World War, however, coming to see social insurance as part of a more ambitious economic program that would include minimum-wage legislation, the nationalization of land and housing, and the encouragement of full employment. José Harris, “Beveridge’s Social and Political Thought,” in Hills, Ditch, and Glennerster, Beveridge and Social Security, 28–29. Beveridge’s mature vision, which Harris characterizes as “classical-republican,” reflected an ethos of “regular work, modest rewards, moral cohesion, family life, communal provision against need, stoic virtue, and mutual self-policing.” Ibid., 35. 20. Britain’s National Health Service, for example, was from the outset to be financed by general taxation rather than individual contributions. Ogus, “Great Britain,” 192. 21. Beveridge, Social Insurance and Allied Services, 12–13. 22. Sidney and Beatrice Webb, Prevention of Destitution, 213. 23. Ibid., 214; cf. 185–92. Although the Webbs opposed unconditional relief, they favored universality as a means to break up the poor laws. See Gilbert, Evolution of National Insurance, 214. Their thinking about the organization of social insurance schemes influenced Beveridge, who remained faithful to their framework, including its disciplinary undertones. See Harris, William Beveridge, 410. 24. On the Webbs and the relationship between prevention and universalism, see Richard Titmuss, “Welfare State and Welfare Society” (1967), in Commitment to Welfare (New York: Random House, 1968), 129–30. On the limited influence of Fabian ideas on the shape of the British welfare state, see E. J. Hobsbawm, Labouring Men: Studies in the History of Labour (London: Weidenfeld and Nicolson, 1964), 252. 25. Richard Titmuss, “The Role of Redistribution in Social Policy” (1965), in Commitment to Welfare, 191. 26. Ibid. 27. Ibid., 196. 28. Baldwin, Politics of Social Solidarity, 30–31. 29. Ibid., 116. 30. Baldwin notes that in the decades after the war, risk pooling in France was confined to groups of social and actuarial peers, and in Germany social insurance remained the province of workers already included in social welfare schemes. Only later on, when demographic and economic changes weakened the middle classes in these countries did one-time objectors to universal welfare demand and achieve broader

Notes to Pages 145–149 / 233

31.

32.

33.

34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44.

45.

risk pooling that would accommodate them as well. Ibid., 206–7. In Finland, to take just one more example, health insurance was blocked during the interwar period by the Agrarian Party, which refused to pay for urban benefits, and was extended to cover the entire population only in 1962. Cutler and Johnson, “Birth and Growth,” 102. In the United States, for example, old-age security insurance is paid for by a highly visible payroll tax, which creates resistance to benefit increases and vertical redistribution. By contrast, in several European countries, pensions are financed more heavily by employers and/or partly out of general tax revenues, including less visible forms of taxation such as the value-added tax. See John B. Williamson and Fred C. Pampel, Old-Age Security in Comparative Perspective (New York: Oxford University Press, 1993), 104. See Eveline Burns, “Private and Social Insurance and the Problem of Social Security,” Canadian Welfare 28, no. 7 (1953): 5–10; Richard Titmuss, “Models of Redistribution in Social Security and Private Insurance” (1965), in Commitment to Welfare, 173–87. For an extended discussion of Burns’s career and contributions, see Sherry Davis Kasper, “Eveline Mabel Burns: The Neglected Contributions of a Social Security Pioneer,” Journal of the History of Economic Thought 34, no. 3 (2012): 321–37. Burns, “Private and Social Insurance,” 6. Ibid., 9. F. A. Hayek, The Constitution of Liberty (1960), in The Collected Works of F. A. Hayek, vol. 17, ed. Ronald Hamowy (Chicago: University of Chicago Press, 2011), 409–10. Ibid., 411. Ibid., 375–76. Ibid., 409, quoting Lewis Meriam and Karl Schlotterbeck, The Cost and Financing of Social Security (Washington, DC: Brookings Institution, 1950), 8, 427. Titmuss, “Models of Redistribution,” esp. 178–84. See also his “Universal and Selective Social Services” (1967) in Commitment to Welfare, 113–23. Burns, “Social Insurance in Evolution,” 199. Eveline M. Burns, “Social Security in Evolution: Toward What?,” Social Service Review 39, no. 2 (June 1965): 129. See Lindert, Growing Public, esp. 176–88. Hugh Heclo argues that two episodes of social learning were essential to the emergence of modern centralized welfare: first, an understanding that unemployment is a function of macroeconomic causes rather than a lack of individual responsibility; and second, the discovery of techniques of aggregate demand management that allowed the continued provision of social services even during periods of economic recession. The latter in particular is attributable to Keynes’s economic work. See Heclo, Modern Social Politics, 65–154. Keynes, Treatise, 327. Whether Keynes’s interpretation of probability allows for a subjective as well as an objective interpretation is a matter of scholarly debate. For a defense of the view that Keynesian probability has a subjective aspect, see Charles R. McCann, Probability Foundations of Economic Theory (London: Routledge, 1994), esp. 38–40. See also Alberto Feduzi, Jochen Runde, and Carlo Zappia, “De Finetti on the Insurance of Risks and Uncertainties,” British Journal of the Philosophy of Science 63 (June 2012): 334, which asserts that Keynesian probabilities are both epistemic, since they are a property of how individuals think, and subjective, since they are relative to the evidence available to each individual. For an invocation of Keynes in

234 / Notes to Pages 149–151

46. 47. 48.

49. 50.

51.

52.

53. 54.

55. 56. 57.

58. 59. 60.

support of a strictly objective view, see Franklin, “Resurrecting Logical Probability,” 277–305. Keynes, Treatise, 3. Stephen M. Stigler, “Francis Ysidro Edgeworth, Statistician,” Journal of the Royal Statistical Society 141, no. 3 (1978): 294, 297. J. M. Keynes, “Francis Ysidro Edgeworth, 1845–1926,” Economic Journal 36, no. 141 (January 1926): 147–48. See also John Aldrich, “Keynes among the Statisticians,” History of Political Economy 40, no. 2 (2008): 287–88. Edgeworth, “Philosophy of Chance (II),” 260, 275; Keynes, Treatise, 114. Edgeworth, “Philosophy of Chance (II),” 263–66, 272–73; Keynes, Treatise, 118–20. Perhaps most significantly, Edgeworth concluded that Keynes’s skepticism on this point did not penetrate to the law of errors, on which the former pinned most of his hopes for the contribution of statistics to the social sciences. Keynes offered four grounds of doubt concerning the relevance of probability and in particular classical expectation to individual conduct: first, that it assumes, along with utilitarian ethical theory, that degrees of goodness are numerically measurable and additive; second, that it assumes degrees of probability are entirely subject to quantification; third, that it ignores the “weights” of arguments or the evidence on which each probability is founded; and finally that it ignores the element of “risk,” or in other words the degree of uncertainty surrounding a particular eventuality. See Keynes, Treatise, 355–62. Edgeworth, “Philosophy of Chance (II),” 278–79: “In private life occasions occur requiring that we should act for the nonce so to speak, or at least without anticipating a succession of similar actions which would afford a practical certainty of advantage in the long run. In public life the same choice may occur. . . . Utilitarian philosophy has been too silent about this difficulty.” On the reception of Keynes’s work and his legacy (or lack thereof) in the field of statistics, see Aldrich, “Keynes among the Statisticians.” Edgeworth, in his review, affirmed as much when, analogizing the question of a probability’s “weight” to the theory of errors, he explained that it is preferable “with Laplace to seek, not that combination of the given observations which is most probably . . . right, but the one which, minimising the detriment incident to the use of fallible observations, maximizes the Expectation of useful results.” Edgeworth, “Philosophy of Chance (II),” 275 (emphasis mine). Keynes, Treatise, 367. See also Keynes’s intriguing but inconclusive proposal for a modified account of mathematical expectation in ibid., 361. Ibid., 22. By contrast, Beveridge, in the Williams’ words, “believed that the form of insurance had an inherent political virtue.” In this sense, social insurance was “a kind of politico-moral theatre,” which, by rejecting a view of the state as dispensing gifts and encouraging instead the habits of financial responsibility, would “lead the working class into the ways of independence.” Karel Williams and John Williams, “Social Insurance and the Allied Services: The Political Utopia of 1942,” in A Beveridge Reader, ed. Karel Williams and John Williams (London: Allen and Unwin, 1987), 47. J. M. Keynes, “Consumers’ Credits and Unemployment. By J. E. Meade,” Economic Journal 48, no. 189 (March 1938): 67–68. Ibid., 69. Ibid., 68.

Notes to Pages 151–154 / 235 61. Ibid., 70. 62. Ibid. 63. See John Maynard Keynes, The General Theory of Employment, Interest and Money (1936; Hertfordshire, UK: Wordsworth Editions, 2017), 97–98. 64. Keynes, Treatise, 366. 65. See Robert Skidelsky, Keynes: The Return of the Master (New York: Public Affairs, 2010), 83–85. The role of epistemic uncertainty is also the focal point of the discussion of Keynes in McCann, Probability Foundations, 95–107. 66. See Charles R. McCann Jr., “On the Nature of Keynesian Probability,” in The Philosophy of Keynes’s Economics: Probability, Uncertainty, and Convention, ed. Jochen Runde and Sohei Mizuhara (London: Routledge, 2003), esp. 39–44. 67. Keynes, Treatise, 361. 68. Paul Davidson, “The Terminology of Uncertainty in Economics and the Philosophy of an Active Role for Government Policies,” in Runde and Mizuhara, Philosophy of Keynes’s Economics, esp. 224–26. 69. See Keynes, General Theory, 136–39. For a very clear discussion of the effects of uncertainty on investment behavior in Keynes, see Skidelsky, Keynes, 89–93. Skidelsky notes that uncertainty about the future yield of assets leads to the use of conventions, such as following the crowd, that are liable to produce sudden changes in collective behavior and lead to volatility. Liquidity, which allows investors to avoid making irrevocable decisions in the face of their uncertainty, thus creates more opportunities for speculation and makes economic life more unpredictable. See also Jochen Runde, “Risk, Uncertainty, and Bayesian Decision Theory: A Keynesian View,” in Keynes, Knowledge and Uncertainty, ed. Sheila Dow and John Hillard (Aldershot, UK: E. Elgar, 1995), 205–9. 70. Bruno de Finetti also interpreted Keynes as part of a resurgence of an epistemic approach to probability in response to frequentism. See Feduzi, Runde, and Zappia, “De Finetti,” 346. Some have suggested that, by the time of the General Theory, Keynes had modified his earlier understanding of probabilities as logical relations and adopted a form of subjectivism instead. See Donald Gillies, “Probability and Uncertainty in Keynes’s The General Theory,” in Runde and Mizuhara, Philosophy of Keynes’s Economics, esp. 118–22. For an argument that Keynes did not alter his view in response to the subjectivist critique because he already had the means to incorporate it, see McCann, Probability Foundations, 56–57. 71. Frank Plumpton Ramsey, “Truth and Probability” (1926), in Studies in Subjective Probability, ed. Henry E. Kyburg, Jr. and Howard E. Smokler (Huntington, NY: Robert E. Krieger, 1980), 41. 72. Ibid., 48. 73. See Henry E. Kyburg, “Subjective Probability: Criticisms, Reflections, and Problems,” Journal of Philosophical Logic 7, no. 1 (May 1978): 158. 74. Ramsey, “Truth and Probability,” 42. 75. Ibid., 41. 76. Ibid., 42. 77. Some subjective accounts followed Keynes in allowing for degrees of belief that are not comparable to others in order of magnitude. For a summary, see Henry E. Kyburg, Jr. and Howard E. Smokler, “Introduction,” in Kyburg and Smokler, Studies in Subjective Probability, 12–13. 78. Ibid., 8. On weak accounts of coherence, the bettor is incoherent if he bets in such a way that he will inevitably lose money on the wager; on strong accounts, he is in-

236 / Notes to Pages 154–156

79. 80. 81.

82. 83. 84. 85.

86.

87.

88. 89.

coherent if he bets in such a way that there is a chance he will lose or no chance he will win. Ibid., 14. Subsequent authors have questioned whether coherence is a sufficient condition for rationality, at least within expected utility theory. See Matthew Adler, Well-Being and Fair Distribution: Beyond Cost-Benefit Analysis (Oxford: Oxford University Press, 2011), esp. 488–89. See Edi Karmi and David Schmeidler, “On the Uniqueness of Subjective Probabilities,” Economic Theory 3, no. 2 (April 1993): 268. Arrow, “Uncertainty,” 947. Ibid., 947–48. Tom Baker contends that it was Arrow who introduced the term “moral hazard” into contemporary legal and policy debate, via the law-andeconomics movement. Baker, “Genealogy of Moral Hazard,” 267–68. On the failure of subjective accounts to offer a descriptive theory of decision making, see Kyburg, “Subjective Probability,” 165–66. R. Sherman Lehman, “On Confirmation and Rational Betting,” Journal of Symbolic Logic 20, no. 3 (September 1955): 251. See also Friedman and Savage, “Utility Analysis,” 279–304. Arrow, “Uncertainty,” 945. Baker makes a related point in noting that, in the wake of Arrow’s article and Joseph Stiglitz’s subsequent analysis of moral hazard, “‘insurance’ is not simply something provided by ‘insurance companies.’ Instead, ‘insurance’ is provided every time that one party’s actions have consequences for the risk of loss borne by another.” Baker, “Genealogy of Moral Hazard,” 272. The similarity of insurance and betting was also emphasized by one of the pioneers of the subjective theory of probability, Bruno de Finetti. For an explication and analysis of his view, see Feduzi, Runde, and Zappia, “De Finetti,” esp. 337–39. Earlier analyses of insurance, starting with Daniel Bernoulli, had begun with the concavity of utility curves, assuming some form of diminishing marginal utility to be a universal feature of human psychology. By the twentieth century, however, risk aversion had come to be understood instead as a taste, distinct from the effects of money on human psychology. The Oxford English Dictionary identifies the first appearance of “risk aversion” as a 1938 article by economist Jacob Marschak, noting that “a change in tastes in the sense of increasing risk aversion leads to decreasing prices of relatively risky assets, or to hoarding, or to both,” and linking risk preferences with entrepreneurialism. J. Marschak, “Money and the Theory of Assets: 1. The Scope,” Econometrica 6, no. 4 (October 1938): 321. Bruno de Finetti, “Recent Suggestions for the Reconciliation of Theories of Probability,” in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Berkeley: University of California Press, 1951), 220. Kenneth J. Arrow, “Utilities, Attitudes, Choices: A Review Note,” Econometrica 26, no. 1 (January 1958): 8. In this context, “uncertainty” means that there is not an objective probability distribution over the possible outcomes. It is noteworthy that the two social choice rules under uncertainty that most obviously resemble insurance, the minimax and maximin strategies, avoid the language of insurance, to say nothing of mutuality or reciprocity between the parties. For instance, in his highly influential personalistic account of the foundations of statistical reasoning, American statistician Leonard Savage reinterpreted the minimax theorem (originally from game theory) to apply to conditions of uncertainty. This rule counsels the individual to choose the act that leads to the smallest possible loss, with loss understood as the difference between

Notes to Pages 156–157 / 237

90.

91. 92.

93. 94. 95. 96. 97. 98. 99.

the income she could obtain if she knew the actual state of the world (or “nature”) and the income she does obtain by choosing any particular outcome without knowing that state. In a group context, where members assign different probabilities to the possible states of nature, the rule dictates that “an act be adopted such that the largest loss faced by any member of the group will be as small as possible.” Leonard J. Savage, The Foundations of Statistics, 2nd rev. ed. (New York: Dover, 1972), 174. Yet while this principle allows for a group decision that remains independent of the parties’ probability assessments, Savage explained, it also ensures that the parties’ opinions do not influence one another or the decision itself. In addition, while the accumulation of further evidence will reduce parties’ expected loss under the rule, it typically does not bring them into greater agreement. Ibid., 174–76. The question of social choice under uncertainty remains a subject of debate in welfare economics. See, e.g., Marc Fleurbaey, “Assessing Risky Social Situations,” Journal of Political Economy 118, no. 4 (August 2010): 649–80; Matthew D. Adler and Chris William Sanchirico, “Inequality and Uncertainty: Theory and Legal Applications,” University of Pennsylvania Law Review 155, no. 2 (December 2006): 279–377. See also Amartya Sen, Collective Choice and Social Welfare (San Francisco: Holden-Day, 1970), 140: “The theory of decision-taking under uncertainty does not yield very definite conclusions on problems of this kind.” Robert J. Aumann, “Agreeing to Disagree,” Annals of Statistics 4, no. 6 (November 1976): 1236–39. In a subsequent paper, Aumann clarified that in addition to common priors, the parties must also have common knowledge of Bayesianism. Robert J. Aumann, “Common Priors: A Reply to Gul,” Econometrica 66, no. 4 (July 1998), 929n2. Aumann, “Agreeing to Disagree,” 1236. See, e.g., Faruk Gul, “A Comment on Aumann’s Bayesian View,” Econometrica 66, no. 4 (July 1998): 923–27; Stephen Morris, “The Common Prior Assumption in Economic Theory,” Economics and Philosophy 11 (1995): 227–53. In a later paper, Aumann appealed to the Harsanyi doctrine, which attributes differences in belief to differences in information, to justify the common prior assumption. Robert  J. Aumann, “Correlated Equilibrium as an Expression of Bayesian Rationality,” Econometrica 55, no. 1 (January 1987): 7. Yet this doctrine has also been widely challenged in multiperson settings. See Giacomo Bonanno and Klaus Nehring, “How to Make Sense of the Common Prior Assumption under Incomplete Information,” International Journal of Game Theory 28, no. 3 (August 1999): 409–34. Aumann, “Common Priors,” 931. Morris, “Common Prior Assumption,” 233. The assumption thus runs counter to what Faruk Gul calls the “Savage-established foundations of statistics.” Gul, “Comment,” 924. Morris, “Common Prior Assumption,” 249. Franklin, “Resurrecting Logical Probability,” 295. See also Hájek, “Reference Class Problem,” 577. My understanding and discussion of these points is indebted to Zabell, Symmetry and Its Discontents, esp. 11–12. For example, ambiguity in language may lead two individuals to interpret the same information differently, resulting in different updated estimates. Joseph Y. Halpern and Willemien Kets, “Ambiguous Language and Common Priors,” Games and Economic Behavior 90 (March 2015): 171–80. See also Harvey Lederman, “People with

238 / Notes to Pages 158–160

100.

101.

102.

103. 104.

105.

106. 107. 108. 109.

Common Priors Can Agree to Disagree,” Review of Symbolic Logic 8, no. 1 (2015): 22–27; Robin Hanson, “Uncommon Priors Require Origin Disputes,” Theory and Decision 61, no. 4 (2006): 319–28. Hájek distinguishes between unconstrained subjectivists, who hold that the individual’s beliefs can be whatever he wants as long as they remain probabilistically coherent, and constrained subjectivists, who attempt to impose additional constraints on rational opinion. One such constraint could be expert opinion. See Hájek, “Reference Class Problem,” 577–80. Neither account, however, presents a clear pathway to interpersonal agreement about probabilities. For an argument from decision theory that mutual insurance will not arise under conditions of uncertainty, see Göran Skogh, “Risk-Sharing Institutions for Unpredictable Losses,” Journal of Institutional and Theoretical Economics 155, no. 3 (October 1999): 510–12. Recent work in welfare economics has endeavored to incorporate subjective and imprecise probabilities into social welfare functions. See Adler, WellBeing and Fair Distribution, 477–551. My argument, however, focuses on the narrower question of intersubjective agreement about particular risks. If indeed risk perceptions are a major driver of welfare policy, as many political economists contend, then the enactment of such policy will rest on citizens’ ability to judge their personal likelihoods of incurring an event as roughly equal to that of their peers. It is this ability that the radical subjectivist account of probability undermines. For an extended account of the link between risk exposure and the demand for social insurance, see Rehm, Risk Inequality and Welfare States. See Richard H. Thaler and Cass R. Sunstein, Nudge: Improving Decisions About Health, Wealth, and Happiness (New Haven, CT: Yale University Press, 2008), 22–39, for a summary of common heuristics and biases. Ibid., 4–6. For a critique of this view and an alternative approach that emphasizes the distinction between quantifiable “risk” and unquantifiable “uncertainty,” see Gerd Gigerenzer, Simply Rational: Decision Making in the Real World (New York: Oxford University Press, 2015). Recently, advocates of an objective Bayesian view have sought to correct some of the deficiencies of the subjectivist account, in particular the difficulties generated by its stance on prior probability assignments. As E. T. Jaynes puts it, the process of translating prior information into a specific prior probability assignment “represents fully half of probability theory, as it is needed for real applications; yet it is entirely absent from orthodox statistics, and only dimly perceived in subjective Bayesian theory.” E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge: Cambridge University Press, 2003), 373. Rather than leaving prior probability determinations entirely to the free choice of the investigator, objective Bayesians hold that it is possible to logically order these priors as more or less reasonable given the information available. See Franklin, “Resurrecting Logical Probability,” 280. Such a view could provide a stronger basis for interpersonal agreement about probabilities than the subjective Bayesian account. John Rawls, A Theory of Justice (Cambridge, MA: Belknap Press of Harvard University Press, 1971), 11. Ibid., 12. Ibid., 13. For precedents, see William Vickrey, “Measuring Marginal Utility by Reactions to Risk,” Econometrica 13, no. 4 (October 1945): 319–33, and “Utility, Strategy, and

Notes to Pages 160–163 / 239

110.

111. 112. 113.

114. 115. 116. 117. 118. 119. 120.

121.

122. 123. 124.

125. 126.

127.

Social Decision Rules,” Quarterly Journal of Economics 74, no. 4 (November 1960): 507–35; John Harsanyi, “Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking,” Journal of Political Economy 61, no. 5 (October 1953): 434–35. But see also Serge-Christolphe Kolm, Justice and Equity (1971), trans. Harold F. See (Cambridge, MA: MIT Press, 1997). For the purposes of this discussion, I will not distinguish between the original maximin rule and its lexicographic variation, which Rawls adopted in response to criticism that the maximin does not always satisfy strong Pareto optimality. Both assume that the individual decision maker will focus on the worst-case scenario. See Amartya Sen, Collective Choice and Social Welfare, 138, and “On Weights and Measures: Informational Constraints in Welfare Economics,” Econometrica 45, no. 7 (October 1977): 1546. William J. Baumol, Economic Theory and Operations Analysis (Englewood Cliffs, NJ: Prentice-Hall, 1961), 370. Rawls, Theory of Justice, 152. See also John Rawls, “Reply to Alexander and Musgrave,” Quarterly Journal of Economics 88, no. 4 (November 1974): 641; cf. Burns, “Priorities for Public Welfare,” 39, noting that the major advantage of social insurance is its complete avoidance of means tests, for “it makes little difference to one’s sense of self-respect whether one has to submit to this procedure to obtain the whole of one’s monthly income or to obtain the missing 8 or 10 percent.” Rawls, Theory of Justice, 101. Ibid., 154–55. John Rawls, “Some Reasons for the Maximin Criterion,” American Economic Review 64, no. 2 (May 1974): 141. Rawls, Theory of Justice, 172. Ibid. 154, 156. Ibid., 172. Ibid., 176. For another argument that the choice of the maximin strategy is akin to “insuring against utter calamity,” see R. M. Hare, “Rawls’ Theory of Justice,” in Reading Rawls: Critical Studies on Rawls’ “A Theory of Justice,” ed. Norman Daniels (New York: Basic Books, 1975), 104. Rawls, Theory of Justice, 26–27. Rawls cites to Edgeworth’s Mathematical Psychics as an example of a work that proposes to derive the principle of utility from contract theory. Ibid., 29. Rawls, “Some Reasons,” 143. Harsanyi, “Cardinal Utility,” 434–35. See Sen, Collective Choice, 141–44; Peter A. Diamond, “Cardinal Welfare, Individualistic Ethics, and the Interpersonal Comparison of Utility,” Journal of Political Economy 75, no. 5 (October 1967): 765–66. Rawls, “Reply,” 650, 652. On the centrality of self-respect to postwar welfare theory, see also Moon, “The Moral Basis of the Democratic Welfare State,” in Gutmann, Democracy and the Welfare State, esp. 32–36. Indeed, Rawls’s critique of existing welfare arrangements found further expression in his mature emphasis on property-owning democracy as an alternative to welfarestate capitalism. As he explained in his preface to the revised edition of A Theory of Justice, welfare states aim to ensure that no one falls below a decent standard of life by redistributing income “at the end of each period, so to speak,” or once individuals have already encountered a misfortune. John Rawls, A Theory of Justice, rev. ed.

240 / Notes to Pages 163–165

128. 129. 130.

131. 132.

133. 134.

135.

(Cambridge, MA: Belknap Press of Harvard University Press, 1999), xv. Such a system may still allow large inequalities of wealth and income that violate the difference principle. By contrast, the aim of a property-owning democracy is to ensure the widespread ownership of productive assets and human capital, putting all citizens in a position to manage their own affairs. This helps to explain why Rawls regarded a social dividend scheme or negative income tax as better reflecting the principle of cooperation, and in particular the view that social gains should be widely shared, than the capitalist welfare state with its ex post redistributive focus. See ibid., 243; and John Rawls, Justice as Fairness: A Restatement, ed. Erin Kelly (Cambridge, MA: Belknap Press of Harvard University Press, 2001), 139–40. For discussion, see Albert Weale, “The Property-Owning Democracy versus the Welfare State,” Analyse and Kritik 35, no. 1 (2013): 37–54. See also Xavier Landes and Pierre-Yves Néron, “Public Insurance and Equality: From Redistribution to Relation,” Res Publica 21, no. 2 (March 2015): 137–54. I am grateful to Elizabeth Anderson for presenting this interpretation to me in a private exchange. Joseph Heath, for example, argues that a market-failures rationale provides the most plausible normative account of social insurance programs and the best explanation of why welfare states arose. Heath, “Three Normative Models.” Elizabeth Anderson, on the other hand, has interpreted social insurance as offering a kind of universal property entitlement. Elizabeth Anderson, “Common Property: How Social Insurance Became Confused with Socialism,” Boston Review 41, no. 4 (July/August 2016): 24–30. Landes and Néron argue that it serves an expressive function in creating a community of citizens who relate morally to one another as equals. Landes and Néron, “Public Insurance and Equality,” 148–50. Robert E. Goodin, “The End of the Welfare State?,” in Ball and Bellamy, TwentiethCentury Political Thought, 216. On the introduction of means-tested public assistance within many insurancebased schemes, see, e.g., E. Philip Davis, Pension Funds: Retirement-Income Security and Capital Markets, An International Perspective (Oxford: Clarendon Press, 1995), 40. See also Williams and Williams, “Social Insurance,” 49, which notes that the coverage provided by Beveridge-style social insurance was never likely to eliminate the need for means-tested aid, despite Beveridge’s suggestions to the contrary. Paul Pierson, Dismantling the Welfare State? Reagan, Thatcher, and the Politics of Retrenchment (Cambridge: Cambridge University Press, 1994), 57, 102–3. On the tendency of Beveridge-style programs to give rise to a kind of dualism rather than egalitarianism as the middle classes opt out or supplement their coverage, see Esping-Andersen, Three Worlds, 25. On a similar note, Elizabeth Anderson’s impassioned plea for earnings-related social insurance relies heavily on class-based support, and in particular a presumed middle-class preference for such systems over minimum-benefits programs. She notes that because “low, flat benefits are too minimal to appeal to the middle classes, who can self-insure at the low levels promised,” and “graded benefits add security against loss of middle-class standing,” Bismarckian systems are more appealing to middle-class voters than their Beveridgean counterparts. Anderson, “Common Property,” 26. Monica Prasad, The Politics of Free Markets (Chicago: University of Chicago Press, 2006), 25. See also Walter Korpi and Joakim Palme, “The Paradox of Redistribution and Strategies of Equality: Welfare State Institutions, Inequality, and Poverty in the Western Countries,” American Sociological Review 63, no. 5 (October 1998): 661–87.

Notes to Pages 166–170 / 241 136. 137. 138. 139. 140. 141.

142. 143. 144. 145.

146. 147. 148.

149.

150. 151.

152.

153.

Dworkin, Sovereign Virtue, 347. Ibid., 74. Ibid., 73–109. Ibid., 332. Ibid., 78. Ibid., 332. For a critique of luck egalitarianism, and in particular its emphasis on personal responsibility, as a justification for social insurance, see Landes and Néron, “Public Insurance and Equality,” 144–47. Dworkin’s critique of both alternative principles is found in ibid., 328–31. Ibid., 332. Ibid., 452. Dworkin acknowledges that insurance against risks such as underemployment and health will be provided at relatively low levels under his scheme. See ibid., 94–99, 314–16. He makes this argument as a function of what individuals with concave utility curves would choose, however, not as a result of what insurance providers would have to offer given the limitations of the market as he conceives it. My point here is that the level of coverage that insurance companies or the state could provide on Dworkin’s account may be even lower than what the average person would choose, given the practical difficulties of working under his assumptions. For a discussion of this problem with community rating, see Landes, “Insurance Underwriting,” 1446. See Dworkin, Sovereign Virtue, 104, noting of participants that the “risk of their fate” is “subjectively equally shared.” Many contemporary economic accounts maintain that the difficulty of sustaining insurance markets for certain types of risk is a major reason for public rather than private provision. Dworkin, however, does not consider how the information level of insurers will affect their behavior and the overall shape of the markets he imagines. In this respect, his insistence on modeling a market seems to play a more confounding than clarifying role in his account. This point was recently given empirical illustration in Richard Breen and Cecilia García-Peñalosa, “Bayesian Learning and Gender Segregation,” Journal of Labor Economics 20, no. 4 (October 2002): 899–922; Thomas Piketty, “Social Mobility and Redistributive Politics,” Quarterly Journal of Economics 110, no. 3 (August 1995): 551–84. Also relevant is empirical work demonstrating that in a specific medical context, the beliefs of non-Bayesians are more accurate than those of strict Bayesians, in the sense of aligning with objective risk frequencies. See Gigerenzer, Simply Rational, 241, citing Nathan Berg, Guido Biele, and Gerd Gigerenzer, Does Consistency Predict Accuracy of Beliefs? Economists Surveyed about PSA (working paper 1308, University of Otago Economics Department, Dunedin, New Zealand, 2013). See Torben Iversen and Philipp Rehm, “The Market for Creampuffs: Big Data and the Transformation of the Welfare State” (working paper, 2019). See Michael Rothschild and Joseph Stiglitz, “Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information,” Quarterly Journal of Economics 90, no. 4 (November 1976): 629–49. Finally, Iversen and Rehm contend, the standard model fails to consider the effects of differences in the level of information, and in particular how greater information undermines cross-class solidarity. Iversen and Rehm, “Market for Creampuffs,” 3–4. Some models assume that in a state of ignorance about their own risks, individuals will look to the overall population and accept its average as their own. While this

242 / Notes to Pages 171–178

154. 155.

156.

157.

assumption certainly has intuitive appeal, on a subjectivist view it is not clear that an insured would take the population average as a substitute for her personal probability when there are so many other valid estimates she could choose instead. This point echoes one made in a different context by Alan Hájek. He notes that while unconstrained subjectivists do not encounter the reference-class problem, as a result of their exclusive focus on coherence, “probability theory becomes autobiography rather than epistemology.” Hájek, “Reference-Class Problem,” 577. See Liukko, “Genetic Discrimination,” esp. 463–68. For example, the EU ruling prohibiting insurers from charging different rates to men and women reportedly had the effect of increasing rather than decreasing the price differential between the sexes. See Patrick Collinson, “How an EU Gender Equality Ruling Widened Inequality,” Guardian, January 14, 2017, https://www.theguardian .com/money/blog/2017/jan/14/eu-gender-ruling-car-insurance-inequality-worse. See Feduzi, Runde, and Zappia, “De Finetti,” 340–42. On the conditionality of all probabilities, see Hájek, “Reference Class Problem,” which concludes that the epistemological version of the reference-class problem is present in all interpretations of probability that have a “genuine claim to being guides to life.” Ibid., 584. On the “new social risks” and their implications for policymaking, see Giuliano Bonoli, “The Politics of the New Social Policies: Providing Coverage Against New Social Risks in Mature Welfare States,” Politics and Policy 33, no. 3 (July 2005): 431–49. CONCLUSION

1.

2. 3.

4.

5. 6. 7.

For just a small sample, see Arrow, “Uncertainty”; Guido Calabresi, The Cost of Accidents (New Haven, CT: Yale University Press, 1970); Nicholas Barr, “Social Insurance as an Efficiency Device,” Journal of Public Policy 9, no. 1 (January–March 1989): 59–82. See Barr, “Social Insurance,” 66. The seminal text of this school is Esping-Andersen, Three Worlds. It may be open to debate whether these are two distinct schools of thought or the second is a novel interpretation of the first. See Rehm, Hacker, and Schlesinger, “Insecure Alliances,” 387, characterizing the latter view as “revisionist.” See Peter Lindert, “Private Welfare and the Welfare State,” in The Cambridge History of Capitalism, vol. 2, ed. Larry Neal and Jeffrey G. Williamson (Cambridge: Cambridge University Press, 2014), 478–79. This trend is particularly striking given that, according to Lindert, such spending ceased to be associated with GDP gains after the 1960s. While tax-based social insurance and assistance did produce GDP gains and greater income security until the 1960s, Lindert argues that since then spending has focused less on promoting human capital and more on sustaining the elderly, with effects on GDP that are more neutral. He attributes this development to a shift in welfare policy away from targeting the needy and toward universalist transfer programs that appeal to middle-class and elderly voters in particular. Ibid., 490. See Ibid., 470. For an articulation of this argument, see Heath, “Three Normative Models,” 37–40. This so-called negativity bias partly accounts for the intensity of public support for the welfare state in affluent democracies. Voters have been found to react more strongly to possible losses than to potential gains of the same amount. Paul Pierson, “Coping with Permanent Austerity: Welfare State Restructuring in Affluent Democracies,” in The New Politics of the Welfare State, ed. Paul Pierson (Oxford: Ox-

Notes to Pages 178–180 / 243

8.

9.

10. 11.

12. 13.

14.

15.

16.

ford University Press, 2001), 413. Lindert refers to the shift toward intergenerational transfers to the elderly as a kind of “mission creep” and acknowledges that “the expansion of public social programs has probably stopped reaping efficiency gains.” Lindert, “Private Welfare,” 467. For example, William Galston argues that this was the case for the private savings accounts proposed by President George W. Bush as part of his failed attempt to reform America’s Social Security system. See William A. Galston, “Why President Bush’s 2005 Social Security Initiative Failed, and What It Means for the Future of the Program” (New York: NYU Wagner, 2007), 4, https://www.brookings.edu/wp -content/uploads/2016/06/20070921.pdf. It has also been said of voucher programs that, while they may increase competition among service providers, they do not necessarily reduce overall expenditures. See Torben M. Andersen and Per Molander, “Policy Options for Reforming the Welfare State,” in Alternatives for Welfare Policy: Reconciling Policy Goals with Demographic Change and Internationalisation, ed. Torben  M. Andersen and Per Molander (Cambridge: Cambridge University Press, 2003), 360. These points are brought out forcefully in Christopher Howard, The Hidden Welfare State: Tax Expenditures and Social Policy in the United States (Princeton, NJ: Princeton University Press, 1997). On the regressive distributive effects of private welfare provision in the United States, see Hacker, Divided Welfare State, 36–40. Globalization and resulting tax competition further raise the question of whether general tax revenues will be an adequate or fair basis for welfare finance in the future. See Assaf Razin and Efraim Sadka, The Decline of the Welfare State (Cambridge, MA: MIT Press, 2005), 3–4; Andersen and Molander, “Policy Options,” 352–54. “Wealth-talent” is the term used by Ronald Dworkin in his critique of such a distributive principle. Dworkin, Sovereign Virtue, 325–27. For the suggestion that social insurance has a greater moral hazard problem than private, however, see Pierre Pestieau, “Social Protection and Private Insurance: Reassessing the Role of the Public Sector Versus Private Sector in Insurance,” Eighteenth Annual Lecture of the Geneva Association, Geneva Papers on Risk and Insurance Theory 19, no. 2 (December 1994): 85, 88–89. The seminal articulation of this argument is Arrow, “Uncertainty,” 948–54. For a helpful overview of the advantages and disadvantages of the different types of healthcare system, see Ronald J. Daniels and Michael J. Trebilcock, Rethinking the Welfare State: The Prospects for Government by Voucher (London: Routledge, 2005), 102–16. See Jacob S. Hacker, The Great Risk Shift: The Assault on American Jobs, Families, Health Care, and Retirement and How You Can Fight Back (Oxford: Oxford University Press, 2006), 137–45. These observations are drawn from the widely respected Kaiser Health Tracking Poll: http://kff.org/interactive/kaiser-health-tracking-poll-the-publics-views-on-the -aca/#?response=Favorable--Unfavorable&aRange=all. For evidence of resistance to the individual mandate, see Kaiser Family Foundation, Data Note: A Snapshot of Public Opinion on the Individual Mandate, March 1, 2012, https://www.kff.org/wp-content/uploads/2013/01/8296.pdf; Bianca DiJulio, Jamie Firth, and Mollyann Brodie, Kaiser Health Policy Tracking Poll: December 2014, December 18, 2014, http://kff.org/health-reform/poll-finding/kaiser-health-policy -tracking-poll-december-2014/; and Ashley Kirzinger, Elise Sugarman, and Mollyann Brodie, Kaiser Health Tracking Poll: November 2016, December 1, 2016, http://

244 / Notes to Pages 180–182

17.

18.

19.

20.

21.

22.

kff.org/health-costs/poll-finding/kaiser-health-tracking-poll-november-2016/. It is worth noting that the ACA was not the first piece of legislation to recognize the problem of coverage for those with preexisting conditions. The Health Insurance Portability and Accountability Act of 1996 (HIPAA) enacted privacy provisions regarding access to patient medical records to protect workers seeking to leave their jobs. It did not prevent insurers from charging higher premiums to some purchasers with preexisting conditions, however. Ashley Kirzinger, Bryan Wu, and Mollyann Brodie, Kaiser Health Tracking Poll: Health Care Priorities for 2017, January 6, 2017, http://kff.org/health-costs/poll-finding/ kaiser-health-tracking-poll-health-care-priorities-for-2017/. In 2016, the Kaiser Family Foundation estimated that, pre-ACA, the percentage of those under age sixty-five with a condition that would have led to a denial of insurance in the individual market was 27 percent, although the figure varies by age, sex, and geographic location. Gary Claxton et al., Issue Brief: Pre-Existing Conditions and Medical Underwriting in the Individual Insurance Market Prior to the ACA, December 2016, http://files.kff.org/ attachment/Issue-Brief-Pre-existing-Conditions-and-Medical-Underwriting-in-the -Individual-Insurance-Market-Prior-to-the-ACA. See Kaiser Family Foundation, Data Note; Olga Khazan, “How Obamacare Helped Trump,” Atlantic, November 9, 2016, https://www.theatlantic.com/health/archive/ 2016/11/how-obamacare-helped-trump/507113/; Rachel Fehr et al., Issue Brief: How Affordable Are 2019 ACA Premiums for Middle-Income People?, March 5, 2019, https:// www.kff.org/health-reform/issue-brief/how-affordable-are-2019-aca-premiums-for -middle-income-people/. See Robert Pear, “Republicans Offer Health Care Bills to Protect Patients (and Themselves),” New York Times, April 20, 2019. Another aspect of this story is the rise in high-deductible job-based plans, which many Americans say have forced them to use up all or most of their savings on healthcare costs. See Noam N. Levey, “Health Insurance Deductibles Soar, Leaving Americans with Unaffordable Bills,” Los Angeles Times, May 2, 2019. For example, the ACA allows insurers to impose surcharges on smokers, which according to one study increased costs for this group and reduced their insurance levels without inducing them to smoke less. See Abigail S. Friedman, William L. Schpero, and Susan H. Busch, “Evidence Suggests that the ACA’s Tobacco Surcharges Reduced Insurance Take-Up and Did Not Increase Smoking Cessation,” Health Affairs 25, no. 7 (July 2016): 1176–83. See Olga Khazan, “If Not Obamacare, Then What?” Atlantic, December 20, 2016, https://www.theatlantic.com/health/archive/2016/12/if-not-obamacare-then-what/ 511130/; Drew Altman, “The Health Care Plan Trump Voters Really Want,” New York Times, January 5, 2017. Dworkin offers a version of this argument in his critique of Rawls’s difference principle: “It seems callous to say that the only people for whom a theory of justice has concern are those whose lives are the most damaged, even though others, who work as hard as they can, are also seriously injured. . . . Politicians who preach fairness to the ‘hard-working middle classes’ . . . are also giving voice to a widespread instinct of justice.” Dworkin, Sovereign Virtue, 331. See, e.g., Anderson, “Common Property”; Greg Weiner, “A Constitutional Welfare State,” National Affairs 29 (Fall 2016). For recent defenses of social insurance in the academic literature, see Landes and Néron, “Public Insurance and Equality”; Heath, “Three Normative Models”; and Marmor, Mashaw, and Pakutka, Social Insurance

INDEX

Acland, John, 61–62 actuarial fairness, 20, 66, 70, 90–91, 101, 121, 128, 145, 147, 181, 191n49 actuarialism, 102, 145–46, 159, 226n130; actuarial insurance, 59, 63–64, 93, 163; actuarial mutual insurance, 46, 105 Addobbati, Andrea, 24 adverse selection, 61, 167, 170, 179 Affordable Care Act (ACA), 179; individual mandate, 180; preexisting conditions, 180; risk pool, 180; undermining of, 180–81. See also Obamacare Agrarian Justice (Paine), 66–67 Alborn, Timothy, 92–93, 201n127 aleatory contracts, 25–26, 29, 31, 75–76, 180; distributive entitlement, link to, 32; insurance, influence on, 33–34 Amicable Society, 40, 200n114, 200n120 Anderson, Elizabeth, 207n106, 240n129, 240n134 annuities, 25–26, 36–37; Church of Scotland, 200n114; life expectancy, 38–39; societies for, 55; and wagers, 35 Ansell, Charles, 59 Antwerp, 24, 195n38 Aristotle: corrective justice, 30–31; distributive justice, 32; Politics, 5, 189n37; regime, conception, 8–9, 189n37, 191n46 Arrow, Kenneth, 154–56, 186n11, 236n85; moral hazard, 236n81, 236n85 Art of Conjecturing, The (Bernoulli), 28, 31 Ashford, Douglas, 226n124, 231n8

Asquith, Herbert, 132 Aumann, Robert, 156 Bacon, Francis, 108 Baker, Tom, 189n33, 213n70, 217n147, 236n81, 236n85 Baldwin, Peter, 130, 144–45, 224n104, 225n117, 229n163, 232–33n30 Barbour, Violet, 193n20 Bayes, Thomas, 55–56, 71–73, 76 Bayes’s theorem, 55, 72–73, 76; decision theory, 154, 156–58, 169, 176 Beck, Ulrich, 189–90n38 Béland, Daniel, 129 Bellhouse, David, 39, 52, 199n108 Bentham, Jeremy, 116–17, 213n74 Bernoulli, Daniel, 19, 85, 87–88, 115, 211n38; St. Petersburg paradox, 83–84; utility curves, 236n86 Bernoulli, Jacob, 29, 32, 34–35, 38, 41, 73, 83; approximation theorem of, 72; The Art of Conjecturing, 28, 31; principle of indifference, 210n24; stability of probability values, 77 Bernoulli, Nicholas, 83 Beveridge, William, 132–33, 140, 142–43, 145, 147–48, 150–51, 168, 232n19, 232n23, 234n57; mean-tested aid, 240n132 Beveridge Report, 140 Bicquilley, Charles-François, 211n47 Bienaymé, I. J., 113

246 / Index Bismarck, Otto von, 89, 124, 127, 131, 140–41, 165, 186n14, 223n85; accident insurance, 125; contributory principle, rejection of, 126; differentiated coverage, 125; health insurance, 125–26; pensions, 126; powerful central government, vision of, 126, 128; social insurance, 124–25 Blanqui, Jérôme-Adolphe, 213–14n84, 216n125 Bonaparte, Napoleon, 73, 224n93 Boole, George, 208n9, 219n22 Boudon, Raoul, 100–103 Bouk, Dan, 188n27 Bourgeois, Léon, 128–29, 225n117 box clubs, 42. See also friendly societies Boyer, G. S., 100–101 Briggs, Asa, 191n47 Buck, Peter, 53, 204n37 Buffon, George-Louis Leclerc de, 87 Burke, Edmund, 51, 67 Burns, Eveline M., 141, 145–46, 231n10, 231n12 Bush, George W., 243n8 Canada, 223n84, 230–31n4 capitalism, 105, 121, 135, 142–43 Catholic Church, 125 Ceccarelli, Giovanni, 194n29, 195n43, 196n50 chance, 5, 25–26, 56, 65, 113–14; and probability, 7 Churchill, Winston, 132–33, 227n134, 228n148 Clark, Geoffrey, 193n14, 200n114, 201n126 commercial insurance, 113; critique of, 101; and exclusivity, 94; life insurance, 92 Committee on Economic Security, 145 Comte, Auguste, 213–14n84 Condorcet, Marquis de, 10, 54, 56, 62, 65, 71–72, 78, 83, 87, 96–97, 99, 106, 111, 152, 208n9, 215n106, 216n125, 219n24; economic liberty, 79; game, metaphor of, 80; insurance, analysis of, 80–82; inverse probability, 76; risk, voluntary and involuntary exchanges, 81–82; The Sketch, 63; social insurance,

proposals for, 63–64; universal mathematical education, promotion of, 77 contractual equity, 24; probability theory, 36, 40, 83–84, 155 contributory principle, 3, 66, 125–27, 131– 33, 140–41, 143, 146, 164, 177–78 cooperative workers’ associations, life insurance, 133 Cordery, Simon, 201–2n133, 228n152 corrective justice, 30–31 Cournot, Antoine Augustin, 107, 111–12, 119, 211n52; solidary risks, 113 Cramer, Gabriel, 212n62 Crépel, Pierre, 211n47, 212n57 Curwen, John Christian, 206n77 Dale, Andrew I., 209n20 d’Alembert, Jean le Rond, 73, 81, 84, 87; statistical averages, critique of, 85 Daston, Lorraine, 33, 39, 84, 95, 189n33, 198n93, 199n108, 209n13; mortality statistics, 198n89 Davidson, Paul, 152 Dawson, Miles, 230n169 decision theory, 152–54, 156, 160, 181 de Finetti, Bruno, 154, 156–57 Defoe, Daniel, 50, 61; An Essay Upon Projects, 49, 202n10 De Morgan, Augustus, 86–87, 148 Denmark, 129–30, 134, 140, 229n163 Deringer, William, 204n51 De Roover, Florence Edler, 194n25 Derthick, Martha, 186n10 desert, 9, 142, 165, 173, 186–87n15 De Swaan, Abram, 190n39 de Witt, Johan, 36–37, 39 Diamond, Peter, 185n2, 185n4 Dicey, A. V., 135 difference principle, 160, 166–67, 244n21 disaggregation, and risk, 50, 101–2, 170–71 distributive claims, 8, 32, 118, 177 distributive justice, 30–32, 163–64, 172–73; and desert, 186–87n15; and equality, 174; insurance, as tool for, 33–34; normative political theory, 15; and risk, 42, 78, 86, 139, 165–67; social insurance, 139 distributive politics, 123, 145, 163

Index / 247 Dodson, James, 40 Domat, Jean, 26–27 Douglas, Mary, 189–90n38 Dutch Book, 153 Duvillard de Durand, Emmanuel-Étienne, 62–63 Dworkin, Ronald, 168; adverse selection, 167; brute vs. option luck, 165–66; wealth-talent, 243n10 economic liberalism, 99; of Condorcet, 77–81 Edgeworth, Francis Ysidro, 10, 119–21; Mathematical Psychics, 117–18, 149; principle of indifference, defense of, 116; principle of utility, 210n28; probability theory and utilitarianism, analogy between, 118; scientific hedonimetry, 117; statistics, turn to, 149–50; sympathy, 222n73; theory of errors, 219–20n34, 234n50, 234n54; utilitarian ethics, 116, 234n52 egalitarianism, 142, 148, 159, 164 Elazar, Yiftah, 203n23, 204n52 Ellis, Robert Leslie, 107–9, 119 Ellsberg, Daniel, 229n162 England, 13, 42, 46, 52, 57–58, 61, 69, 86–87, 107, 114–15; enclosure in, 53; mutual society for, 61; poor law, 131. See also Great Britain Equitable, 40–41, 44–46, 51, 53, 57, 62 equity, 39–40, 139, 147 Esping-Andersen, Gøsta, 231n5 Essay Upon Projects, An (Defoe), 49, 202n10 Ewald, François, 89, 98, 103, 188–89n31, 189n33, 215n112 exchangeability, 154, 157 fairness, 9, 37, 50, 51, 53, 69, 82, 155–56, 166–67, 178; contractual, 83, 164, 174; distributive, 122; of insurance, 31, 40, 47, 113; and justice, 161, 163–64; mathematical expectations, 28, 30; and rationality, 10 Fechner, Gustav, 221n60 Fermat, Pierre de, 27–28 Finland, 232–33n30

Flemming v. Nestor, 3 Fourier, Charles, 100 Fourier, Jean-Baptiste-Joseph, 88–89, 94– 95, 217n129, 218n3 France, 12–13, 46, 62, 66, 69, 73, 91, 96, 100–102, 107, 123–24, 133–34, 140, 223n85; census in, 71, 209n19; early pensions in, 224n93; localism, persistence of, 128; mutual aid societies, 97, 127; mutualism, strength of in, 127–28; social insurance laws, 97–99, 127–29; and solidarity, 129; state pension fund, 97, 126 Franklin, Benjamin, 38 Franklin, James, 93, 157, 193–94n23, 195n34, 195n38, 196n52 Freeden, Michael, 100 French Revolution, 1, 51 frequentism, 14, 70–71, 105, 111, 148–50, 152, 153–54, 157, 159, 223n85; chance gap, 136; class-based actuarialism of, 115; common good, 13, 137; common sense, 119; critique of, 176; empirical observation, emphasis on, 107; and identity, 176; mutual insurance, 106; nature of chance, 113–14; objections to, 135–36; objective interpretation, 109, 119; principle of indifference, rejection of, 107; probabilistic equality, 110, 113; probability values, interpretation of, 107–9; and randomness, 107, 110, 114; risk-collectivism, 134, 138, 141; and risk-pooling, 110, 115, 138; and social insurance, 110, 115, 122, 127, 131, 136; solidarity model of, 115, 135, 176; and utilitarianism, 115, 119–21 Friedman, Milton, 192n6 friendly societies, 13, 42, 44–45, 50–53, 62, 97, 100, 129, 228n148, 228n152; and exclusivity, 43, 94, 201–2n133; life insurance mathematics, 58; movement to reform, 57–61; mutuality, alternative model of, 43, 94; mutual responsibility, ethos of, 128; and probability theory, 58, 205n65; providential basis, 91–92; sociability and affective ties, appeal to, 92. See also box clubs Fries, Jakob Friedrich, 107

248 / Index Galston, William, 243n8 gambling, 26, 93, 150, 152; insurance, association with, 53–54; and tontines, 66; utilitarianism, association between, 162 games of chance, 25–29, 34, 36, 39, 80, 83–84; fair price, 30; natural events, difference between, 72 game theory, 160, 236–37n89 Gauss, Carl Friedrich, 210n28 Gephart, William, 230n169 Gérando, Joseph-Marie de, 60, 216n118 Germany, 107, 123, 130–31, 140; poor law system, 124–25; social insurance, 124–26 Gibaud, Bernard, 217–18n149 Gillispie, Charles Coulston, 208n9, 214n88 Girardin, Émile de, 57, 100, 102–3 globalization, 243n9 Goodin, Robert, 164 Graunt, John, 37 Great Britain, 12, 51, 55, 59, 91–93, 123, 134, 142, 188n31, 223n84, 226n124, 226–27n131, 230–31n4, 232n20; census in, 71; means tests, 131; pensions, 131–32; social insurance, 131; unemployment insurance, 132–33; welfare policy, 116, 140, 143. See also England; Scotland; Wales Green, T. H., 225n117 guilds, 21, 42, 193n13 Hacker, Jacob, 134, 187–88n26, 232n13 Hacking, Ian, 6, 121, 189n33, 189n34, 190n39, 196n51, 197n65, 198–99n99, 209n13, 217n129, 218n1, 218n3, 223n85 Hahn, Roger, 73, 209n12 Hájek, Alan, 135–36, 230n167, 238n100, 241–42n153 Hald, Anders, 199n101, 210n24 Hall, Peter, 11, 47, 202n7 Halley, Edmund, 36–39, 52 Harris, Bernard, 201–2n133, 232n19 Harsanyi, John, 162, 167 Hayek, Friedrich, 146–47 healthcare, 154, 167, 179 Health Insurance Portability and Accountability Act (HIPAA), 243–44n16

Heath, Joseph, 240n130 Heclo, Hugh, 47, 233n44 Hennock, E. P., 227n132, 228n137 Heyde, C. C., 215n102 Hobbes, Thomas, 48 holism, 114, 128, 223n85; in frequentism, 106, 109 Holmes, Oliver Wendell, Jr., 123 Hume, David, 113 Huygens, Christiaan, 27, 36, 197n63, 199n108; fair equivalent wager proof, 28–31, 196n56 indifference principle. See principle of indifference individualism, 15, 68, 103; and aggregation, 91, 100; social control, 98 industrialization, 121, 127 inequality, 9, 53, 63–64, 116, 165; as form of oppression, 54 insurance, 10–11, 26, 66–67, 70, 90, 98, 110, 122, 154–55, 158, 163, 167; actuarial fairness, 20, 147; aggregate effects of, 113; aleatory contracts, influence on, 33–34; asymmetric information, problem of, 169–70; as bilateral contract, 63; burden-sharing partnership, 34; characteristics of, 64; vs. charity, 99; as commercial exchange, 13, 17, 25; common good, 62, 100, 104; development of, 12; distributive equity, noncommercial tool for, 81; distributive justice, 33–34; dual character of, 135; as egalitarian, 142, 148; equality and security, 103; as equitable distributive arrangement, 12, 25; exclusionary side of, 102, 181; as fair exchange, 24; fairness of, 31; fiscal restraint, 177; flexibility of, 129; frequentist view of, 111; gambling, association with, 17, 53–54; harmonizing character of, 142; and identity, 128; individualism and aggregation, 91, 100, 104; individual responsibility, 142; institution of, 113; as involuntary exchange, 82; Janus-faced distributive appeal of, 148; legitimizing of, 141–42; models of, 18; moral expectation, 82, 87–88;

Index / 249 moral hazard, 179; mutually sharing burdens, 17; personal and collective benefit, promise of, 103; pragmatic solidarity, 106; premiums, 23, 93; preventative approach, 143; and probability, 80; probability calculations, 71–72; probability theory, 150; and public order, 89; and reciprocity, 62; as responsible economic choice, 69; and risk, 18, 21, 34, 88, 91, 147; risk aversion, 19; risk exchange, 18–19, 25; risk groups, 182; risk pooling, 18–19, 24–25, 68, 77–78, 86–87, 102, 114– 15, 121, 147, 179; risk reduction, and speculation, 25; sea loans, resembling of, 22–23; self-determination, 79, 96–97; as social duty, 96–97; social order, securing of, 174; social welfare policy, 138; and solidarity, 128–29, 133, 139, 141, 144–45, 159, 164–65, 168, 170–72, 176, 178, 226n130; spreading risk, 77–78, 86–87; and uncertainty, 19, 23; uncertainty, and caution, 87; as voluntary action, 81, 106–7; as wagers, similar to, 24–25; and welfare state, 147, 175. See also commercial insurance; life insurance; maritime insurance; mutual insurance; probabilistic insurance; public health insurance; social insurance inverse probability, 55, 70–71, 76 Ireland, 58 Ismay, Penelope, 51–52, 92, 202n134, 203n19, 205n65, 214n93 Iversen, Torben, 170, 188n27, 241n152

insurance, stance on, 150–51; A Treatise on Probability, 148, 152; uncertainty, treatment of, 152

Jaynes, E. T., 238n105 justice, as fairness, 161, 163–64 just regime, 4–5

labor movements, 122, 124, 131–32 labor unions, 126, 131 Lacroix, Sylvestre François, 86 Landes, Xavier, 192n9, 240n130, 241n141 Laplace, Pierre-Simon, 55, 71–72, 78, 82, 86–88, 99–100, 107, 138, 148, 156, 217n129; equiprobable cases, 69; interest in matters of civic import, 208n9, 214n88; Philosophical Essay on Probabilities, 73; principle of nonsufficient reason (indifference), 75–76, 108; probability of causes, 73–74, 77; Rule of Succession, 74; as transitional figure, 209n13 Larocque, André-Jean de, 62–63 law of large numbers, 95; and Bernoulli, 35; Bernoulli and Poisson, compared, 215n102 Leibniz, Gottfried Wilhelm, 32, 34, 38; distributive justice, 30–31 liberalism, 8, 48–49, 63–64, 69, 139, 175; economic, 99; laissez-faire, 128 Life Assurance Act (1774), 54, 93 life insurance, 35, 39, 41, 45, 51, 53; cooperative workers’ associations, 133; friendly societies, 58; industrial insurance, 93; national life insurance, 62 Lindert, Peter H., 226n129, 242n4, 242– 43n7 Locke, John, 48 Logic of Chance, The (Venn), 108, 115, 119 London Assurance, 200n114 lotteries, 26, 120 luck egalitarianism, 165–67 Luxembourg Commission, 98–99

Kahneman, Daniel, 158 Kaye, Joel, 31, 197–98n79 Keith-Lucas, B., 206n81 Keynes, John Maynard, 10, 154, 221n47; ergodic processes, 152; full employment, 151; on gambling, 150, 152; principle of indifference, 209n22; probability, view of, 148–49, 152–53; social

Macnicol, John, 214n90, 228n137, 228n139 maritime insurance, 22, 25, 41, 80, 82, 87; as club good or service, 24; risk as tradable good, 23 Marmor, Theodore, 187n16, 190n39 Marschak, Jacob, 236n86 Marshall, Alfred, 225n117

250 / Index Marshall, T. H., 186n12 Maseres, Francis, 61 Mashaw, Jerry, 187n16, 190n39 mathematical expectation, 46, 69, 81–82, 90–91, 96, 109, 150; in a posteriori probability, 34–39; in a priori probability, 32–34, 39; mathematical formula for, 28; and wagering, 27–30 mathematical probability, 12, 17, 27, 36, 45; aleatory contracts, 25–26; annuity and life insurance contracts, 39; and chance, 25–26; inverse probability, 55– 56, 71–76, 116; as normative, 7, 32, 90– 91, 120, 155, 173; and property, 52–54; Rule of Fellowship, 26; single events, 76–77, 87, 108–9, 111, 119, 154 Mathematical Psychics (Edgeworth), 117–18, 149, 239n121 mathematics, 9, 37, 49, 56, 61, 67, 73, 91, 173; common sense, 119; life insurance, 35, 39–40, 52–53, 58; promise of, 76; rationalizing power of, 70; social order, 76 Meade, J. E., 151 Medicaid, 179, 181 Medicare, 179, 185n2 Mill, John Stuart, 107–11, 119 minimax theorem, 236–37n89 mining industry, 224n97 Mirowski, Philip, 118, 221n46, 221n60, 222n74 Mohun, Arwen, 189–90n38, 229n163 Moivre, Abraham de, 38, 40, 72–73 Montmort, Pierre Rémond de, 31, 83; distributive entitlement, 32 Moon, J. Donald, 189n32 moral expectation, 77–78, 82–83, 86–88, 112; and utilitarianism, 113, 115–16 Morgan, William, 40, 46, 51, 200n120, 205n57, 214n94 Morris, Stephen, 156–57 mortality statistics, 33, 36–37, 71 Moss, David, 224n92 mutual insurance, 45, 50, 52, 54, 56, 59–60, 63, 79, 86, 113, 155; and frequentism, 106; as voluntary affair, 97, 106, 129, 133. See also social insurance mutualism, 59, 94, 127–28, 133, 136 mutuality, 2, 41, 43, 132–33

mutual societies, 94, 104, 122, 133–34; voluntary aid, 127 Nacol, Emily, 48, 188–89n31 Napoleonic period, 121 Napoleon III, 89, 97–98, 102, 104, 124–28, 215–16n113, 217–18n149 National Health Service (NHS), 144, 232n20 natural rights, 115, 118 Néron, Pierre-Yves, 240n130, 241n141 Netherlands, 230–31n4 New Deal, 122, 134, 179 Noonan, John, 194n24 Obama, Barack, 179–80 Obamacare, 179–80. See also Affordable Care Act (ACA) Observations on Reversionary Payments (Price), 53–54, 56–57 Orloff, Ann Shola, 223n84 Orszag, Peter, 185n2, 185n4 Paine, Thomas, 99; Agrarian Justice, 66–67 Pakutka, John, 187n16, 190n39 Parijs, Philippe van, 207n106, 208n111 Paris Commune, 27 Pascal, Blaise, 27 paternalism, 104, 158 Peirce, Charles Sanders, 110, 119–20, 153 Petty, William, 49 philosophical empiricism, 107 Philosophical Essay on Probabilities (Laplace), 73 Pigou, Arthur C., 121 Piron, Sylvain, 25 Plato, 4–5 Poisson, Siméon-Denis, 77, 94–95, 99– 100, 214n86, 215n102 Polanyi, Karl, 226n130 polarization, 15–16, 168–69 policy paradigm, 11, 47, 78, 100, 122–23, 131, 145 Politics (Aristotle), 5, 189n37 poor laws, 57–58, 65, 124, 131 Porter, Theodore M., 96, 107, 218n3, 222n66 Port-Royal Logic, 26–27 power-resources theory, 186n13

Index / 251 Prasad, Monica, 165 Price, Richard, 39, 46, 51–52, 55, 61, 72, 76, 96–97, 106, 200n112; expectation of life, 38; Observations on Reversionary Payments, 53–54, 56–57 Priestley, Joseph, 63 principle of indifference, 75, 77, 89, 104, 107–8, 117–18, 166–67, 209n22, 210n24; critique of, 110–11; defense of, 116; equiprobability model, interpretation of, 76 probabilistic equality, 39, 79–80, 110, 113, 116–17, 167, 174 probabilistic expectation, 28, 81, 150 probabilistic insurance, 45, 90, 163, 165; as impersonal and impartial, 43; life, 21–22; mutual, 71, 78; social, 15, 159; as voluntary contract, 49 probabilistic justice, 12–14, 29, 33, 42, 47, 60, 67, 80, 128–29, 173; expectation, as term, 27–28; individual benefit and common good, 46; as term, 20, 191n49 probability, 11, 16–17, 30, 34, 44, 54, 56, 58, 72, 86, 91, 95, 98, 104, 107, 113, 168; aleatory aspect, 6, 70, 75–77, 82, 105, 128, 134, 148, 166–67, 181, 197n65; a posteriori, 69, 75, 77–78, 103; a priori, 75, 108; associationist epistemology, link to, 75–76; and chance, 7; classical, 69, 111, 209n13; dual character of, 4, 6–7, 14, 47–48, 90; empiricist view, 148–49, 153, 181; epistemic aspect of, 6, 70, 75–77, 82, 148–49, 166–67, 181, 197n65; equipossibility interpretation of, 32, 116; and equity, 20; and experience, 55, 76, 82, 87, 108–9, 111, 114, 116, 119–20, 157; and fairness, 80–82, 155–56; frequentist interpretation of, 70–71, 106–9, 114, 116, 119–20, 134, 148–49, 176; Janus faces of, 6, 68; moral expectation, 83–84; objective side of, 105, 149; philosophy of, and early welfare thinking, 115; political applications of, 99–100; quantification and calculation, association with, 6; and risk, 47, 121–22, 155–56; and statistics, 122; subjective view of, 148–49, 155–58, 170, 238n101; as term, 6; and uncertainty, 139; and utility, 155–56

probability calculus, 44, 58, 63, 68–69, 78, 84, 90, 118, 148, 153 probability of causes, 73–74. See also inverse probability probability theory, 6, 46–47, 53, 63, 68, 70, 84, 135, 138–39, 142, 163, 171, 223n85; and chance, 12; contractual equity, 40; distributive justice, 42; friendly society reform, 58; and insurance, 150; normative character, shift in, 155; normative claims, 4; and political economy, 116; utilitarianism, 118; and utility, 119; welfare state, development of, 174; welfare thinking, 173 probability values, 33, 106–7 public health insurance, 2, 179 Quetelet, Adolphe, 89, 94, 96, 99–100, 107, 112, 215n106; average man composite, 95, 98, 103–4; on insurance, 213n7; interpretation of probability, 217n129; responsibility, promoting of, 97 Ramsey, Frank Plumpton, 153 rationality, 91, 155; and agreement, 156– 57; and coherence, 154; and utility, 91 Rawls, John, 137, 164, 169; and decision theory, 160; difference principle, 160, 166–67, 244n21; distributive justice, 163, 165; maximin criterion, 160–62, 239n110; property-owning democracy, 239–40n127; social contract, 15, 159; theory of justice, 14, 167; A Theory of Justice, 139, 158–59, 168; on utilitarian principle, 161–62; veil of ignorance, 159–62, 170 reasoning, as form of wager, 139 reciprocity, 15, 28, 58, 60, 63, 101, 141, 158, 168; common good, 62; and cooperation, 92; distributive justice, 172; and exchange, 31; and security, 51 Rehm, Philipp, 170, 241n152 responsibility, 41, 58–60, 64, 97–98, 103, 143, 166; and accidents, 123–24; collective, 96, 179; familial, 97; individual, 114–15, 123–24, 147, 151; mutual, 128; personal, 62–63, 107, 129, 134, 142, 165, 174, 178 Revolution of 1848, 97

252 / Index Rights of Man (Paine), 65 risk, 65, 77, 85, 88, 91, 107, 115, 137–39, 159, 171, 173, 181; as collectivized, 106; concept of, 4, 17, 135; and disaggregation, 101–2, 170; independence and fungibility of, 23; as independently tradable good, 23; and insurance, 18, 21, 34; maritime contracts, 12, 23; origins of, 12; and probability, 47, 121–22; risk aversion, 19, 236n86; as social, 42; social significance of, 7; sociology of, 10; as term, 187n17; and uncertainty, 18, 78, 234n51; welfare states, 9, 121, 135, 175 risk aversion, 19, 236n86; subjective risk preferences, 158, 192n7 risk pool, 14, 18–20, 24–25, 62, 68, 78, 101–2, 105, 110, 114–15, 121, 129–30, 134–35, 138–39, 144–45, 147–48, 170–71, 177, 179, 181, 230n170, 232– 33n30; Affordable Care Act (ACA), 180; and solidarity, 164–65 Roman law, 22; Roman maritime loans, 21 Roosevelt, Franklin D., 145 Rosanvallon, Pierre, 226n130 Rose, George, 57 Rose Act, 57 Rothschild, Emma, 54, 79, 206n91 Royal Exchange, 200n114 Royal Society, 51, 72 Rubinow, Isaac, 134 Rule of Succession, 74, 76–77, 90 Saint-Simon, Henri de, 213–14n84 Savage, Leonard J., 192n6, 236–37n89 Scotland, 58–59. See also Great Britain Scottish Widows’ fund, 200n112 Second Empire, 127, 215–16n113 Seneta, E., 215n102 Sidgwick, Henry, 222n73, 222n76 Simmons, Dana, 216n116, 216n127, 220n40 Simpson, Thomas, 72 Sismondi, Jean Charles Léonard de, 98 Sketch, The (Condorcet), 63 Skocpol, Theda, 224n91 smallpox, 85 Smith, Adam, 54, 79, 118 social contract, 5–6; recasting of, 159;

social insurance, 48–49, 121; tradition of, 8, 118, 128; and uncertainty, 159 Social Democrats, 124–26 social insurance, 1, 16, 44–45, 67, 79, 83, 86, 98, 102, 124, 134, 150–51, 163–64, 173; amorphous quality of, 179; as annuity, 3; atomist-statist account of, 91, 94, 158; class-based self-interest, appeal to, 145; collective agreement, and security, 121; commercial insurance, compared, 7, 46, 94, 170–71; conflicting distributive claims, 8, 142, 144; contributory principle, 125–26, 140–41, 143; critique of, 145–46; defense of, 14; desert, 165, 186–87n15; as distributive regime, 4, 8–9, 15, 139, 176–77, 191n46; duality of, 8, 14–15, 17, 135, 148; as earned through contributions, 3, 66, 96, 103, 143, 147, 178, 215n110; economic self-interest, as tool of, 3; egalitarian aims, limitations of, 169; emergence of, 122; and entitlements, 178; equity, and redistribution, 147; flexibility or plasticity of, 125, 142, 171–72; and frequentism, 14, 110, 122, 127, 131, 136; friendly societies, 61; group-based, 106; harmonizing impulse of, 168; and identity, 168; individualist methodology of, 94; and liberalism, 8, 48, 64–65, 139, 175; middle classes, constituency for, 144–45; as mixed regime, 8, 142, 144, 178–79, 181, 191n46; mutual aid, 3; mutuality, 2; opposing tendencies to, 169; personal responsibility, 177–78; as policy paradigm, 11, 47, 78, 100, 122–23; political majority, as driving force of, 170; as politico-moral theater, 234n57; private insurance, 170–71; private insurance, as substitute for, 169; private insurance, confusion between, 145–46; probabilistic psychology of, 168; protection, form of, 142–43, 170; purpose of, 64; and risk, 4, 7, 9, 17, 65, 94, 115, 121, 137, 139, 154–55, 168, 171, 176, 188–89n31; risk classes, 127; risk-collectivist account of, 122–23, 127; risk groups, 122, 130; risk pooling, 115, 129–30, 135, 144–45; and security, 182; self-protection, as form of, 3; self-

Index / 253 sufficiency, 2; social contract theories, 48–49, 121; social equality, 3; and solidarity, 139, 168–69, 172; widespread adoption of, 140; working class, security for, 105. See also insurance; mutual insurance socialism, 3, 103, 124, 128 Social Security, 1, 134–35, 243n8; Board of Trustees, 2; confusions, 3; debates over, 2; right to, 3 Social Security Act, 134, 145; Clark Amendment, 229n158 social welfare, 113, 138, 140, 147, 153; frequentist case for, 118–21 Society for Equitable Assurances on Lives and Survivorships. See Equitable solidarity, 128–29, 133, 139, 141, 144, 159, 168, 171–72; classless, 145; of middle classes, 145; of risk pool, 164– 65; “subsidizing,” 170; and welfare state, 176, 178 Soto, Domingo de, 194n29 Soviet Union, 232n19 statistics, 6–7, 13, 107, 117–18, 149–50, 156; and probability, 122, 158; statistical induction, 72; statistical insurance, 80, 93, 174; statistical life insurance, 84–86; statistical probabilities, 174 Stedman Jones, Gareth, 62, 65, 99, 215– 16n113, 216n125 Steinmetz, George, 224n102 Stigler, Stephen M., 74, 149, 208n9, 210n28, 210n30, 213n70 Stiglitz, Joseph, 236n85 Stolleis, Michael, 124 St. Petersburg paradox, 83–84 subjective probability, 14, 153–56, 158–59, 161, 238n101 Sweden, 140, 230–31n4 Sylla, Edith Dudley, 197n63 sympathy, 111, 118, 120, 220n42, 222n73 Tawney, R. H., 225n117 theories of justice, 15, 137, 167 Theory of Justice, A (Rawls), 139, 158–59, 168 Titmuss, Richard, 144, 147, 163, 186n12, 230n2 tontines, 65; and gambling, 66, 207n104

torts, 67; tort law, 123 Treatise on Probability, A (Keynes), 148, 152 Trump, Donald, 180–81 Turgot, Anne-Robert-Jacques, 63, 79 Tversky, Amos, 158 uncertainty, 6, 152, 156, 162–63, 165, 236–37n89; as problem for justice, 5; rational choice, 154; social contract, 159 United States, 12, 54–55, 70–71, 122–23, 126, 140, 180; employers, as influential, 134; healthcare in, 179; state role in insurance, rejection of, 133; welfare state, 133–34, 141; work accidents, 133 universalism, 147, 164–65 usury, 23, 26 utilitarianism, 13–14, 161, 221n60; calculus, 117; equality of distribution, 116–18; frequentist view, 115, 119–21; gambling, association between, 162; moral expectations, 113, 115–16; probability theory, 118 utility, 13, 19, 37, 77, 90, 102, 116–17, 154–56; probability theory, 119; and rationality, 91; utility curve, 84, 87–88, 119; utility curve, concavity of, 87, 115, 119, 192n6, 241n145; value, 82, 84, 94, 118 Van D’Elden, Karl H., 21 Venn, John, 109–12, 114, 120; epistemology, 218n7, 218n9; The Logic of Chance, 108, 115, 119; utilitarianism, recommendation of, 115–16 Villermé, Louis René, 220n40 voluntarism, 125, 128, 133 wager’s fair price, 29–30 Wagner’s Law, 177 Wales, 57. See also Great Britain Webb, Beatrice, 133, 143, 147 Webb, Sidney, 133, 143, 147 welfare policy, 10, 14, 70–71, 78, 89, 91, 121, 126, 135–36, 144–45, 154–55, 159, 163, 165; risk perceptions, 170–71, 238n101; risk pooling, 147–48, 170–71 welfare states, 7, 11–12, 46–47, 65, 67, 96, 99, 104, 115–16, 140, 148, 151, 154–

254 / Index welfare states (continued) 55, 173, 177, 182; actuarial fairness, 20; critics of, 178; empirical political science of, 15; frequentist idea of social insurance, 14, 134; “hidden,” 178; insurance, association with, 147, 175; mathematical probability, interconnected development of, 106; privatizing alternatives, 178; rise of, 121, 163–64, 176; and risk, 9, 121, 135, 170, 186n13; and solidarity, 168–69, 176, 178; undeserved hardship, 66, 133, 141, 181

Wildavsky, Aaron, 189–90n38 Willett, Allan H., 219–20n34 Witt, John Fabian, 133 work-injury compensation, 96, 123–24, 134, 141 World War I, 122 World War II, 11–12, 14, 104, 129, 140, 176 Zabell, S. L., 219–20n34