A New Theory of Cultural Archetypes: Capturing Global Unity and Local Diversity 3031244818, 9783031244810

Table of contents :
Preface
References
Acknowledgements
Contents
About the Authors
List of Figures
List of Tables
Chapter 1: Introduction
1.1 Research Objectives
1.2 The Theory of Archetypes
1.3 The Welzel Meta-Values
1.4 Key Concept Definitions
References
Chapter 2: The New Approach
2.1 Archetypal Analysis (AA)
2.2 Choice of the Number of Archetypes
2.3 Measurement Requirements for AA
2.4 The E & WVS Data on the Welzel Meta-Values
2.5 Subsampling Procedures for AA
2.6 Multidimensional Scaling Map
References
Chapter 3: The Unity and Diversity of the Global Matrix
3.1 Experiments with Varying Subsample Sizes
3.2 Comparison of Random and Weighted Random Subsamples
3.3 The Global Archetypes
3.4 Country Compositions (t)
3.5 The Global Matrix for t = Wave 7
3.6 Cultural Map Coordinates
3.7 Key Takeaways
References
Chapter 4: The Dynamics of the Global Matrix
4.1 The Cultural Map, 1981 to 2021
4.2 Measuring Five Aspects of Cultural Change
4.3 Calibrating the Magnitude of Cultural Change
4.4 A Two-Speed World
4.5 Major Country Trends
4.6 Regional Examples of Change
4.7 Key Takeaways
References
Chapter 5: Multiple Trends in a Two-Speed World
5.1 Our Objectives and Methods
5.2 Archetypal Compositions Represent Heterogeneity Well
5.3 Multiple Trends in the Global Matrix
5.4 How Did the “World” Change?
5.5 A Snapshot of the Current World
5.6 Concluding Thoughts
Reference
Technical Appendix A
Imputation of Missing Data
References
Technical Appendix B
The Means of Sets of Compositions Also Sum to 1
Technical Appendix C
R Packages Used in Our Work
Technical Appendix D
Future Roadmap for the Archetypal Analysis of Culture
Index

Citation preview

A New Theory of Cultural Archetypes Capturing Global Unity and Local Diversity David Midgley Sunil Venaik Demetris Christopoulos

A New Theory of Cultural Archetypes

David Midgley • Sunil Venaik Demetris Christopoulos

A New Theory of Cultural Archetypes Capturing Global Unity and Local Diversity

David Midgley INSEAD Fontainebleau, France

Sunil Venaik University of Queensland Brisbane, QLD, Australia

Demetris Christopoulos National and Kapodistrian University of Athens Athens, Greece

ISBN 978-3-031-24481-0    ISBN 978-3-031-24482-7 (eBook) https://doi.org/10.1007/978-3-031-24482-7 © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover pattern © Melisa Hasan This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The cultural values of nations have been a topic of popular discussion and scholarly study ever since Herodotus wrote about the Persians in the fourth century BC. These values are thought to influence the interactions between people from different nations and also to determine how people within a country behave in their society. While the differences between countries (international heterogeneity) have been extensively studied, these are often reduced to a simplistic comparison between central tendencies such as national averages, ignoring the fact that many individuals are not in the least like their national averages on various cultural values. Disregarding the differences within countries (intranational heterogeneity) is a critical gap in the literature that we argue also results in a flawed picture of the differences across countries. The aim of our book is to fill this gap, by comprehensively examining both the similarities and differences among people within countries (intranational homogeneity and heterogeneity), as well as across countries (international homogeneity and heterogeneity). We believe that the reason for omitting intranational differences is not ignorance of the phenomenon, we all know that our fellow citizens may hold different values to us, rather it is the lack of an appropriate methodology for handling this form of heterogeneity. Previously researchers were reduced to tabling country standard deviations, which say that people “differ” but provide no insight on how they differ. Or more sophisticated analysts might apply multivariate techniques such as cluster analysis or latent profile analysis to form subgroups within a country. Techniques which essentially replace one average with a set of averages, which again v

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may oversimplify heterogeneity, and often also present important challenges in identifying the “right” number of subgroups for a particular situation. The first important breakthrough in our research was when, a decade or more ago, we realized that these techniques were a dead end in terms of adequately representing heterogeneity and something better was needed. That something better turned out to be “archetypal analysis” invented by Adele Cutler and Leo Breiman in 1994 [1] but, at the time we discovered it, mostly applied in the physical rather than social sciences. Archetypal analysis represents a totally different mindset to the majority of multivariate techniques in that it looks to the edges of the data for insights, rather than the centre. By selecting a small set of distinctly different patterns at the edges of the data, the archetypes, this technique provides a parsimonious representation of heterogeneity, but one which is readily understandable. Each individual case in the data then becomes a composition of these patterns, where the different proportions of this composition reflect the relative importance of the various archetypes in the makeup of that case, analogous to the way in which bronze is an alloy of copper and tin and various other metals. The second important breakthrough in our research, and our contribution to the methodology of applying archetypal analysis in general, is when we realized that geometry provides a powerful way to choose the right number of archetypes to capture the heterogeneity inherent in any data set. Later we will show that if your data has D independent dimensions, you need at least D + 1 archetypes, typically D + 2, and potentially up to 2D, to capture this heterogeneity adequately. However, in our work, extending beyond D + 2 is never necessary, so there is a practical limit on the complexity of the resulting archetypes and compositions, making them readily comprehendible. This breakthrough was important as it removed our uncertainty over what was the right number of archetypes, plus the simplicity of our solutions enabled us to see more clearly the difference and similarities within and between countries, and over time. Here we apply these ideas to secular and emancipative values, using the construct measures developed by Christian Welzel [2], and available for the 117 countries we study here through data from the European and World Value Surveys [3], [4]. The four-archetype country compositions of these secular and emancipative values that we present in our book show the world to have both cultural unity across countries and diversity within countries, which is contrary to the simplistic, albeit popular view of the

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world being culturally homogeneous within and heterogeneous across countries. We also show how countries evolve at different speeds, along different paths, and in different directions over the four decades we study from 1981 to 2021. This is important since there is a relative lack of understanding in the literature of the nature of cultural change in different countries, wherein culture is either assumed to be relatively static worldwide, or change is regarded as monotonic, largely towards greater emancipation. Overall, archetypes and compositions reveal our world to be rich, complex, and dynamic, painting a more subtle and insightful picture of global culture than previous approaches. It is for this reason we hope you will find this book useful and, perhaps, different from the many previous studies of cultural values. Fontainebleau, France; Brisbane, Australia; Athens, Greece  November 1st, 2022 

David Midgley Sunil Venaik Demetris Christopoulos

References [1] A. Cutler and L. Breiman, ‘Archetypal Analysis’, Technometrics, vol. 36, no. 4, pp. 338–347, 1994. [2] C.  Welzel, Freedom Rising: Human Empowerment and the Quest for Emancipation. New York: Cambridge University Press, 2013. [3] EVS, ‘EVS Trend File 1981-2017EVS Trend File 1981–2017’. GESIS Data Archive, 2021. https://doi.org/10.4232/1.13736. [4] C.  Haerpfer et  al., ‘World Values Survey Time-Series (1981–2020) Cross-­ National Data-Set’. World Values Survey Association, 2021. https://doi. org/10.14281/18241.15.

Acknowledgements

This work was funded by the INSEAD Research and Development Committee. We are also grateful to the World Value Survey organization for giving us advance access to their July 2021 integrated database.

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Contents

1 Introduction  1 2 The New Approach 15 3 The Unity and Diversity of the Global Matrix 33 4 The Dynamics of the Global Matrix 55 5 Multiple Trends in a Two-Speed World 89 Technical Appendix A109 Technical Appendix B111 Technical Appendix C113 Technical Appendix D117 Index119

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About the Authors

David Midgley  joined INSEAD in 1999 as Professor of Marketing and is now Emeritus. Previously he was Foundation Chair at the Australian Graduate School of Management, and he has also held visiting positions at the University of California, the University of Pennsylvania, and Stanford University. Midgley is a graduate in science, management, and marketing from the Universities of Salford and Bradford. He has over 120 publications, including papers in leading journals such as the Journal of Consumer Research, Journal of Information Technology, Journal of International Business, Journal of Marketing Research, Journal of Marketing, Marketing Science, Management Science, Organization Science, and Research Policy. He has also written several books, including The Innovation Manual and more recently Strategic Marketing for the C-Suite. His principal areas of research are innovation, strategy, and international business. Sunil  Venaik is Associate Professor of International Business at the University of Queensland Business School. He is recognized as being in the top one percent of international business researchers worldwide in the last 50  years, based on his publications in the Journal of International Business Studies. He is a graduate of the Indian Institute of Technology Kharagpur, the Indian Institute of Management Ahmedabad, and the Australian Graduate School of Management. He has held visiting research fellowships at INSEAD, NUS Singapore, IIM Ahmedabad and Udaipur, ANU Canberra, and Stockholm Business School. He has extensive experience in industry including as the CEO of a mid-­size ­enterprise. He has over 100 publications, including papers in leading journals such as the xiii

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Journal of International Business, Organization Science, Journal of World Business, and in community forums such as The Conversation. Demetris Christopoulos  completed his PhD studies in 2017 from the National and Kapodistrian University of Athens. He has a physics degree from Patras University. He has devoted many years in deep learning mathematics and his research field is Noisy Numerical Analysis. He has worked as a market researcher and maths tutor. Since 2015 he has been a multimedia producer at INSEAD, France. He has written many works that challenge fundamental theories of modern physics, while his Big Datarelated works include global temperature, gravitational waves, psychology, and COVID-19. He has published in Journal of Atmospheric and SolarTerrestrial Physics, International Journal of Mathematics and Scientific Computing and he is the co-author of the book A Primer for Deterministic Thermodynamics and Cryodynamics. His work at ResearchGate sets him at the upper 4% of all members.

List of Figures

Fig. 1.1 Fig. 1.2 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6 Fig. 4.7 Fig. 4.8 Fig. 4.9 Fig. 4.10 Fig. 4.11 Fig. 4.12 Fig. 4.13 Fig. 4.14 Fig. 4.15

The cultural map 10 The cultural change compass 12 Archetypal spanning hull for k = 319 Archetypal spanning hull for k = 420 Archetypal spanning hull for k = 520 Reduction in the index of resampling variability as subsample size increases (country compositions) 38 Wave 7 compositions for Egypt and Sweden 43 Wave 7 compositions of China, Japan, and the USA 43 Wave 7 compositions for 83 countries 45 MDS coordinates of 83 Wave 7 Countries 51 The cultural map coordinates of 398 country compositions spanning 1981 to 2021 57 Chile’s dynamics 59 Norway’s dynamics 67 New Zealand’s dynamics 68 China’s dynamics 72 India’s dynamics 74 Japan’s dynamics 75 The USA’s dynamics 76 Ethiopia’s dynamics 78 South Africa’s dynamics 79 Bangladesh’s dynamics 80 Germany’s dynamics 81 Greece’s dynamics 82 Brazil’s dynamics 83 Australia’s dynamics 85 xv

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List of Figures

Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 5.4 Fig. 5.5

The cultural map 1981 to 2021 91 Cultural change compasses for China, India, Japan, and the USA 95 Compasses for Rwanda, Chile, Northern Ireland, and Germany 99 Compasses for Croatia, Bulgaria, Egypt, and Bangladesh 101 A geographical map of 92 country compositions 106

List of Tables

Table 1.1 Table 1.2 Table 1.3 Table 2.1 Table 2.2 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 3.7 Table 3.8 Table 3.9 Table 3.10 Table 3.11 Table 3.12 Table 3.13 Table 3.14 Table 4.1 Table 4.2 Table 4.3 Table 4.4

Four archetypes for the two Welzel Meta-Values Illustrative individual compositions Measurement of the two Welzel Meta-Values E&WVS population coverage of global regions (%) E&WVS countries and survey samples by waves Subsampling fractions for countries with/without calibration weights Descriptive statistics Archetypal spanning hull coverage of the data (percentages) Rates of convergence as subsample size increases Global archetype profiles (estimated population means) by subsample size Counts of overlapping confidence intervals for compositions Comparison of weighted and unweighted compositions for extreme cases The four archetypes and their 95% confidence intervals Country compositions for Wave 7 Example 84% confidence intervals for Wave 7 compositions Overlapping pairs of 84% confidence intervals for compositions Countries on the Wave 7 Convex Hull Example 84% confidence intervals for Wave 7 MDS coordinates Key takeaways The four archetypes: Base elements of a country composition… Compositions and coordinates for countries on the Convex Hull Chile’s compositions and coordinates by wave Changes in the culture of 92 countries

5 6 8 22 24 35 36 36 37 39 40 40 41 46 48 49 52 52 53 58 58 60 62 xvii

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List of Tables

Table 4.5 Table 4.6 Table 4.7 Table 4.8 Table 4.9 Table 4.10 Table 4.11 Table 4.12 Table 4.13 Table 4.14 Table 4.15 Table 4.16 Table 4.17 Table 4.18 Table 4.19 Table 4.20 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 5.9 Table 5.10

Quadrant definitions 65 The change in Norway’s composition resulting in a Change Index of 45% 67 The change in New Zealand’s composition resulting in a Change Index of 11% 68 The Magnitude of Cultural Change by Time Span of Observation70 China’s composition and coordinates 72 India’s composition and coordinates 74 Japan’s composition and coordinates 75 The USA’s cultural composition and coordinates 76 Ethiopia’s composition and coordinates 78 South Africa’s composition and coordinates 79 Bangladesh’s composition and coordinates 80 Germany’s composition and coordinates 81 Greece’s composition and coordinates 82 Brazil’s composition and coordinates 84 Australia’s composition and coordinates 85 Key Takeaways from the analysis of 92 countries 86 The four archetypes: Base elements of a country composition… 92 Quadrant definitions 92 Examples of within and between country heterogeneity 93 Compositions are more subtle than averages 93 Examples of different forms of “Emancipation” 94 Converging trends for USA and Japan, but different processes of cultural change 96 14 Countries with Little Change 97 Changes in the compositions of the eight example countries with easterly and westerly headings 100 Summary of the eight cultural change processes around the compass102 Key takeaways: Multiple trends in a two-speed world 104

CHAPTER 1

Introduction

Abstract  This chapter introduces our research objectives and the theory of archetypes around which our work is based. The chapter also defines the core concepts of this theory for use later throughout the book. In contrast to typical approaches to conceptualizing and analysing social science data, archetypes are found at the edges of the data, and not the centre, because the patterns at the edges are clearer and more distinct. We can then represent individuals and, by aggregation, countries as compositions of these distinct patterns, and these compositions provide a simple way of understanding heterogeneity, both across and within countries. Overall, we believe that this approach goes deeper than the simplistic stereotypes that are often used to compare countries, and in doing so has the potential to yield better insights into the similarities and differences between countries, as well as how these may be changing over time. The chapter also introduces the two Welzel meta-values we use to illustrate our approach and to investigate cultural heterogeneity and dynamics for 117 countries over the four decades from 1981 to 2021. Keywords  Archetypes • Cultural compositions • Global matrix • Cultural map • Cultural compass

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. Midgley et al., A New Theory of Cultural Archetypes, https://doi.org/10.1007/978-3-031-24482-7_1

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1.1   Research Objectives We all have things that we regard as important in life—our values—some of which are personal, some of which are shared with other members of our society. For example, Australians are thought to value “mateship”, the English “stoicism” and the Greeks “philotimo,” a sense of honour [1]. But these are stereotypes (often represented in social science by national averages) and we know this is an oversimplification, in fact there is great heterogeneity of values not only across but also within countries. One Australian may value “mateship,” another may not. Equally we may find English or Greek individuals who hold this value of mateship, just as we will find others who do not. We find unity across the globe through those who hold similar values to us, just as we find diversity through those who hold different values. The central purpose of our research is to develop a simple and insightful approach to represent this heterogeneity—with the primary objective of understanding the unity and diversity of values around the globe. We call this approach the “theory of archetypes” which we implement through a machine learning algorithm called “archetypal analysis.” In a nutshell, this theory represents individuals as compositions of four abstract value profiles—archetypes—which, taken together, provide a parsimonious and powerful representation of the heterogeneity which we observe in human culture. Just as we understand bronze to be a composition of copper and tin, and other metals, here we represent individuals as compositions of these four archetypes. By then analysing countries as properly constructed aggregates of individuals, we can answer questions such as what is the composition of Country X compared with Country Y? Or how did the composition of Country Z change over the last ten years? The archetypal analysis algorithm allows us to identify these archetypes and compositions from social science data, with the additional advantage that archetypes identified across both space and time provide a common platform for studying how compositions change. We regard human values as dynamic and so we have a secondary objective of showing how the global matrix of country compositions evolves over time. This dynamic perspective contrasts with, and complements, other perspectives on cultural values which regard values as more static, for example, the well-­ known Hofstede values [2]. Here we illustrate our approach through data on two important meta-­ values which we obtained from the European and World Value Surveys [3,

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4]. These two meta-values—Secular and Emancipative Values—were developed by Christian Welzel [5], building on earlier work by Inglehart [6] and Inglehart and Welzel [7]. Each meta-value summarizes a range of values that have important consequences for individual human actions and the development of countries. The data we use for our archetypal analysis spans 117 countries and 587,079 respondents in the seven waves of surveys carried out over four decades from 1981 to 2021. Four decades during which the world changed immensely, with the fall of the Soviet Union, economic globalization, the war on terror, the rise of the World Wide Web, and climate change, to name but some of the many changes that occurred over this period. The structure of the remainder of this chapter is as follows. First, we introduce the Theory of Archetypes, then we briefly discuss the Welzel meta-values we use to illustrate our approach, and finally, within the context of these meta-values, we introduce and define the key concepts we will use in the rest of the book, namely global archetypes, country compositions, the global matrix of these compositions, the cultural map and its associated country coordinates as a common platform for studying cultural dynamics, and the cultural compass as a useful tool for understanding these dynamics.

1.2  The Theory of Archetypes The idea of archetypes is not new; indeed, the origins of the concept lie deep in history with Plato’s discussion of “pure forms” [8], and the English word archetype itself derives from the ancient Greek archetypos, or “archetypal” a combination of the verb “to begin” and the noun “type” [9]. However, our theory of cultural archetypes is new, and strikingly different to previous approaches in the literature, so first it is important to be clear on what an archetype is, where we might find them, and why representing individuals and nations as compositions of archetypes provides a powerful lens on culture, before we discuss the specifics of cultural archetypes in the remainder of this chapter, and the computational algorithms for identifying archetypes and compositions in Chap. 2. And here, while we start from the philosophical foundation of archetypes, we extend these ideas into the geometry of multidimensional spaces to provide the basis for Chap. 2. Archetypes. To Plato, pure forms were what today we might call abstract universals, and all real examples of any form are copies which

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resemble, but are not, the universal. Think of geometric forms such as a circle or square (two-dimensional) or sphere (three-dimensional). We all hold an abstract concept of these in our minds and we can recognize them in the many objects and images we see every day, even though there is enormous heterogeneity in these objects and images. Similarly, in our theory an archetype is a universal pattern of values which we hold in our minds and can recognize examples of in real people, even though these examples may be variants of this universal. Take a simplified and Western example, namely an individual who goes to church on Sunday, flies their country’s flag in their garden, celebrates their national day and votes for a conservative party. We might label such individuals “traditionalists” even though they may go to churches belonging to different religions, live in different nations and vote for parties with different priorities. This is the basic idea of an archetype applied to human beings, a universal we can recognize in individuals, even though the individuals belonging to this universal are not identical. In passing, we should note that, although our concern is with cultural values, the idea of archetypes is found and applied in many other fields (e.g., the vertebrate and invertebrate archetypes in biology). Universals/archetypes are key to the classification, interpretation and understanding of phenomena, and to the construction of useful theories of such phenomena. Archetypes are found at the edges. Pure forms are abstractions, and in social science data we find them by looking to the edges and not to the centre. This is a critical point and sets out the theory of archetypes and archetypal analysis as radically different to the standard ways in which social scientists conceptualize and analyse their data. Read the typical journal article or research text in this field and you will see averages, either averages of the totality of the data or of subgroups of these data. Equally you will often see statistical techniques applied such as cluster or latent profile analysis that essentially form subgroups and provide some average-­ based summary of these subgroups. In contrast, archetypes are found at the edges of the data because there we find the clearest and most distinct patterns across the dimensions of interest. Take a simple two-dimensional example such as we have here for the two Welzel meta-values. Then one archetype may represent an (abstract) individual who scores highly on both dimensions. Following Welzel (2014, Chap. 2), the secular scale distinguishes those who place high importance on the institutions and norms of their society (score = 0) from those who do not (score = 1), so this dimension can be thought of as

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Sacred versus Secular values. And the emancipative scale distinguishes those who place high importance on obedience to authority (score = 0) from those who place high importance on freedom from authority (score = 1), so this dimension can be thought of as Obedient versus Emancipative values. Hence an individual who scores highly on both can be labelled as Secular & Emancipative or SecEma for brevity and shown as Archetype 4 in Table 1.1. And the other archetypes may be the combinations of similarly high and low values on each scale, that is, low-low, low-high, high-­ low as also illustrated and labelled in Table 1.1. Table 1.1. previews the results of our analyses of the European and World Values Surveys (hereafter E&WVS) data for 117 countries and these four archetypes are discussed at more length in Chap. 3, where we also provide their confidence intervals. Here, the important point is that these four profiles come from the edges of the data, not the centre. These are distinctly different and immediately recognizable individuals, whereas in our analyses the “average individuals” at the centre of the data measures 0.38 on the secular scale and 0.44 on the emancipative scale, and so are much less distinct or recognizable. In Chap. 2 we formalize these ideas, introduce the algorithm we use for identifying archetypes from multivariate data, and we discuss how to choose the right number of archetypes to represent these data. For the latter, we introduce a new idea based on geometry rather than statistical fit and, in doing so, respond to Kroeber and Kluckhohn who, in their seminal book on culture, suggested that matrix algebra or topology might be better approaches to data analysis than typical statistical methods because “cultural behavior is patterned and never randomly distributed” [10], p. 162. Archetypes provide just such patterns, and a powerful lens though Table 1.1  Four archetypes for the two Welzel Meta-Values Archetype 1: Sacred & Obedient (SacObe) 2: Sacred & Emancipated (SacEma) 3: Secular & Obedient (SecObe) 4: Secular & Emancipated (SecEma) Average individual

Secular valuesa

Emancipative valuesb

0.00 0.09 0.89 0.89 0.38

0.01 0.90 0.16 0.97 0.44

Continuous scale from 0 = Sacred values to 1 = Secular values Continuous scale from 0 = Obedient values to 1 = Emancipated values

a

b

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which we can understand the heterogeneity of our culture data. Furthermore, for the Welzel meta-values, our geometrical approach indicates that four is the right number of archetypes to capture the heterogeneity of global culture, with the four profiles shown in Table  1.1. We should also note that, if desired, the idea of archetypes can be readily extended to more than two dimensions, but here we will focus on two as this is the case for the Welzel data. Individuals and countries as compositions of archetypes. There is a second and equally important difference between the theory of archetypes and typical approaches, and that lies in conceptualizing individuals and countries as compositions of archetypes. Hence rather than say individual X “belongs” to a particular archetype as might be the case, say, with methods such as cluster analysis, here we say that individual X is composed of all archetypes, but with specific proportions for each. This compositional perspective is analogous to our metal alloy example, bronze can have different proportions of copper and tin and other metals according to its purpose. Analogously, we can say that different individuals have different proportions of the four archetypes. Table 1.2 illustrates three examples of such individual compositions drawn from our research. For example, individual “a” is closest to a pure abstraction, with a proportion of 0.74 for the first archetype and low proportions for the other three, whereas individual “b” is closest to the “average” individual with relatively equal proportions of the four archetypes. Individual “c” represents one of the many other patterns that are possible and seen in our analyses. In effect, we conceptualize the Welzel meta-values of all the individuals in our data as being composed of the same four basic elements, the archetypes in Table 1.1. For this reason, we use the symbols SacObe, SacEma, SecObe, and SecEma throughout the book, just as we would use the symbol Cu for copper or Sn for tin. Every individual is then a composition of Table 1.2  Illustrative individual compositions Archetype proportions in the compositions… Individual a b c

1: SacObe

2: SacEma

3: SecObe

4: SecEma

0.74 0.24 0.10

0.11 0.26 0.10

0.12 0.27 0.41

0.03 0.23 0.39

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these four archetypes, with each having their own particular “formula” given by the relevant proportions of the archetypes in their composition. Compositions are an integral part of the archetypal analysis algorithm presented in Chap. 2 and they have the important advantage that since they do not put individuals in boxes, they avoid the often intractable problem of defining those boxes. More importantly, they help us move beyond simple stereotypes as the archetypal perspective reveals the inherent heterogeneity of human values. Through the concepts of archetypes and archetypal proportions we reveal and summarize this heterogeneity with (1) a small number of abstractions which capture the differences in these data simply and clearly, and we then (2) represent every individual in the data as a composition with specific proportions for each of these abstractions. Further, if we have a representative sample of individuals for a country, we can aggregate their compositions into a composition for that country, a composition that is built from the “bottom-up” and fully reflects the demographics of the country. We discuss how we do this in Chaps. 2 and 3, but in principle it results in an identical table to Table 1.2 where “a”, “b’, and “c”, now stand for countries rather than individuals.

1.3  The Welzel Meta-Values At this point it is perhaps useful to say a few words on why the Welzel meta-values provide a good illustration of the theory of archetypes and archetypal analysis. We should note that “meta-values” is our terminology and we adopted it because each dimension is a summary index of four, more specific sub-indices, and each of these sub-indices are in turn measured by three questionnaire items in the E&WVS, as shown in Table 1.3. For the exact phrasing of the questions and coding of the responses (including inverse coding) the reader is referred to the online appendix to Welzel’s book [11]. Note the meta-values are formative indices [12] and not latent variables and Welzel provides a justification for taking this approach to measurement in his book, as well as a detailed discussion of item selection and various tests of dimensionality and construct validity. For our purposes we accept these as valid measures of secular and emancipative values. Our reasons for selecting the Welzel meta-values to illustrate our approach are threefold. First, they represent broad and important sets of cultural values that are clearly consequential for the functioning of society,

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Table 1.3  Measurement of the two Welzel Meta-Values Welzel Meta-Values

Sub-indices Questionnaire items (summarized)

Secular values

Defiance

The inverse of: •  Respect for authority •  National pride • Devoutness Disbelief The inverse of: •  Importance of religion • Religiosity •  Religious practice Relativism Non-conformity to norms about: •  Avoiding fares on public transport •  Cheating on taxes •  Accepting a bribe Scepticism The inverse of trust in: •  The armed forces •  The police •  The courts Emancipative values Autonomy Children are encouraged to learn at home: • Independence • Imagination •  Not obedience Equality The inverse of: •  Men have more right to a job •  Men make better political leaders •  University education is more important for a boy Choice Acceptance of: • Homosexuality • Abortion • Divorce Voice The importance of: •  Giving people more say in government decisions •  Protecting freedom of speech •  More say in jobs and community

for they go to the heart of the relationships between individuals, and between individuals and the traditions and institutions of their society. As such they also vary considerably between countries. Second, to our knowledge, the Welzel meta-values have been measured for more countries and over longer periods of time than other value models, as they are available for 117 countries and all seven waves of the European &World Value Surveys over four decades. In contrast, the

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Hofstede values [2] are only available for 76 countries and are largely derived from data collected in 1967–1973 [13], and the GLOBE values [14] are only available for 62 countries for 2004 and 24 countries in 2014. Furthermore, the E&WVS data is based on representative samples of national populations, whereas both Hofstede and GLOBE collected their data from managers, which limits their applicability to country-level analyses. Finally, while the Schwartz values [15] are also measured for samples representative of country populations, they are only available for two of the seven waves of the E&WVS. Third, and on a more technical aspect, the two Welzel meta-values meet the measurement requirements for archetypal analysis by having an adequate number of unique values and being largely independent of each other, a topic we will discuss in Chap. 2.

1.4   Key Concept Definitions We complete this chapter by defining the key concepts we will use in the rest of the book, namely global archetypes, country compositions, the cultural map and its associated country coordinates, and the cultural compass. Global archetypes. We identify our archetypes from the full set of available data, that is 117 countries, 398 country surveys and 587,079 respondents. The 117 countries represent 90% of the world population in 2021. It is unlikely that increasing coverage of this population to 100% would change the profiles of these archetypes to any extent, so they can reasonably be regarded as “global.” As they are identified from the totality of the data, they also cover the period 1981 to 2021. Definition: Global archetypes are the set of four profiles derived from the two Welzel meta-values, and which best capture the heterogeneity in E&WVS data for 117 countries over the period 1981 to 2021, as shown in Table 1.1 above. The global archetypes are denoted by the four symbols SacObe, SacEma, SecObe, and SecEma. Country compositions and the global matrix. All 587,079 respondents have a set of proportions associated with the global archetypes and identified by their country and the year of the survey they responded to. By aggregation we can then calculate an equivalent set of proportions for each country and year, showing how each country is associated with the global archetypes at that time.

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Definitions: (i) Country compositions are the set of four archetypal proportions for each country and year. Example, for Albania in 2008 the composition is: SacObe = 0.31, SacEma = 0.17, SecObe = 0.33, SecEma= 0.19, which is derived from a sample of 1,432 individuals surveyed in the Wave 5. (ii) The global matrix is the full set of country compositions derived from the 398 country surveys, and available in our online materials. The cultural map and associated country coordinates. While it is easy to compare the compositions of two or three countries, understanding the similarities and differences between country compositions over a larger number of countries is challenging. As we will discuss in more depth in Chap. 2, we therefore analysed the global matrix by multidimensional scaling methods to provide a simpler picture of these differences, resulting

SecObe +2 Obedient

Secular +1

SacObe

0 −2

−1

0

+1

−1 Sacred −2 SacEma

Fig. 1.1  The cultural map

+2

Emancipated

SecEma

1 INTRODUCTION 

11

in a two-dimensional map, where each dimension is a contrast between two archetypal proportions in the compositions, as illustrated in Fig. 1.1. Dimension 1 contrasts Sacred & Obedient (SacObe) with Secular & Emancipated (SecEma), whereas Dimension 2 contrasts Secular & Obedient (SecObe) with Sacred & Emancipated (SacEma). We call this multidimensional scaling solution the “cultural map” and each country’s composition has a set of coordinates showing its position on this map. The quadrants of this map also have simple interpretations which we have labelled (clockwise) as “Secular”, “Emancipated”, “Sacred”, and “Obedient.” Taking the “Secular” quadrant as an example, the interpretation is as follows, namely, a country composition falling in this quadrant has relatively higher proportions of the two secular components of its composition (SecObe & SecEma), and relatively lower proportions of the two sacred components (SacObe & SacEma), compared to countries in other quadrants. Definition: The cultural map is a two-dimensional representation of the similarities and differences between country compositions over the period between 1981 and 2021. Each country composition has a set of coordinates within this space. Example, Belarus, 1990, Dimension One = 0.49 and Dimension Two = 0.39, which falls in the “Secular” quadrant since SecObe and SecEma are relatively high at 0.29 and 0.26 respectively, i.e., summing to 0.55 of the composition. The cultural change compass. Since many countries change their coordinates on the map over time it is useful to understand the direction in which they move. We therefore use an analogy to the compass as a tool to represent these directions, simplified to the four cardinal and four inter-­ cardinal points. By analogy, Dimension One of the cultural map shown in Fig. 1.1. then becomes west (negative) to east (positive), and Dimension Two, north (positive) to south (negative). The inter-cardinal points (north-east, south-east, south-west, and north-west) are also useful because they can indicate a balance between the relevant sacred and secular proportions of the country compositions. For example, moving in a north-east direction from the centre of the map implies a balance between SecObe and SecEma in the changing composition. However, most countries are not at the centre, so we need to understand their starting coordinates as well as their direction of change. These ideas and the cultural change compass are illustrated in Fig.  1.2, using the examples of Spain which moves approximately in a south-east direction on the culture map from 1981 to 2017, and as a contrast, Ethiopia, which essentially moves

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D. MIDGLEY ET AL.

N

2 NW

NE

1

D2

0

19

81

W

Sp

ain

2007

2020 Ethiopia

−1

E

20

17

SW

SE

−2 S

−2

−1

0 D1

1

2

Fig. 1.2  The cultural change compass

west on the map from 2007 to 2020. Thus, Spain’s values become emancipated over time, whereas Ethiopia’s sacred values strengthen over time. The subsequent chapters of the book provide further explanations of the core concepts discussed above, describe the methodologies we use to apply these ideas, and present our various results in depth. Specifically, Chap. 2 explains the archetypal analysis algorithm we used for this work and illustrates how geometry provides the best way to choose the appropriate number of archetypes. Chapter 2 also discusses the subsampling methods we use to estimate population values and confidence limits for our archetypes, country compositions and cultural map coordinates, and for the latter we also discuss our approach to the multidimensional scaling of compositional data. Chapter 3 discusses the various subsampling experiments we conducted to establish the key parameters associated with this method, and to evaluate whether sample biases needed to be corrected by

1 INTRODUCTION 

13

the calibration weights provided for this purpose by E&WVS. Chapter 3 then introduces our first set of results and explains the various formats we use to present and interpret these results by focusing on the latest E&WVS surveys (Wave 7, 2018–2021). Overall, Chap. 3 provides a snapshot of the global matrix as of 2021. Chapter 4 then focuses on how this matrix has changed from 1981 to 2021, looking at various examples of how country compositions and cultural map coordinates have changed over this period, including those trajectories that do and those that do not fit the thesis of increasing emancipation advanced by Welzel [5]. In essence, Chap. 4 more fully describes the heterogeneity in cultural values, within countries, across countries, and over time. Finally, Chap. 5 sets out the major conclusions we draw from these results, particularly concerning the speed of cultural change and the multiple trends in global culture that our compositional approach identifies.

References 1. ‘Cultural Atlas’, Cultural Atlas. http://culturalatlas.sbs.com.au/ (accessed Sep. 07, 2022). 2. G.  Hofstede, Cultures’s Consequences: International Differences in Work-­ Related Values. Beverly Hills: Sage, 1980. 3. EVS, ‘EVS Trend File 1981-2017EVS Trend File 1981–2017’. GESIS Data Archive, 2021. https://doi.org/10.4232/1.13736. 4. C.  Haerpfer et  al., ‘World Values Survey Time-Series (1981–2020) Cross-­ National Data-Set’. World Values Survey Association, 2021. https://doi. org/10.14281/18241.15. 5. C.  Welzel, Freedom Rising: Human Empowerment and the Quest for Emancipation. NewYork: Cambridge University Press, 2013. 6. Inglehart, R., Modernization and Postmodernization: Cultural, Economic, and Political Change in 43 Societies. Princeton, NJ: Princeton University Press, 1997. 7. R.  F. Inglehart and C.  Welzel, Modernization, Cultural Change, and Democracy: The Human Development Sequence. Cambridge: Cambridge University Press, 2005. 8. ‘Theory of forms’, Wikipedia. Sep. 03, 2022. Accessed: Sep. 07, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Theory_ of_forms&oldid=1108307850 9. ‘Definition of ARCHETYPE’. https://www.merriam-­webster.com/dictionary/archetype (accessed Sep. 07, 2022).

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10. A. L. C. Kroeber, and C. Kluckhohn, Culture: A Critical Review of Concepts and Definitions. Cambridge, MA: Peabody Museum, 1952. 11. ‘Freedom Rising Online’, Cambridge University Press. https://www.cambridge.org/fr/academic/subjects/politics-­i nternational-­r elations/ comparative-­p olitics/freedom-­r ising-­h uman-­e mpowerment-­a nd-­q uest-­ emancipation, https://www.cambridge.org/fr/academic/subjects/politics-­ international-­relations/comparative-­politics (accessed Sep. 07, 2022). 12. T. Coltman, T. M. Devinney, D. F. Midgley, and S. Venaik, ‘Formative versus reflective measurement models: Two applications of formative measurement.’, J. Bus. Res., vol. 61, no. 12, pp. 1250–1262, 2008, https://doi.org/10.1016/j. jbusres.2008.01.013. 13. V.  Taras, P.  Steel, and B.  L. Kirkman, ‘Improving national cultural indices using a longitudinal meta-analysis of Hofstede’s dimensions’, J.  World Bus., vol. 47, no. 3, pp.  329–341, Jul. 2012, https://doi.org/10.1016/j. jwb.2011.05.001. 14. ‘GLOBE Project’. http://www.globeproject.com (accessed Sep. 07, 2022). 15. S. H. Schwartz, ‘Are There Universal Aspects in the Structure and Contents of Human Values?’, J. Soc. Issues, vol. 50, no. 4, pp. 19–45, 1994.

CHAPTER 2

The New Approach

Abstract  In this chapter we outline the main features of the methodologies we employ to estimate individual and country compositions, show how the latter vary between countries, and how countries evolve over time. We start by explaining the archetypal analysis algorithm, including the important topic of choosing the number of archetypes, where we present a new method based on geometry which we believe is superior to previous approaches. We then discuss the E&WVS data available for our work on Welzel meta-values, which is necessary for understanding the strengths and limitations of subsequent analyses, but also shows why the technique of subsampling is needed to determine appropriate population estimates and confidence intervals for our results. Finally, we conclude with a short discussion of multidimensional scaling (MDS), the method we use to generate the culture map and country coordinates from the country compositions, and which enables us visualize country similarities, differences, and trends. Keywords  Archetypal analysis • Subsampling • Multidimensional scaling

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. Midgley et al., A New Theory of Cultural Archetypes, https://doi.org/10.1007/978-3-031-24482-7_2

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2.1   Archetypal Analysis (AA) Given a data set Y of n observations on d variables, the archetypal analysis (AA) algorithm seeks to identify matrices A (‘row-stochastic’) & B (‘column-­stochastic’) such that the squared Frobenius norm is minimized.

RSSE  Y  ABY 2

Where RSSE is the residual sum of squared errors. The matrix BY, which has dimensions k by d, represents the k archetypes (in rows) on the d variables (in columns). The matrix A, which has dimensions n by k, represents the mixture of archetypes (in columns) for each observation (in rows). The matrix B, which has dimensions k by n, represents the mixture of data (in rows) for creating the archetypes (in columns). The matrices BY and A are of particular importance here, the BY archetypes providing the “pure forms” of the previous chapter and A being essentially a set of k proportions describing the “composition” of each observation in terms of these k archetypes. The originators of the AA algorithm, Cutler & Breiman [1], proved that if k > 1, the archetypes themselves lie on the exterior surface of the data, that is the convex hull.1,2 Early implementations of AA relied on matrix inversion to solve for these quantities. However, matrix inversion has poor convergence properties, even for small data sets, and to overcome these problems Mørup & Hansen introduced an algorithm, Principal Convex Hull Analysis (PCHA) that works with a transposed data set, X = YT (dimensions d rows by n columns) [2]. The objective function to be minimized then becomes ∥X − XCS∥2, where the matrix of archetypes is XC (dimensions d by k) and the compositions C (dimensions n by k). Furthermore, Mørup & Hansen provide mathematical proofs that PCHA produces solutions that are invariant to the affine transformation and scaling of the data and, critically, are rotationally unambiguous unlike, for example, factor analysis. Mørup & Hansen’s algorithm was originally written in the MATLAB language and then ported to the Python language by Aslak [3]. For our 1  The convex hull is the smallest convex shape enclosing the given data, and the analogy of a rubber band stretched around these data is often used to help understand this concept. 2  For k = 1 the solution is the means of the d variables and not an archetype in our definition since it represents a centre rather than an exterior point. We have, however, incorporated that case in the software for completeness and because the RSSE for k = 1 can be used to normalize the RSSEs of k > 1 solutions for interpretability.

2  THE NEW APPROACH 

17

work we ported the Python version to the R statistical language [4], creating an R package “archetypal” which is available on the Comprehensive R Archive Network (CRAN) [5]. We have also extended the algorithm, particularly by including several methods for providing an initial approximation of the archetypes. Like many optimization algorithms the better the initial “guess” at the solution the more rapidly and more reliably the algorithm will converge to the eventual minimum. Our major contribution here is to recognize that if d is small (< 6) then methods exist for identifying points on the convex hull of any data set (notably those based on the Qhull library [6]). These typically provide good initial solutions, considerably reduce computation times, and increase the chances of converging to a minimum, which is important in our work because we employ subsampling methods which require generating AA solutions for hundreds of subsamples.3 Essentially, since AA works with data points that lie on the convex hull, identifying these points accelerates convergence by narrowing the number of possible values for k, as the hull contains only a small number of data points compared to the complete set of data. Indeed, sometimes the solution is found without any iteration if the k initially selected data points correspond to the best fit.

2.2  Choice of the Number of Archetypes Typically, the number of archetypes, k, is chosen by examining a plot of the residual sum of squares generated by solutions with a range of differing k values, say 1 to 10, and identifying the elbow point (analogous to the point of diminishing returns for the “scree plot” used in factor analysis). However, we note that AA typically fits data sets very well, as it has a relatively large number of parameters compared with other methods, particularly the individual compositions in the matrix A with dimension n by k. Consequently, the residual sum of squares is often small and decreases smoothly as k increases, making identification of elbow points difficult or worse, subjective. We have also found that the apparent elbow point varies with the number of values for k that are plotted, for example a plot of the range k = 1 to 20 may lead the investigator to a different conclusion to a 3  d < 6 is a practical limit as beyond this computation of the hull becomes increasingly expensive with Qhull methods. If d ≥ 6 our package provides alternative methods for identifying initial solutions, including one that approximates the convex hull through dimension reduction (the package function find_outmost_projected_convexhull_points).

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plot of the range k = 1 to 10. Elbow points are thus a hazardous way to choose the number of archetypes. We think the better solution to the choice of k lies in the basic geometry of dimensions and shapes. Let us take the case where d = 2, which is both the simplest case for AA and the case we have here with the two Welzel meta-values. The simplest shape we can fit to a two-dimensional space is a triangle (2-simplex) and a triangle has three vertices, i.e., archetypes. So, a general rule might be that we require at least d + 1 archetypes for a d-dimensional space. With the corollary that k can never be ≤ d. But of course, a triangle may or may not cover the data set adequately, depending on how the individual points are distributed in the space. Anecdotally, from the many plots of data we see in books on multivariate analysis, social science data tends to be distributed as ellipsoids rather than triangles. That observation might lead us to suggest that we require at least d + 2 archetypes to cover ellipsoids adequately. Our solution to determining whether the solution for a specific data set should be d + 1, d + 2, d + 3, etc., is to invent the concept of an archetypal spanning hull. This is simply the hull defined by the k archetypes, from which we can calculate what percentage of the data points lie within this hull and use this percentage to evaluate whether k provides adequate coverage of the actual data or not. This concept is best seen through examples, so in Figs. 2.1, 2.2 and 2.3 we present plots from our work on the two Welzel meta-values, with respectively three (d + 1), four (d + 2) and five (d + 3) archetypes. All three figures are based on the same large subsample of the E&WVS data (n = 15,912), with each case in the data shown as a point. The archetypes resulting from the application of AA to these data are then identified as A1, A2, etc. These archetypes in turn define the archetypal spanning hull which is shown as a dotted line enclosing a varying number of these data points across the Figs. 2.1, 2.2 and 2.3. For Fig. 2.1, the archetypal spanning hull for k = 3, which is a triangle, covers 81.5% of the data points, primarily by covering the bulk of the data which lies in the center of the figure. But as can be seen, this triangle omits many of the outlying data points, data which contains important information about heterogeneity. In Fig. 2.2 the spanning hull for k = 4, which is rectangular, covers 97.4% of the data points, primarily because the addition of an extra vertex to the spanning hull allows it to include more of these outlying points. In our opinion, coverage of these outlying points is important because they represent markedly different variations from the

2  THE NEW APPROACH 

19

Fig. 2.1  Archetypal spanning hull for k = 3

mainstream. For example, the many data points representing low values of the two meta-values which are omitted by the spanning hull for k = 3. Finally, in Fig. 2.3, the spanning hull for k = 5, which is a pentahedron, covers a small number of extra data points for a total coverage of 97.7%. Clearly, for this example, moving from k = 4 to k = 5 produces diminishing returns (an increase of only 0.3% coverage). In the next chapter we will table results that show this example is not unique, in general for the two Welzel meta-values, three archetypes fail to cover outlying regions of the data, four archetypes provide excellent coverage of the totality of the data, and five archetypes add little to this coverage. Heuristically, our work with the Welzel meta-values supports a d + 2 rule for choosing the number of archetypes, k.4 A final comment here concerns the independence of the dimensions. The discussion above assumes the dimensions are substantively independent of each other and this is true for the two Welzel meta-values (see Chap. 3, Table 3.2). If a researcher had, for instance, a large battery of inter-correlated measures, it would be necessary to apply the appropriate 4  The concept of an archetypal spanning hull and its coverage of the data can be extended to d > 2 if required. Extension to three dimensions is straightforward and for four or more dimensions, three-dimensional approximations can be used.

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Fig. 2.2  Archetypal spanning hull for k = 4

Fig. 2.3  Archetypal spanning hull for k = 5

multivariate technique to identify the effective dimensions in their data. For example, using confirmatory factor analysis to identify the Big Five personality traits from a 100-item personality inventory, where d in this case would equal 5 and our d + 2 rule would suggest 7 archetypes, although

2  THE NEW APPROACH 

21

theoretically any number up to 2d = 32 might be required, depending on the distribution of the data in the five-dimensional space.

2.3  Measurement Requirements for AA AA with the PCHA algorithm requires continuous multi-valued variables. This is the case for the Welzel meta-values which are calculated from a battery of 24 separate questionnaire items, rescaled to a 0 to 1 metric, and have thousands of unique numeric values for the sizes of subsamples used here. Thus, the Welzel meta-values are effectively continuous and multi-­ valued. If a researcher only has more restricted metrics, such as the typical five-point or seven-point survey item, it may be necessary to use other AA algorithms (see [7] for one approach). We also do not standardize the meta-values as they are measured on the same metric and have similar means and variances. Standardization might be necessary if a researcher has variables measured on very different scales. However, we warn against ipsatization (standardization by respondent-level means and/or standard deviations), often seen in the culture literature. For AA, this procedure smooths the convex hull and distorts the multivariate distribution of data points, such as to render the results uninterpretable and largely meaningless.

2.4  The E & WVS Data on the Welzel Meta-Values We draw our data from the European and World Value Surveys that were completed in seven successive waves between 1981 and 2021. We are grateful to the World Value Survey organization for giving us advance access to their July 2021 integrated database which includes the two Welzel meta-values,5 along with the constituent items of these constructs and other descriptive variables [8]. This database contains 223,293 individuals responding to the European Value Survey and 431,082 individuals responding to the World Value Survey over the seven waves, for an initial total of 654,375 respondents. Welzel uses regression methods to impute the meta-values in the cases where individual questionnaire items are missing from a response to the survey [9] and the resulting imputed meta-­ values are widely accepted, so most cases in this data set can be regarded  Identified as variables Y010 and Y020 in the integrated dataset, with the SPSS variable labels “SACSECVAL-Welzel Overall Secular Values” and “RESEMAVAL-Welzel emancipative values.” 5

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as complete.6 We did find cases where the meta-values were absent and a number of duplicated responses, so after deleting these cases our final respondent total is 587,079, drawn from 117 countries7 and 398 country surveys. The more substantive issue is that the E&WVS calibration weights [10] that can be used to correct for over or under-sampling of population subgroups are only available for 81 countries, 221 surveys and 355,052 respondents. E&WVS surveys are conducted face-to-face with respondents drawn from a nationally representative random sample, which is a major strength of their methodology. However, as with all such surveys it is harder to obtain face-to-face interviews with some subgroups than others, so response rates may vary by subgroup, potentially creating sample biases towards the more accessible respondents. The full set of 117 countries represents 90.2% of the world population in 2021 [11], together with 94.3% of the world GDP (PPP) for the same year [12], whereas the restricted set of 81 countries with E&WVS calibration weights represents 56.6% of the world population and 77.1% of world GPD, that is, a substantially reduced coverage of the globe compared to the 117 countries. Table  2.1 shows, for the six United Nations global regions, the percentage of the regional population covered by the available country surveys over time. To simplify the table, time is divided into three eras, namely 1981–2001 (“the end of history”), 2002 to 2011 (“the war on terror”) and 2012 to 2021 (“new era”). Critically, the set of 81 Table 2.1  E&WVS population coverage of global regions (%) Region

117 countries and 398 surveys

81 countries and 221 surveys

1981–2001 2002–2011 2012–2021 1981–2001 2002–2011 2012–2021 Africa Asia Europe Latin America North America Oceania

41.0 88.5 99.9 83.8 100.0

35.4 85.8 99.0 78.0 100.0

48.9 93.8 96.8 85.3 100.0

28.5 3.9 89.3 63.0 100.0

12.8 36.4 99.0 50.4 100.0

31.3 46.3 96.8 67.1 100.0

72.6

71.9

70.9

60.3

60.1

59.7

 Technical Appendix A provides more details on the imputation of missing data.  Strictly a small number of surveys are for territories rather than countries, namely Hong Kong, Kosovo, Macao, Northern Cyprus, Northern Ireland, Palestine, and Puerto Rico. 6 7

2  THE NEW APPROACH 

23

countries has notably poorer coverage of Africa and Asia, particularly Asia in the first era and Africa in the second (numbers in bold). So, from the perspective of developing a global platform of data for our analyses, the full set of 117 countries is preferred because of its better regional coverage. Yet we would also like to correct any substantial biases in the survey samples if we want to claim our results are representative of the countries concerned, and that is only possible for the restricted set of 81 countries. Our solution to this dilemma is to construct two sets of subsamples for the 81 countries and their 221 associated surveys; that is, with and without the application of the E&WVS calibration weights, analyze these through AA, and then compare the results to assess the difference these weights make. We will present these comparisons in more detail in the next chapter but to foreshadow the main conclusion, we find no statistically significant differences between the results for most country surveys. We cannot make the same assessment for the countries and waves without calibration weights but based on our analysis of the 81 countries the risk of drawing an incorrect inference about these appears to be low. Hence, we have chosen to focus our subsequent discussion on the full set of 117 countries. Table 2.2 details the countries and the available samples by survey wave for this set. The smallest of these samples is 234 individuals (Montenegro Wave 3) and the largest 4372 (Turkey Wave 4) and the mean sample size across all countries and waves is 1475. The first quartile of these sample sizes is 1042, hence 75% of the surveys have more than 1000 respondents, which is a sample size often used in opinion polling and market research to ensure reliable results. Of the 117 countries, there are 25 with only one wave of survey data, 14 with two waves, 24 with three waves, 19 with four waves, 19 with five waves, 10 with six waves and 6 countries with all the seven of the waves available.8

2.5  Subsampling Procedures for AA The challenge in applying AA to these data are the substantial differences in the sample sizes of country surveys. We would like each to carry equal weight in the analysis so that that our global archetypes do indeed represent the globe rather than just those countries with larger sample sizes. The obvious solution to this challenge is to draw equal sized subsamples 8

 Argentina, Germany, Spain, South Korea, Mexico, and Sweden.

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D. MIDGLEY ET AL.

Table 2.2  E&WVS countries and survey samples by waves Country

ISO

Albania Andorra Argentina Armenia Australia Austria Azerbaijan Belgium Burkina Faso Bangladesh Bulgaria Bahrain Bosnia & Herzegovina Belarus Bolivia Brazil Canada Switzerland Chile China Colombia Cyprus Czechia Germany Denmark Dominican Republic Algeria Ecuador Egypt Spain Estonia Ethiopia Finland France United Kingdom Georgia Ghana Greece Guatemala

ALB AND ARG ARM AUS AUT AZE BEL BFA BGD BGR BHR BIH BLR BOL BRA CAN CHE CHL CHN COL CYP CZE DEU DNK DOM DZA ECU EGY ESP EST ETH FIN FRA GBR GEO GHA GRC GTM

Wave 1 Wave 2 Wave 3 Wave 4 Wave 5 Wave 6 Wave 7

785

977

990

995

1074 1987 2045

1267

1418

1440 1977

2597

1821

1432 1001 980 1439 1407 1402 1408 1496 1472

1019 1098 1466 1002

1451 1032

1497 863

2290

1197

1198

1445

971

2057

886

1403

1532

1753 1677 1244 1478 958

1141

1496 2155 2437 992 1661 3012 1978 1575 3977 1449

1476

964

1434 1004 998 1497 1802 1626 1782

1200 1517 1200

1180

1924 1160 999

1191 945

2499

1206 1046

2996 3149 969

1123 2005

1799 1869 926

1717

992 2055 1511 999 2027

1528 2057 1735 4018 3135 992 3032 1520 940 1710 2120 3319

408 1262

2037

1115 1114

3797 817

1197 1000

542 960 1446

981

3000 2226 827 978 1515

1992 1042

3045 2575 1433 1485 1948 2483 2496 2822 1529 1454 1000

1151 1202 1523 1181 1509

1202 1552

1197 1182 1204 1286 1223 1185 1863 1782 2186 1196 1163

(continued)

2  THE NEW APPROACH 

25

Table 2.2  (continued) Country

ISO

Hong Kong SAR China Croatia Haiti Hungary Indonesia India Ireland Iran Iraq Iceland Italy Jordan Japan Kazakhstan Kenya Kyrgyzstan South Korea Kosovo Kuwait Lebanon Libya Lithuania Luxembourg Latvia Macao SAR China Morocco Moldova Mexico North Macedonia Mali Malta Myanmar (Burma) Montenegro Mongolia Malaysia Northern Cyprus Nigeria Nicaragua Northern Ireland Netherlands

HKG HRV HTI HUN IDN IND IRL IRN IRQ ISL ITA JOR JPN KAZ KEN KGZ KOR KOS KWT LBN LBY LTU LUX LVA MAC MAR MDA MEX MKD MLI MLT MMR MNE MNG MYS NCY NGA NIC NIR NLD

Wave 1 Wave 2 Wave 3 Wave 4 Wave 5 Wave 6 Wave 7 1211 1191

998

1301

2069 1472

1943

1126

951

644

2342 992

1892

913 996 1795 939 2379

2485 1979 1705

1501 3199 3977

2666 1195

886 1247

770

688 1971 836

1000

937 1860 1211 1269

1237

1242

1042 1199

781 2319 1194 1050

1200 1485

1200 2176 1500 1500 1199 1168 1200 2091

950

992 1185

871 1042 920

1281 1509 1386

967 1493 947

1236 996 1488 1045

1183 2453 1532

1498 1199 1610 2254 1203 1289 1246 1259 1182 1245

1200 1404

1022

1668

1437

358 234

989

1500 1371

1013

1354 1200 466

997 298 1036

298 980

1989

2018 871 992

2531

1111 1999

1300

1736 1095

1200 974 1638 1313

1759

1237 1200

1836

2356

(continued)

26 

D. MIDGLEY ET AL.

Table 2.2  (continued) Country

ISO

Norway New Zealand Pakistan Peru Philippines Poland Puerto Rico Portugal Palestinian Territories Qatar Romania Russia Rwanda Saudi Arabia Singapore El Salvador Serbia Slovakia Slovenia Sweden Thailand Tajikistan Trinidad & Tobago Tunisia Turkey Taiwan Tanzania Uganda Ukraine Uruguay United States Uzbekistan Venezuela Vietnam Yemen South Africa Zambia Zimbabwe

NOR NZL PAK PER PHL POL PRI PRT PSE QAT ROU RUS RWA SAU SGP SLV SRB SVK SVN SWE THA TJK TTO TUN TUR TWN TZA UGA UKR URY USA UZB VEN VNM YEM ZAF ZMB ZWE

Wave 1 Wave 2 Wave 3 Wave 4 Wave 5 Wave 6 Wave 7 937

1210

1124 1146 1173 1200 1127 1163

1103

2089 904 1999 1494 1200 1002 717 935

1369 2297

796 1197 1189 1200 948

1378

1122 985 1983 1393 1200 1322 1119 1200

991

1054 1801

1224 1995

994 2248

2776 3319 1506

1455 1503

836

1526 937 1007

1237 1259 1076 1001 1007

1173 1157 936 1010

2563 1229 2155 1801 1531 1002

979

4372 765

1788

2617 987 1525 1195

1281

2574

2907

1227 1159 1002 1002 1198

2322 984 1201

1200 977

1472

2991 1002

2978 1484

1059 1479 2439 1527

1597 1802

1971

2006

1056 1198 1195 997 1175 1599 1191

1500 978 2202 1495

1437 1413 1067 1189 1480 1200 1202 2371 1222

1571 2582

1200 970 3509 1500

1215

2  THE NEW APPROACH 

27

from each country survey and this immediately points us to the technique of subsampling [13]. Subsampling is a technique which builds on the insight that a subsample of a base sample is also a valid sample of the target population. Hence a subsample of a E&WVS country sample is a valid sample of that country’s population. Subsampling draws multiple such subsamples from the base sample without replacement and, since it allows choice of subsample size, enables us to draw equal-sized subsamples from each country survey. The better-­ known technique of bootstrapping would not allow us to follow this strategy since it requires resamples of equal size to the original sample. Bootstrapping would also not be practicable from a computational point of view, since AA is expensive in computing cycles, whereas the small sizes typically used in subsampling ( n being one heuristic) does make AA feasible. As with bootstrapping, the strength of subsampling comes from multiple draws which provide population estimates and confidence intervals for the variables of interest. In the case of subsampling, the confidence intervals derive from experiments with subsamples of differing size, which allow the researcher to examine how the variability of the subsamples decreases as their size increases (as basic sampling theory would imply) and thus determine the rate at which subsample estimates will converge to the population values. This rate of convergence can then be used to calculate the appropriate confidence intervals around the estimates from any chosen set of subsamples, as follows. For a given subsample size drawn j times from the base sample, let θi be the value of a variable obtained from the ith subsample and θp be the estimate of the population value of this variable (typically the mean of the j subsamples). Further, let the deviations between subsample values and population estimate be defined as di = θi − θp, for i = 1 to j. The dispersion of these deviations can then be represented by taking the width of their distribution at a small number of quantile pairs (e.g., d0.90 − d0.10) and the average of the natural logarithms of these widths can be used as an index of resampling variability [13]. This index should, in principle, decrease as subsample size increases. Using a small number of subsample sizes, a simple regression between the index and the log of the subsample size allows the rate of convergence, R, to be estimated as minus the slope of the regression line. For any subsample size, resampling errors are then calcuss R lated as, ei  R  di for i = 1 to j and where ss = the size of the subsample sb

28 

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and sb = the size of the base sample. The distribution of these resampling errors can then be used to establish confidence intervals at the desired level of significance. As to the number of subsamples to draw, we use 100 here based on the resampling literature [14] which also parallels our experience with subsampling and AA, namely that there are diminishing returns to drawing more than 100, unless it is required to establish confidence intervals at higher levels of significance than two sigma (95%). This can be done but only at the cost of considerably increased computing time, for example three sigma would require 1000 subsamples and four sigma 10,000. The 100 equal-sized subsamples can be drawn randomly from the available data and these draws can also be corrected for differing subgroup response rates through the E&WVS calibration weights. There are three additional considerations for our work here; (1) aggregation of individual compositions to the country level, (2) alignment of outputs from subsamples, and (3) the appropriate index of resampling variability for our three quantities (archetypes, compositions, and coordinates) given these are not single variables as in the discussion above. Aggregation. Applying AA to a subsample of Welzel meta-values results in a set of archetypes and, at the individual respondent level, compositions with a set of proportions for each archetype. Since our unit of analysis is a country at a point in time, we aggregate these individual compositions using the country and wave identification variables in the E&WVS data and calculating the corresponding country mean for each proportion in the composition.9 We define the set of k mean proportions for a country as its composition, and here we have 398 such compositions corresponding to the available country surveys. These are provided in the online appendix to this book. Alignment of outputs. There is no guarantee that the set of archetypes identified from each subsample will be output in the same order, and the same order is necessary to calculate the population estimates of the compositions. Kleshchevnikov provides an algorithm for aligning archetypes which we adapted for our work [15]. The resulting R code aligns multiple sets of archetypes around one designated target set, and we perform this alignment 100 times using each individual set as the target in turn. We then choose the alignment with minimum variation as the best ordering 9  Technical Appendix B provides a formal proof that the means of sets of archetypal proportions also sum to one.

2  THE NEW APPROACH 

29

solution. Once archetypes are ordered, putting the proportions in individual compositions into the same order follows in a straightforward manner, and then population means for both can be calculated. Indices of subsampling variability. Application of subsampling theory to country compositions is also straightforward. We calculate a sub-­ index of resampling variability for each proportion in the composition in the manner described above and take the mean of all these sub-indices to provide an overall index. This works well because the overall index is based on a large matrix (for example, 398 rows by four archetypal weights), which lessens the impact on any outlying sub-index on the overall mean value. However, for archetypes, this is not the case. The matrix is small (four archetypes by two meta values in our case) and, since the sub-indices are in natural logarithms, one value which is markedly different to the others can overly influence the overall mean. So here we use a one-step robust estimator for the overall index, using the R function onestep from the package WRS2 [16]. One-step robust estimators are designed to address the problems of estimating from small samples.

2.6  Multidimensional Scaling Map The term multidimensional scaling (MDS) covers several well-established algorithms for visualizing the similarities/dissimilarities between a set of objects or cases from a dataset, algorithms that differ primarily in their assumptions about the level of measurement of the data (for example, metric versus non-metric multidimensional scaling). These algorithms use the totality of the distances between the cases as their input—that is n! distances, where n = number of cases—and produce a configu n  2 ! 2 ! ration of the cases in a space, typically of low dimensionality, that is a “map” of the cases, and for us a culture map of countries. Note that our cases are compositions and, since these are constrained to sum to one, standard Euclidean distances are not appropriate and instead a distance metric from compositional data analysis is required [17]. Here we use the Aitcheson distance, which uses log-ratios, defined as the natural logarithms of the composition proportions divided by their geometric mean [18]. Distances between these transformed proportions are then Euclidean and MDS can be applied. For the Aitcheson distances, we use the aDist function from the R package robCompositions [19] and for MDS

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the mds function from the R package smacof [20],10 with the level of measurement defined as ratio corresponding to the nature of the transformed proportions. Calculation of indices of subsampling variability for the resulting country coordinates on the MDS map then follows the same procedure as for country compositions. The strength of MDS lies in its use of the distance matrix to identify the best configuration for the data, thus using the maximum information possible from the data set. In the next chapter, we present results that show MDS has the highest rate of convergence and consequently the narrowest confidence intervals of our various analyses, which stems from its use of a distance matrix that is derived from 398 country compositions. MDS also produces a holistic view of our data, configuring all these country compositions into a common coordinate system, and thus facilitating the identification and interpretation of both differences and similarities between countries and trends over time. This holistic view is necessary given the wealth of possible comparisons provided by 117 countries and 398 country compositions visualized over four decades. Hence, we mainly rely on MDS maps to report such comparisons in Chaps. 3 and 4. Next, in Chap. 3, we apply the methods above to conduct subsampling experiments, evaluate whether it is necessary to correct sample biases, and present our first set of results for the global archetypes, country compositions and the culture map.11

References 1. A. Cutler and L. Breiman, ‘Archetypal Analysis’, Technometrics, vol. 36, no. 4, pp. 338–347, 1994. 2. M. Mørup and L. K. Hansen, ‘Archetypal analysis for machine learning and data mining’, Neurocomputing, vol. 80, pp. 54–63, 2012, doi: https://doi. org/10.1016/j.neucom.2011.06.033. 3. U.  Aslak, ‘py_pcha’. Sep. 02, 2022. Accessed: Sep. 13, 2022. [Online]. Available: https://github.com/ulfaslak/py_pcha. 4. R Core Team, ‘R: a language and environment for statistical computing’. R Foundation for Statistical Computing, Vienna, Austria, 2021. 5. D. Christopoulos, archetypal: Finds the Archetypal Analysis of a Data Frame. 2022. [Online]. Available: https://CRAN.R-­project.org/package=archetypal.  A full list of all the R packages we used in our work is provided in Technical Appendix C.  We would also point out that there are several ways in which the overall approach outlined in this chapter can be improved and extended with further research and software development, and we list the principal ones in Technical Appendix D. 10 11

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6. ‘Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point’. http://www.qhull.org/ (accessed Sep. 13, 2022). 7. S. Seth and M. J. A. Eugster, ‘Probabilistic archetypal analysis’, Mach. Learn., vol. 102, no. 1, pp.  85–113, Jan. 2016, doi: https://doi.org/10.1007/ s10994-­015-­5498-­8. 8. C.  Haerpfer et  al., ‘World Values Survey Time-Series (1981–2020) Cross-­ National Data-Set’. World Values Survey Association, 2021. doi: https://doi. org/10.14281/18241.15. 9. ‘Freedom Rising Online’, Cambridge University Press. https://www.cambridge.org/fr/academic/subjects/politics-­i nternational-­r elations/ comparative-­p olitics/freedom-­r ising-­h uman-­e mpowerment-­a nd-­q uest-­ emancipation, https://www.cambridge.org/fr/academic/subjects/politics-­ international-­relations/comparative-­politics (accessed Sep. 07, 2022). 10. GESIS-Leibniz-Institut Für Sozialwissenschaften, ‘European Values Study (EVS) 2017: Weighting Data’, GESIS Pap., 2020, doi: https://doi. org/10.21241/SSOAR.70113. 11. U.  N. P.  Division, ‘Home Page | Data Portal’, Population Division Data Portal. https://population.un.org/dataportal/ (accessed Sep. 13, 2022). 12. ‘GDP, PPP (current international $) | Data’. https://data.worldbank.org/ indicator/NY.GDP.MKTP.PP.CD (accessed Sep. 13, 2022). 13. D.  N. Politis, J.  P. Romano, and M.  Wolf, Subsampling. New  York: Springer, 1999. 14. B. Efron, D. Rogosa, and R. Tibshirani, ‘Resampling Methods of Estimation’, in International Encyclopedia of the Social & Behavioral Sciences: Second Edition, Elsevier Inc., 2015, pp.  492–495. doi: https://doi.org/10.1016/ B978-­0-­08-­097086-­8.42165-­3. 15. V. Kleshchevnikov, ‘vitkl/ParetoTI’. Mar. 01, 2022. Accessed: Sep. 13, 2022. [Online]. Available: https://github.com/vitkl/ParetoTI/blob/510990630 da589101c6a8313571c96f7544879da/R/align_arc.R. 16. P.  Mair and R.  Wilcox, ‘Robust Statistical Methods in R Using the WRS2 Package’, Behav. Res. Methods, vol. 52, pp. 464–488, 2020. 17. J. Aitchison, The statistical analysis of compositional data. London: Chapman & Hall, 1986. 18. J.  Aitchison, C.  Barceló-Vidal, J.  A. Martín-Fernández, and V.  Pawlowsky-­ Glahn, ‘Logratio analysis and compositional distance’, Math. Geol., vol. 32, no. 3, pp. 271–275, 2000. 19. P. Filzmoser, K. Hron, and M. Templ, Applied Compositional Data Analysis. With Worked Examples in R. Springer International Publishing. Springer Nature Switzerland AG, Cham, Switzerland, 2018. 20. P. Mair, P. J. F. Groenen, and J. de Leeuw, ‘More on multidimensional scaling in {R}: smacof version 2’, J. Stat. Softw., 2021.

CHAPTER 3

The Unity and Diversity of the Global Matrix

Abstract  In this chapter we discuss the results we obtained by applying the methodologies outlined in Chap. 2. We first present the results of the experiments we did with different subsample sizes, which allowed us to estimate confidence intervals for the three quantities of interest here, namely, global archetypes, country compositions, and cultural coordinates. We then compare the results obtained with simple random samples to those where we also adjusted the probability of selection according to subgroup response rates using the E&WVS calibration weights. Here we conclude that the differences between the two sampling approaches are sufficiently small that the simpler approach is preferred because it allows us to expand our coverage of the globe from 81 to 117 countries, including several major countries which would otherwise be omitted as calibration weights are not available, and to expand our common platform of data from 221 to 398 country surveys. We then estimate the archetypes, compositions, and coordinates from these 398 surveys, however for the remainder of this chapter we focus primarily on those results that relate to Wave 7 of the E&WVS surveys (2017 to 2021). This focus provides a snapshot of global culture based on the latest available data at the time of writing and for the 83 countries included in Wave 7. It also allows us to illustrate our results in a relatively straightforward manner, without the complication of dynamics. Cultural dynamics are then addressed in the subsequent chapter, building on the ideas presented here, particularly the

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. Midgley et al., A New Theory of Cultural Archetypes, https://doi.org/10.1007/978-3-031-24482-7_3

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two-dimensional MDS map of global culture which we introduce in this chapter. Finally, we close the chapter with some conclusions on the unity and diversity of the global matrix, as seen through the lens of the Wave 7 snapshot. Keywords  Subsampling experiments • Confidence intervals • Global matrix • Cultural map • Wave 7

3.1   Experiments with Varying Subsample Sizes We chose ranges of subsample sizes to reflect the data available for the two analyses. For the first set of 117 countries and 398 country surveys subsampled equally at random we chose sizes ranging from 15,920 to 23,880, that is 40 to 60 individual respondents per country survey. For the second set of 81 countries and 221 country surveys, where E&WVS calibration weights are also available, we chose sizes ranging from 8840 to 15,912, that is 40 to 72 per country survey. These two ranges follow the subsampling literature in that the subsample sizes are small in comparison to the original base sample (587,079 for the 117 countries and 355,052 for the 81 countries), with the strength of the approach deriving from the 100 repeated draws we use here. The two ranges also reflect the fact that some of the additional countries in the first set have smaller base sample sizes (the overall mean survey size is 1475 for the set of 117 countries versus 1607 for the set of 81 countries). It is necessary to take these survey size differences into account to avoid oversampling these additional countries. Table 3.1 shows the fractions of the survey base sample subsampled at each chosen size for the two sets, namely the median and 95th percentile value for this fraction, where the latter shows the impact on the smaller country surveys at the margin. While some country surveys are subsampled more heavily than others, these fractions all remain sufficiently small in magnitude that each draw selects different individuals from the previous draws and the proportion of individuals drawn into more than one subsample remains low across the set of 100 subsamples (approximately 5%). The two sets of 100 subsamples then provide robust bases from which to estimate population values and confidence limits.

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Table 3.1  Subsampling fractionsa for countries with/without calibration weights Set 1: 117 Countriesb

Set 2: 81 Countriesc

Country Total Median 95th Total Median 95th survey subsample subsampling percentile subsample subsampling percentile subsample sizee fractionf subsampling sizee fractionf subsampling sized fractionf fractionf 40 44 52 60 68 72

15,920 17,512 20,696 23,880

0.03 0.04 0.04 0.05

0.05 0.05 0.06 0.07

8840 9224 11,492 13,260 15,028 15,912

0.03 0.03 0.04 0.04 0.05 0.05

0.04 0.05 0.06 0.07 0.07 0.08

The total subsample size divided by the base sample size, where the base sizes are 587,079 for 117 countries and 355,052 for 81 countries b Based on 398 country surveys and 100 equal random subsamples of the sizes indicated in the table c Based on 221 country surveys and 100 equal random subsamples of the sizes indicated in the table, where the probability of selection is weighted to correct for variations in subgroup response rates using E&WVS calibration weights d The number of respondents randomly selected per country survey e The total size of the subsample, that is the country subsample size multiplied by the number of country surveys available f Statistics based on the distribution of the sampling fractions across 100 subsamples of the indicated sizes a

Characteristics of the Subsampled Welzel Meta-Values. If we examine the population estimates for the means and standard deviations of the largest subsample sizes in each set (23,880 and 15,912 respectively), we find they are highly similar, as shown in Table 3.2. The other statistic of importance for AA is the independence of the two meta-values, where we show the correlation between the two in the table and, since correlation assumes a linearity that may not be present, a non-­ parametric measure of this association, mutual information. Both show the two meta-values can be regarded as independent dimensions for the purposes of AA, the correlation indicating only 13% shared variance and mutual information, which is expressed in information bits, showing in fact a lower degree of association. Identifying the number of archetypes. We first determined the appropriate number of archetypes, again by taking the largest subsample size for each set, generating 100 subsamples of this size, applying AA with

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Table 3.2  Descriptive statistics Set 1: 117 Countries

Set 1: 81 Countries

Secular values

Emancipative values

Secular values

Emancipative values

Mean Standard deviation

0.38 0.18

0.44 0.18

0.39 0.18

0.46 0.18

Correlation Mutual information

0.36 0.12

0.36 0.13

Table 3.3  Archetypal spanning hull coverage of the data (percentages) Set 1: 117 Countries Archetypes 3 4 5

Set 2: 81 Countries

Minimum coveragea

Mean coveragea

Maximum Coveragea

Minimum coveragea

Mean coveragea

Maximum Coveragea

52.0 96.1 97.1

76.0 97.5 98.3

88.8 99.0 99.2

68.8 96.1 96.8

81.8 97.6 98.3

87.6 98.9 99.4

Statistics from the archetypal analysis of 100 subsamples with differing numbers of archetypes e.g. for 3 archetypes the minimum coverage observed in Set 1 was 52.0%, the mean 76.0% and the maximum 88.8% a

three, four and five archetypes to each subsample, and examining the degree to which the archetypal spanning hull covers the data across the 100 solutions at each number of archetypes. Table 3.3 shows these coverage statistics and confirms that four archetypes is the best choice. While three archetypes achieve a good degree of coverage, they omit important data that fall outside their triangle and which four archetypes cover well, and five archetypes add very little to the coverage of four archetypes. Rate of convergence. We next generated four archetypes, country compositions, and cultural (MDS) coordinates for each of the 100 subsamples, and then estimated their population values and associated error distributions from the 100 sets of archetypes, compositions, and coordinates. This process was repeated for each subsample size. The reduction in the width of the error distributions as the subsample size increases enabled us to calculate the rates of convergence for each quantity and from these

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37

rates and the error distributions derive the necessary confidence intervals. (See Chap. 2 for more details on these points). The rates of convergence are shown in Table 3.4, while Fig. 3.1 shows one example of how the index of resampling variability decreases with subsample size, namely for the country compositions since these become the main vehicle for the results we present in this chapter. As can be seen in the Table, the rates of convergence for the two sets are similar, with the cultural coordinates having the highest rate and therefore the narrowest confidence intervals. The other striking feature of these experiments with different subsample sizes is the four archetypes identified from each subsample size are essentially identical, both within a set and when comparing the two sets, as shown in Table 3.5. Archetypes are exterior points, and as such tend to be similar across large sample sizes. Given this result, the E&WVS calibration weights make no difference, and hence we would prefer the better global coverage of the first set of 117 countries. But is this true for country compositions? To answer this important question, we next turn to an analysis of the similarities and differences between compositions estimated with and without application of these calibration weights.

3.2   Comparison of Random and Weighted Random Subsamples This analysis is only possible for the 81 countries and 221 country surveys in the second set where the E&WVS calibration weights are available. For these data, we generated country compositions with and without these weights and examined whether the confidence intervals of these compositions overlap. For this comparison we used the largest subsample of 15,912 respondents and 84% confidence intervals. Why 84%? Non-overlapping 84% intervals are a commonly used heuristic for testing whether the mean Table 3.4 Rates of convergence as subsample size increases

Estimated quantity Global archetypes Country compositions Cultural coordinates

Set 1: 117 Countries

Set 2: 81 Countries

0.38 0.41 0.46

0.31 0.35 0.43

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D. MIDGLEY ET AL.

Fig. 3.1  Reduction in the index of resampling variability as subsample size increases (country compositions)

values of two quantities differ at the p ≤ 0.05 level of significance, as overlap of the standard 95% intervals may mask significant differences in the means [1]. If the 84% intervals do not overlap, then their means are different. Here, we use this heuristic to facilitate testing when we have many such intervals to compare as is the case for this comparison of 221 weighted and unweighted compositions. We should also note that the compositions have four components—the proportions—so there is a question of how to assess overlapping confidence intervals. Here we count how many of these four proportions overlap and use this count as an indicator of the degree of overlap. A count of four would then indicate complete overlap of the confidence intervals, whereas less than four would indicate significant differences between the population weighted and unweighted compositions on two or more components.

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39

Table 3.5  Global archetype profiles (estimated population means) by subsample size Set 1: 117 Countries Subsample size

Secular values

Set 2: 81 Countries Emancipative values

Archetype 1: Low on both meta-values 15,920 0.01 0.02 17,512 0.00 0.01 20,696 0.01 0.01 23,880 0.00 0.01

Subsample size

Secular values

8840 0.01 9724 0.01 11,492 0.01 13,260 0.01 15,028 0.01 15,912 0.01 Archetype 2: Low on secular values, high on emancipative values 15,920 0.11 0.89 8840 0.12 17,512 0.10 0.89 9724 0.11 20,696 0.10 0.90 11,492 0.12 23,880 0.09 0.90 13,260 0.10 15,028 0.11 15,912 0.10 Archetype 3: High on secular values, low on emancipative values 15,920 0.87 0.16 8840 0.86 17,512 0.87 0.16 9724 0.87 20,696 0.88 0.16 11,492 0.88 23,880 0.89 0.16 13,260 0.87 15,028 0.88 15,912 0.87 Archetype 4: High on both meta-values 15,920 0.89 0.97 8840 0.89 17,512 0.89 0.97 9724 0.89 20,696 0.89 0.97 11,492 0.90 23,880 0.89 0.97 13,260 0.90 15,028 0.90 15,912 0.91

Emancipative values 0.02 0.03 0.02 0.02 0.02 0.02 0.90 0.91 0.91 0.91 0.92 0.92 0.20 0.19 0.19 0.19 0.19 0.18 0.96 0.96 0.96 0.97 0.97 0.97

Table 3.6 details the overlap counts, and the results are striking. Most of the confidence intervals completely overlap (187 of 221 or 84.6%) and only 34 (15.4%) have significant differences at p ≤ 0.05. If we examine the latter 34, we find no overlap at all for Singapore Wave 4 and only one overlapping proportion for North Macedonia Wave 7 and Croatia, also Wave 7. There are then 31 remaining cases where two or three proportions of the composition overlap but not all four.

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Table 3.6  Counts of overlapping confidence intervals for compositions Number of overlapping proportions

Number of compositions

Zero One Two Three Four Total number of compositions

1 2 17 14 187 221

Table 3.7  Comparison of weighted and unweighted compositions for extreme cases Country compositions (proportions) Country

Wave Euclidean distance

North Macedonia

7

0.06a

Singapore

4

0.05

Croatia

7

0.05

Basis

SacObe SacEma SecObe SecEma

Weighted Unweighted Weighted Unweighted Weighted Unweighted

0.39b 0.34b 0.40 0.43 0.33 0.29

0.25 0.27 0.24 0.26 0.27 0.29

0.21c 0.20c 0.21 0.18 0.21 0.20

0.16 0.19 0.15 0.13 0.20 0.23

Between the calibration weighted and unweighted compositions The pairs of weighted and unweighted proportions shown in normal text are significantly different at p ≤ 0.05 c The confidence limits for pairs of weighted and unweighted proportions shown in bold text overlap a

b

These three extreme cases are worth examining to ascertain whether the statistically significant differences are also meaningful differences. The relevant compositions are shown in Table 3.7, ordered by the Euclidean distance between the weighted and unweighted values, and with the overlapping proportions for Croatia and North Macedonia shown in bold text. The differences are most likely meaningful but not major. For example, the rank order of the component magnitudes is identical for the weighted/ unweighted compositions of North Macedonia and Singapore but not for Croatia where it differs somewhat. For the other 31 compositions with fewer overlapping proportions, these differences are smaller and possibly less meaningful, though we do note that for some countries there are systematic differences across several survey waves (namely, Argentina and Italy for three waves, and Germany and Singapore for two waves).

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41

On balance, the fact that 85% of the compositions overlap, and only 15% show differences, whether idiosyncratic or systematic, indicates to us that basing our results on the unweighted set of 117 countries is the better choice. Not only does this set cover world population and GDP better, but it also adds major countries to the analysis, such as Bangladesh, Ethiopia, India, and Japan, whose cultures add to the richness of the global matrix. We leave the question of why there are no differences for most compositions to future research. Speculatively, and given that there is clear variation in the calibration weights evident in these data, it might be that the demographic factors used to establish these weights are not strongly associated with meta-value compositions. From this point, we focus our discussion on the set of 117 countries and 398 country surveys where we draw 100 subsamples equally from each survey at random, and we choose the largest subsample size on which to base these results (23,880), since it has the narrowest confidence intervals.

3.3  The Global Archetypes The four archetypes and their standard 95% confidence intervals are shown in Table 3.8, together with the descriptive labels we use for them and for their associated archetypal weights. These labels follow directly from the two Welzel meta-values, which are continuums ranging from sacred to secular and from obedient to emancipated. Hence, SacObe is our label for the archetype which is low on the continuum for both meta-values (0.00, 0.01), representing an (abstract) individual who places importance on sacred and obedient values, whereas SecEma is our label for an archetype which is high on both meta-values (0.89, 0.97), representing an individual Table 3.8  The four archetypes and their 95% confidence intervals Secular values (sacred-secular) Archetype Label

Lower bound

Mean Upper bound

1 2 3 4

0.00 0.08 0.87 0.87

0.00 0.09 0.89 0.89

SacObe SacEma SecObe SecEma

0.01 0.10 0.92 0.91

Emancipative values (obedient-emancipated) Lower bound

Mean

Upper bound

0.01 0.88 0.14 0.96

0.01 0.90 0.16 0.97

0.02 0.92 0.18 0.98

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who places importance on secular and emancipative values. The other two labels are for the two archetypes which are low on one meta-value and high on the other. SacEma representing an individual who places importance on sacred and emancipative values (0.09, 0.90), and SecObe who places importance on secular and obedient values (0.89, 0.16). As can be seen in the Table, the confidence intervals are narrow and, with one exception, non-overlapping. The exception is the overlap between the upper bound on secular values for archetype 3 (0.92) and the corresponding lower bound for archetype 4 (0.87), and a follow-on test with 84% confidence intervals reveals that the mean values of these two archetypes are not statistically different (p  >  0.05). However, they do clearly differ on emancipative values (mean values of 0.16 versus 0.97), so in conclusion we can regard all four archetypes as distinct. Moreover, being derived from 117 countries and 398 surveys, spanning 1981 to 2021, they provide a common platform for developing country compositions which we can then compare between countries and/or over time. In our metal alloy analogy, these archetypes become the base elements of the composition, much as copper and tin are base elements of bronze, and as such are also fixed constants for subsequent analyses. It is important to be clear on what these confidence intervals mean and not fall into common misconceptions that they are a statement of precision, or of the magnitude of the population mean. Rather, our interpretation is they represent numbers that are not statistically different from the mean estimate at the chosen level of significance [2]. Also, for the rest of this chapter, we focus on the Wave 7 results from the common platform to provide a snapshot of the latest data we have available. Wave 7 covers 83 countries, with examples from all seven continents, and where individuals were surveyed during the period from 2017 to 2021 (median 2018). This snapshot allows us to introduce and illustrate our country compositions and culture coordinates in a straightforward manner, without the complication of time. In the following chapter we then build on these ideas to examine the dynamics of culture values over time.

3.4   Country Compositions (t) A country composition is the set of archetypal proportions for a country at a point in time, t. We make the time t explicit because, unlike the archetypes themselves, we regard compositions as dynamic quantities. Figure 3.2 shows two such compositions, namely for Wave 7 and for two very different countries, Egypt, and Sweden. Egypt was surveyed in 2018 and

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Sweden in 2017. It is immediately evident from the figure that Egypt has a much higher proportion for the archetype representing sacred and obedient values than Sweden (SacObe, 0.64 for Egypt versus 0.11 for Sweden), and Sweden has a correspondingly higher proportions on the archetypes for sacred and emancipative values (SacEma, 0.18 for Egypt versus 0.41 for Sweden) and for secular and emancipative values (SecEma, 0.05 for Egypt versus 0.36 for Sweden). The proportions for archetype representing secular and obedient values are approximately the same for both countries (SecObe, 0.13 for Egypt versus 0.12 for Sweden). Figure  3.2 thus contrasts a country, Egypt, whose values are largely sacred and obedient with another, Sweden, whose values are largely emancipated but in two different forms, namely, sacred emancipated and secular emancipated. Figure 3.3 shows a second example, for the three largest global economies, China, Japan, and the USA. The compositions of the two Asian nations, China, and Japan are markedly different, with, for example, the proportion for secular and emancipative values being higher for Japan compared with China (SecEma, 0.26 for Japan versus 0.17 for China), and that for sacred and obedient values being higher for China compared with SacObe

SacEma

SecObe

SecEma

Egypt

EGY

Sweden

SWE

Fig. 3.2  Wave 7 compositions for Egypt and Sweden SacObe

SacEma

SecObe

SecEma

China

CHN

Japan

JPN

United States

USA

Fig. 3.3  Wave 7 compositions of China, Japan, and the USA

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Japan (SacObe, 0.36 for China versus 0.24 for Japan). Indeed, the composition for Japan is essentially the same as that for the USA, differing only in small amounts (maximum difference of 0.04). These results might not fit popular perceptions but at least for the Welzel meta-values Japan has far more in common with the West than with Asia.

3.5  The Global Matrix for t = Wave 7 Figure 3.4 presents similar bar charts for all 83 Wave 7 countries. The numeric values for these compositions are given in Table 3.9. There are two important observations we can make from Fig. 3.4. First, the global matrix is unified through the fact that every country has all four proportions of the composition to a greater or lesser degree. There is no country composition with a proportion of zero. The minimum values for these proportions are as follows: for the sacred and obedient archetype, 0.11 (Sweden), for the sacred and emancipated archetype, 0.13 (Iraq), for the secular and obedient archetype, 0.09 (Denmark), and for the secular and emancipated archetype, 0.05 (Egypt). The broad implication of this result is whichever of the four archetypes aligns best with our own Welzel values; we can always find a reasonable proportion of individuals aligned with the same archetype in any one of these 83 countries. This result also holds for all 117 countries across all waves, the minimum being 0.03 for the secular and emancipated proportion of Jordan for the Wave 5 survey (2007). Second, visually there is considerable diversity across the compositions of these 83 countries, and while some compositions are highly similar, for example Iceland and Norway, others are very different, for example Nigeria and Switzerland. Comparisons of pairs of countries leads naturally to a discussion of confidence intervals and in Table 3.10 we present some examples of the intervals for the 83 Wave 7 countries. If we express the width of these intervals as a percentage of the individual country proportions, and average this percentage across all 83 countries, it represents 6.0% for SacObe, 6.5% for SacEma, 8.1% for SecObe, and 9.4% for SecEma. Hence, these are relatively narrow confidence intervals, providing a good basis for comparing the similarities and differences between countries.

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SacEma SecObe SecEma

Fig. 3.4  Wave 7 compositions for 83 countries

SacObe

ALBANIA ANDORRA ARGENTINA ARMENIA AUSTRALIA AUSTRIA AZERBAIJAN BANGLADESH BELARUS BOLIVIA BOSNIA BRAZIL BULGARIA CANADA CHILE CHINA COLOMBIA CROATIA CYPRUS CZECHIA DENMARK ECUADOR EGYPT ESTONIA ETHIOPIA FINLAND FRANCE GEORGIA GERMANY GREECE GUATEMALA HONG KONG (CHN) HUNGARY ICELAND INDONESIA IRAN IRAQ ITALY JAPAN JORDAN KAZAKHSTAN KENYA KYRGYZSTAN LEBANON LITHUANIA MACAO (CHN) MALAYSIA MEXICO MONGOLIA MONTENEGRO MYANMAR NETHERLANDS NEW ZEALAND NICARAGUA NIGERIA NORTH MACEDONIA NORWAY PAKISTAN PERU PHILIPPINES POLAND PORTUGAL PUERTO RICO ROMANIA RUSSIA SERBIA SINGAPORE SLOVAKIA SLOVENIA SOUTHKOREA SPAIN SWEDEN SWITZERLAND TAIWAN TAJIKISTAN THAILAND TUNISIA TURKEY UKRAINE UNITED KINGDOM UNITED STATES VIETNAM ZIMBABWE

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Table 3.9  Country compositions for Wave 7 Country

ISO

Albania Andorra Argentina Armenia Australia Austria Azerbaijan Bangladesh Belarus Bolivia Bosnia & Herzegovina Brazil Bulgaria Canada Chile China Colombia Croatia Cyprus Czechia Denmark Ecuador Egypt Estonia Ethiopia Finland France Georgia Germany Greece Guatemala Hong Kong SAR China Hungary Iceland Indonesia Iran Iraq Italy Japan Jordan Kazakhstan

ALB AND ARG ARM AUS AUT AZE BGD BLR BOL BIH BRA BGR CAN CHL CHN COL HRV CYP CZE DNK ECU EGY EST ETH FIN FRA GEO DEU GRC GTM HKG HUN ISL IDN IRN IRQ ITA JPN JOR KAZ

SacObe

SacEma

SecObe

SecEma

0.40 0.20 0.28 0.49 0.21 0.21 0.42 0.54 0.31 0.39 0.38 0.34 0.34 0.17 0.28 0.36 0.38 0.29 0.39 0.22 0.14 0.42 0.64 0.26 0.56 0.19 0.21 0.47 0.18 0.35 0.30 0.24 0.26 0.13 0.51 0.50 0.50 0.29 0.24 0.61 0.39

0.29 0.37 0.26 0.20 0.38 0.38 0.22 0.22 0.17 0.22 0.26 0.29 0.24 0.33 0.23 0.21 0.27 0.29 0.27 0.24 0.49 0.25 0.18 0.28 0.27 0.39 0.36 0.24 0.42 0.32 0.27 0.22 0.29 0.44 0.24 0.23 0.13 0.36 0.30 0.21 0.20

0.17 0.15 0.23 0.21 0.13 0.14 0.22 0.16 0.32 0.24 0.20 0.19 0.25 0.18 0.26 0.26 0.20 0.20 0.19 0.26 0.09 0.21 0.13 0.22 0.11 0.13 0.15 0.18 0.12 0.16 0.22 0.28 0.20 0.10 0.17 0.17 0.27 0.15 0.20 0.12 0.25

0.14 0.28 0.23 0.10 0.27 0.27 0.13 0.08 0.21 0.15 0.15 0.18 0.18 0.32 0.23 0.17 0.15 0.23 0.15 0.28 0.29 0.13 0.05 0.24 0.07 0.28 0.28 0.11 0.28 0.17 0.21 0.26 0.25 0.33 0.09 0.10 0.10 0.19 0.26 0.05 0.15 (continued)

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Table 3.9  (continued) Country

ISO

Kenya Kyrgyzstan Lebanon Lithuania Macao SAR China Malaysia Mexico Mongolia Montenegro Myanmar (Burma) Netherlands New Zealand Nicaragua Nigeria North Macedonia Norway Pakistan Peru Philippines Poland Portugal Puerto Rico Romania Russia Serbia Singapore Slovakia Slovenia South Korea Spain Sweden Switzerland Taiwan Tajikistan Thailand Tunisia Turkey Ukraine United Kingdom United States Vietnam Zimbabwe

KEN KGZ LBN LTU MAC MYS MEX MNG MNE MMR NLD NZL NIC NGA MKD NOR PAK PER PHL POL PRT PRI ROU RUS SRB SGP SVK SVN KOR ESP SWE CHE TWN TJK THA TUN TUR UKR GBR USA VNM ZWE

SacObe

SacEma

SecObe

SecEma

0.39 0.49 0.37 0.28 0.23 0.36 0.32 0.24 0.37 0.49 0.17 0.20 0.40 0.54 0.34 0.13 0.58 0.38 0.41 0.35 0.34 0.34 0.39 0.33 0.31 0.38 0.28 0.20 0.23 0.19 0.11 0.17 0.30 0.41 0.34 0.47 0.47 0.30 0.21 0.25 0.34 0.53

0.25 0.17 0.24 0.25 0.22 0.24 0.22 0.15 0.27 0.17 0.36 0.38 0.22 0.20 0.27 0.45 0.16 0.23 0.24 0.31 0.33 0.41 0.28 0.19 0.24 0.29 0.23 0.37 0.16 0.31 0.41 0.36 0.22 0.16 0.23 0.20 0.25 0.17 0.39 0.34 0.20 0.23

0.21 0.24 0.23 0.24 0.29 0.23 0.26 0.36 0.20 0.24 0.16 0.14 0.23 0.19 0.20 0.10 0.18 0.24 0.21 0.16 0.16 0.11 0.18 0.29 0.25 0.17 0.26 0.16 0.35 0.18 0.12 0.15 0.26 0.31 0.25 0.22 0.17 0.32 0.14 0.16 0.28 0.15

0.15 0.10 0.16 0.23 0.27 0.17 0.20 0.26 0.16 0.10 0.32 0.28 0.14 0.08 0.19 0.33 0.07 0.16 0.14 0.18 0.17 0.14 0.15 0.19 0.21 0.16 0.23 0.28 0.26 0.31 0.36 0.32 0.22 0.12 0.18 0.11 0.11 0.20 0.26 0.25 0.18 0.08

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Table 3.10  Example 84% confidence intervals for Wave 7 compositions SacObe

SacEma

SecObe

SecEma

Country

Lower

Upper

Lower

Upper

Lower

Upper

Lower

Upper

Estonia Vietnam Lithuania … Norway Netherlands Iceland

0.25 0.33 0.27

0.27 0.35 0.29

0.27 0.20 0.24

0.28 0.21 0.26

0.21 0.27 0.24

0.23 0.28 0.25

0.23 0.18 0.22

0.25 0.19 0.23

0.12 0.16 0.12

0.14 0.17 0.14

0.44 0.35 0.43

0.46 0.36 0.45

0.09 0.15 0.09

0.11 0.17 0.10

0.32 0.31 0.32

0.34 0.33 0.35

If we then test for overlapping confidence intervals, we find that of the æ 83 ö 83! = 3403 possible pairs of compositions, only 40 pairs ç ÷= è 2 ø ( 83 - 2 )! 2 ! overlap on all four proportions, whereas we might expect 170 simply by chance at p = 0.05. For completeness, these overlapping pairs are shown in Table 3.11 and include our example of Iceland and Norway above. Interestingly, while some pairs are geographically close to each other (for example, Bosnia & Herzegovina, and Montenegro), some are not (for example, Bulgaria and Thailand). Geographical proximity does not necessarily equal cultural proximity. That said, like our example of Nigeria and Switzerland above, the other 3377 pairings (or 99.2% of all possible pairings) are statistically different (p ≤ 0.05). Therefore, in general, country compositions are distinct. However, it is difficult to comprehend thousands of comparisons across four archetypal proportions, which is why we used multidimensional scaling (MDS) to simplify the analysis. MDS allows us to show the similarities and differences between the compositions in a space with fewer dimensions than four. MDS also uses the distances between all possible pairings of the compositions to identify the best fitting configuration for these compositions, and this overall configuration is therefore potentially a more robust construct than the individual compositions themselves. Indeed, for the set of pooled data with 117 countries and 398 compositions, an excellent MDS model can be obtained with only two dimensions (the fit statistic, “stress,” for two dimensions averages 0.017 across 100 subsamples, with a maximum of 0.023, both of which represent excellent fits, [3]). The resulting set of 398 two-dimensional coordinates then provides a robust “map” of culture over countries and time.

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Table 3.11  Overlapping pairs of 84% confidence intervals for compositionsa Country…

Compared to…

Albania Andorra Andorrab Andorra Andorra Argentina Australia Australia Australia Austria Austria Bangladesh Bulgaria Bosnia & Herzegovina Bosnia & Herzegovina Bosnia & Herzegovina Bosnia & Herzegovina Belarus Bolivia Brazil Switzerland Chile Chile Colombia Colombia Cyprus Cyprus Ecuador Finland France Greece Greece Hong Kong SAR China Indonesia Iceland Kyrgyzstan South Korea Mexico Poland Romania

Romania Austria France New Zealand Slovenia Lithuania Austria United Kingdom New Zealand United Kingdom New Zealand Zimbabwe Thailand Colombia Cyprus Kenya Montenegro Ukraine Peru North Macedonia Netherlands Slovakia Taiwan Cyprus Montenegro Montenegro Romania Philippines New Zealand Slovenia Poland Portugal Macao SAR China Iran Norway Myanmar (Burma) Mongolia Serbia Portugal Singapore

Cases where the confidence intervals overlap on all four proportions of the composition Pairs in bold text also overlap in the MDS results, see subsequent discussion

a

b

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3.6   Cultural Map Coordinates Figure 3.5 illustrates the 83 Wave 7 countries by plotting the MDS coordinates that result from the pooled analysis. The full map based on 117 countries and 398 compositions will be discussed in the next chapter. The associated data and labels for Fig. 3.5 are given in Table 3.12. Figure 3.5 identifies the nine exterior countries (the convex hull of the Wave 7 countries) by their ISO code and year, similarly the country closest to the centre of the coordinate system (Malaysia for Wave 7), and the other countries simply by their ISO codes. We also use the biplotting method to overlay arrows showing the correlation between the original compositional data and the two dimensions of the map itself (see Chap. 2 for more details on this point). There are two important observations we can make about the MDS dimensions shown in Fig. 3.5. First, Dimension One is well aligned with the arrows for SacObe to the left and SecEma to the right, so essentially contrasts the proportions for these two archetypes in the composition. For example, at the left, the composition for Egypt has a proportion of 0.64 for SacObe and a proportion of 0.05 for SecEma, whereas on the right, the composition for Sweden has a proportion of 0.11 for SacObe and a proportion of 0.36 for SecEma. This is the most extreme contrast we observe on these two archetypal proportions as Egypt has the highest proportion for SacObe in the Wave 7 data and Sweden the highest proportion for SecEma. Dimension Two then captures the secondary contrast between SecObe and SacEma. This can be seen if we take the two extreme compositions on this dimension as examples, namely Mongolia and Denmark. Mongolia has values of 0.36 for SecObe and 0.15 for SacEma, whereas Denmark has the opposite profile of 0.09 and 0.49, reflecting the contrast between a former satellite state of the Soviet Union, with a continuing emphasis on secular obedience, and a Scandinavian nation whose history emphasizes freedom and the Protestant religion. Second, visually there are much greater differences between compositions on Dimension One (D1) than Dimension Two (D2)—that is, the “cloud” of points shown on the map has the overall shape of an ellipsoid which is relatively wider on D1 and relatively narrower on D2. In that sense D1 is more important than D2, an observation which is confirmed by analysis since D1 accounts for 80% of the variance in the inter-composition distances, whereas D2 accounts for only 20% (statistics derived from regressions of one- and two-dimensional multidimensional scaling solutions on the observed inter-composition distances, using the pooled data

−2

−1

0

−2

EG_2018

SacObe

JO

BD

−1

ZW

NG

ET_2020

PK

ID

IR

AM

MM KG

GE TR

TN

IQ_2018

TH BG

RU VN

BR

0 D1

PR_2018

GR PL PT

TW

HR

CL SK LT AR

US

HU

EE JP

DE

ES FR SI AD AT GB AU NZFI

CZ

HK MO

MN_2020 KR_2018

SacEma

IT

GT

RS

BY UA

MX

MY_2018 MK

CN KZ BO PE

LB KE BA CO CY ME RO SG AL

NI

EC PH

AZ

TJ

Fig. 3.5  MDS coordinates of 83 Wave 7 Countries

D2

1

2

SecObe

CA

NO

1

DK_2017

NL CH

IS_2017

SE_2017

SecEma

2

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Table 3.12  Countries on the Wave 7 Convex Hull Label

Country

Year

SacObe

SacEma

SecObe

SecEma

D1

D2

DK_2017 EG_2018 ET_2020 IQ_2018 IS_2017 KR_2018 MN_2020 PR_2018 SE_2017

Denmark Egypt Ethiopia Iraq Iceland South Korea Mongolia Puerto Rico Sweden

2017 2018 2020 2018 2017 2018 2020 2018 2017

0.14 0.64 0.56 0.50 0.13 0.23 0.24 0.34 0.11

0.49 0.18 0.27 0.13 0.44 0.16 0.15 0.41 0.41

0.09 0.13 0.11 0.27 0.10 0.35 0.36 0.11 0.12

0.29 0.05 0.07 0.10 0.33 0.26 0.26 0.14 0.36

1.10 -1.45 -1.06 -0.71 1.24 0.60 0.56 -0.09 1.41

-1.14 -0.18 -0.57 0.59 -0.99 0.71 0.76 -0.90 -0.77

Table 3.13  Example 84% confidence intervals for Wave 7 MDS coordinates Dimension 1

Dimension 2

Country

Lower

Upper

Lower

Upper

Azerbaijan Lebanon Peru … Sweden Iceland Egypt

−0.38 −0.13 −0.15

−0.34 −0.08 −0.10

0.05 0.01 0.10

0.10 0.06 0.16

1.37 1.18 −1.51

1.47 1.29 −1.39

−0.81 −1.04 −0.23

−0.73 −0.95 −0.15

of 398 compositions). Country compositions therefore differ most in the proportions for the two archetypes which represent the biggest contrast in individual values, namely SacObe versus SecEma. Turning now to the MDS coordinates for individual countries, Table 3.13 shows examples of the confidence intervals in the same format as shown earlier for country compositions. Averaged across all 83 countries, the width of these intervals is 0.07 coordinate units for D1 and 0.06 for D2, which are again relatively narrow confidence intervals. If we test for overlapping confidence intervals, then we find for the 3403 possible pairings only 26 pairs ( 0.05). Hence the overall movement looks more like a linear trend, especially as Australia’s economic, political, and social landscape is relatively benign during this period [12].

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SecObe

2

1

D2

0

SacObe

SecEma 3

5 6

7

−1

−2

SacEma

The coordinates of Waves 5, 6 are not significantly different @ p = .05

−2

−1

0

1

2

D1

Fig. 4.15  Australia’s dynamics

Table 4.19  Australia’s composition and coordinates Wave

Survey year

3 5 6 7

1995 2005 2012 2018

SacObe

SacEma

SecObe

SecEma

D1

D2

0.27 0.25 0.25 0.21

0.34 0.35 0.37 0.38

0.16 0.15 0.15 0.13

0.23 0.25 0.23 0.27

0.40 0.53 0.47 0.71

−0.47 −0.53 −0.56 −0.66

4.7   Key Takeaways The key takeaways from this chapter are summarized in Table 4.20, with the seventh summarizing our overall conclusion from this chapter, namely there is no single trend in these results. In Chap. 3 we looked at the global matrix from a static perspective, whilst here in this chapter we examined it from a dynamic perspective. In the next chapter we bring these two perspectives together to ask what we have learned about both our compositional approach to understanding the heterogeneity in cultural values, and about the evolution of the global matrix, where we also identify the many ways in which the world as a whole is changing.

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Table 4.20  Key Takeaways from the analysis of 92 countries Number

Takeaway

Support

1

The cultural map has face validity

2

Culture is dynamic

3

For many countries the magnitude of change is substantial

4

There is a two-speed world

5

The cultural values of the four major countries have different trajectories

6

There are several other examples of different trends on the cultural map

7

The global matrix is evolving in complex, time varying and different ways—there is no single trend in country values

Differentiating between countries with high proportions of SacObe to the west (e.g., Jordan 2007) and countries with high proportions of SecEma to the east (e.g., Sweden 2006). And between countries with high proportions of SecObe to the north (e.g., Estonia 1999) and countries with high proportions of SacEma to the south (e.g., Denmark 2017). For most countries, the compositions and coordinates are statistically different from wave to wave of their E&WVS surveys. The median change index of 11% of the maximum possible change represents a noticeable shift in the country’s cultural composition (e.g., New Zealand). 46 countries experienced a change greater than or equal to this amount. The magnitude of cultural change varies considerably from countries that change little over long time spans (e.g., China) to those that change rapidly over short time spans (e.g., Ethiopia).  •  China: small change from Secular to Obedient   •  Japan: large change from Secular to Emancipated   •  India: small change, remains Sacred   •  USA: large change from Sacred to Emancipated For example:  • Bangladesh moves north  • Ethiopia moves west  • Greece moves west-southwest  • Norway moves south-southeast Takeaways 2 to 6 above.

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References 1.  ‘History of the People’s Republic of China’, Wikipedia. Sep. 24, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia. org/w/index.php?title=Histor y_of_the_People%27s_Republic_of_ China&oldid=1112094006#Xi_Jinping_and_the_fifth_generation_(2012%E 2%80%93present) 2. ‘History of India (1947–present)’, Wikipedia. Sep. 25, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php? title=History_of_India_(1947%E2%80%93present)&oldid=1112209703 3.  ‘History of Japan’, Wikipedia. Sep. 25, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_Japan&oldid=1112332497#Heisei_period_(1989%E2%80%932019) 4. ‘History of the United States’, Wikipedia. Sep. 25, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title= History_of_the_United_States&oldid=1112214075#Great_Recession 5. ‘History of Ethiopia’, Wikipedia. Sep. 20, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_Ethiopia&oldid=1111342628 6. ‘History of South Africa’, Wikipedia. Sep. 22, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_South_Africa&oldid=1111758097 7. ‘History of Bangladesh’, Wikipedia. Sep. 22, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_Bangladesh&oldid=1111763806 8. ‘Religion in Germany’, Wikipedia. Sep. 22, 2022. Accessed: Sep. 25, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Religion _in_Germany&oldid=1111687994 9.  ‘History of Germany’, Wikipedia. Sep. 14, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title= Histor y_of_Germany&oldid=1110313106#Federal_Republic_of_ Germany,_1990%E2%80%93present 10. ‘History of Greece’, Wikipedia. Sep. 18, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_Greece&oldid=1110950820 11. ‘Economic history of Brazil’, Wikipedia. Sep. 25, 2022. Accessed: Sep. 25, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Economic_ history_of_Brazil&oldid=1112212012#Post-­R eal_Plan_economy_(199 4%E2%80%932010) 12. ‘History of Australia’, Wikipedia. Sep. 24, 2022. Accessed: Sep. 26, 2022. [Online]. Available: https://en.wikipedia.org/w/index.php?title=History_ of_Australia&oldid=1112087790

CHAPTER 5

Multiple Trends in a Two-Speed World

Abstract  In this final chapter we summarize the key steps in our new approach, before discussing how archetypal compositions help us understand the heterogeneity in cultural values between and within countries, and over time. We then focus on the three key results from our analyses of cultural change. First, we show how the compositional approach reveals that the apparent convergence between the values of the USA and Japan is likely driven by different processes of cultural change. Second, we discuss China, India, and 12 other countries whose cultures changed little over several decades. Third, we identify the multiple trends in our results for the remaining 76 countries. As noted by Welzel, emancipation is the major trend, but the compositional approach reveals that it comes in at least two distinct forms, and also that many countries are evolving in opposing directions to these. Finally, we present our latest estimate of how we see the world through a compositional and geographic perspective, before closing with some thoughts on the nature of the global matrix of cultural values. Keywords  Multiple trends • Compositional perspective • Global matrix

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/978-­3-­031-­24482-­7_5.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. Midgley et al., A New Theory of Cultural Archetypes, https://doi.org/10.1007/978-3-031-24482-7_5

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5.1   Our Objectives and Methods We start by briefly summarizing the previous four chapters, highlighting the key steps in our approach to understanding heterogeneity in cultural values across the globe and over time. In Chap. 1 we introduced the core ideas of this approach—the theory of archetypes and archetypal analysis—and set out two objectives for our current research. First to understand the unity and diversity of these values through a global matrix of country compositions, and second to show how this global matrix evolves over time. In Chap. 2 we provided the methodological details behind archetypal analysis and illustrated how we applied these ideas to the E&WVS survey data through subsampling. In doing so, we argued that geometry—the archetypal spanning hull—is the better way to choose the appropriate number of archetypes as other metrics may ignore informative examples of heterogeneity. In Chap. 3 we reported on our experiments with different subsample sizes and also with adjusting the probability of selection for subgroup response rates for those countries where E&WVS calibration weights are available. Here we concluded that the trade-off between coverage of the globe and reducing response biases favours coverage of the globe. The differences between adjusting and not adjusting for these biases appear to be small, but the latter allows us to include several major countries where calibration weights are currently not available. We then introduced the two-dimensional MDS map of global culture which helps facilitate the comparison of country compositions. We also showed that the archetypes, country compositions, and map coordinates are robust constructs with relatively narrow confidence limits, and then examined the global matrix we derived from the latest E&WVS data, a snapshot of 83 Wave 7 countries. Finally in Chap. 4, we analysed those countries where two or more waves of E&WVS surveys were available, looking at trends over time both at the individual country level and by classifying countries according to the magnitude of their movement on the cultural map and the length of time between their earliest and latest survey. Chapter 4 thus extends our perspective to multiple time periods and provides insights into cultural change based on a common platform of 398 country-wave compositions and map coordinates for 92 countries, which spans the years 1981 to 2021.

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5.2  Archetypal Compositions Represent Heterogeneity Well Figure 5.1 shows the cultural map based on these 398 country-wave compositions. The country compositions, built on the four distinct archetypes shown in Table 5.1, provide sharp contrasts between countries and over time. This can be seen from the overall distribution of the data into the four quadrants of this map, where each quadrant implies the relative importance of some archetypal profiles over the others, as detailed in Table 5.2. The maximal contrasts between the four countries labelled on the exterior hull of the data in Fig. 5.1 reinforce this conclusion. For Dimension One of the map, Jordan (2007) is profoundly different to Sweden (2006) as the former’s composition more emphasizes sacred obedience and the latter more secular emancipation. And for Dimension Two, Denmark (2017) is profoundly different to Estonia (1999) as the former’s

SecObe 2

EE_1999

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SacObe

SecEma

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SE_2006 JO_2007

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SacEma −2

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Fig. 5.1  The cultural map 1981 to 2021

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Table 5.1  The four archetypes: Base elements of a country composition… Archetype

Value profile

SacObe SacEma SecObe SecEma

Sacred & Obedient Sacred & Emancipated Secular & Obedient Secular & Emancipated

Table 5.2  Quadrant definitions Quadrant

The composition is relatively HIGHER in…a

The composition is relatively LOWER in…a

Secular Emancipated Sacred Obedient

SecObe & SecEma SacEma & SecEma SacObe & SacEma SacObe & SecObe

SacObe & SacEma SacObe & SecObe SecObe & SecEma SacEma & SecEma

Compared to the mean composition of SacObe = 0.35, SacEma = 0.25, SecObe = 0.22, SecEma = 0.18

a

composition more emphasizes sacred emancipation and the latter more secular obedience. Between-country heterogeneity is therefore well captured through the archetypes and compositions. Yet even in these four exterior countries we do not see homogeneity. Table 5.3 demonstrates that none of their compositions are unary, all have at least some proportion of the four basic elements. For example, while Jordan (2007) has a dominant proportion of 0.70 for SacObe that still implies the other 0.30 of its composition reflects different value profiles, and so even these extreme examples display considerable within-country heterogeneity. Table  5.3 also shows two major countries, France (2008) and Japan (2005), as examples of the opposite—interior—case, country-­ waves whose composition is almost equally composed of each of the four elements. Note that a composition with a proportion of 0.25 for each of the four elements would be, in one sense, maximally diverse. So, France (2008) and Japan (2005), and several other country-waves not discussed here, are close to maximally diverse. And of course, there are 392 other country-waves inside the hull with different compositions to these, represented by the data points on Fig. 5.1. Thus, archetypal compositions capture both between and within-country heterogeneity well, and our analyses show that both forms of heterogeneity are of considerable magnitude when we consider the full span of the E&WVS data for 117 countries, 398 country-wave coordinates, and the period from 1981 to 2021.

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Table 5.3  Examples of within and between country heterogeneity Country

Year

SacObe

SacEma

SecObe

SecEma

Jordan Sweden Denmark Estonia France Japan

2007 2006 2017 1999 2008 2005

0.70 0.11 0.14 0.26 0.25 0.23

0.21 0.32 0.49 0.12 0.26 0.26

0.07 0.18 0.09 0.39 0.23 0.24

0.03 0.40 0.29 0.23 0.26 0.26

Table 5.4  Compositions are more subtle than averages Country

Year

Denmark 2017 Sweden 2017

Secular values Emancipative values SacObe SacEma SecObe SecEma 0.38 0.46

0.74 0.74

0.14 0.11

0.49 0.41

0.09 0.12

0.29 0.36

The existence of within and between country heterogeneity is well known, the challenge has been how best to represent this heterogeneity. A challenge we believe we have met through the vehicle of archetypes and compositions, which provide a representation that is simple, yet insightful. Four element compositions are simple to comprehend and yet as shown above and in the previous chapters, provide considerable insight into each country at different points in time. This insight is also more subtle than that provided by other metrics, such as country averages, a conclusion which is best illustrated by looking at countries that are, on the surface, highly similar. Here we choose Denmark and Sweden, countries which, at least to those living outside Scandinavia, might be considered highly similar in their secular and emancipative values. The 2017 compositions for these two countries are shown in Table 5.4. The table also includes the country average values for the two Welzel meta-traits (population estimates from the same 100 subsamples as used for the compositions). If we look at the country averages, we will say that Sweden is slightly more secular than Denmark but identical in terms of emancipative values. Yet if we look at the compositions we see a subtlety, in that the balance between SacEma and SecEma is different between the two countries, such that Denmark’s average is more driven by the sacred than the secular form of emancipation (0.49 versus 0.29) and Sweden’s is more balanced between the two forms (0.41 versus 0.36). The two countries are in fact noticeably different. The compositional approach thus reveals that it is the configurations of the two meta-values in the population that is of

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Table 5.5  Examples of different forms of “Emancipation” Country

Year

D1

D2

Italy Netherlands Centre

2018 2017

0.23 1.01

−0.54 −0.46

SacObe

SacEma

SecObe

SecEma

0.29 0.17 0.35

0.36 0.36 0.25

0.15 0.16 0.22

0.19 0.32 0.18

importance, not just each meta-value in isolation. There is also a mindset difference between averages and compositions, in that averages may lead to stereotypes and a false assumption of relative homogeneity in country values, whereas compositions explicitly show this is not the case at all. Finally, it is important to underline what the quadrants of our cultural map mean from the compositional perspective, which is the relative emphasis within the basic elements of the composition rather than homogeneity, since no nation in our data is homogenous. Table 5.5 provides two informative examples from the Emancipated quadrant, Italy which emphasizes Dimension 2 of the map and the Netherlands that emphasizes Dimension 1. Both are relatively emancipated in the sense their SacEma and SecEma proportions are greater than those for the centre of the map. However, Italy has a markedly lower proportion of SecEma than the Netherlands (0.19 versus 0.32), whereas both have similar proportions for SacEma. Hence Italy displays less of that particular form of emancipation connected with defiance, disbelief, relativism, and scepticism (the components of secular values) than the Netherlands, again demonstrating the importance of configurations of meta-values rather than each in isolation. Similar examples and conclusions can be drawn from the other three quadrants of our map.

5.3   Multiple Trends in the Global Matrix We start by examining the trends of the four major countries, whose cultural change compasses are shown in Fig. 5.2. Over the lengthy observed periods for these countries, the USA and Japan converge to the Emancipated quadrant, albeit with totally different trajectories, whereas China and India change little. Table 5.6 provides further details on the convergence of the USA and Japan and suggests that the processes of cultural change for these two countries are different. The earliest survey for the USA places it in the Sacred quadrant but over the 27 years we observe there is a 0.13 decrease in the proportion for SacObe and a corresponding 0.11 increase in the

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Fig. 5.2  Cultural change compasses for China, India, Japan, and the USA

proportion for SecEma, with the other elements of the composition remaining almost the same. This corresponds to an east-northeast trajectory from Sacred to Emancipated, albeit one close to cardinal east (86°). In contrast, Japan starts in the Secular quadrant and over 29 years its composition sees a decrease of 0.07 in the proportion for SecObe and an increase of 0.08 in the proportion for SacEma, again with the other elements remaining similar. This approximately corresponds to a south-­ southeast trajectory from Secular to Emancipated (165°). So, while the latest coordinates and compositions of both countries are similar, the USA has undergone a process of secular emancipation to reach this state and

27 29

E SSE

19 13

Change Index (%) Sacred Secular

Earliest Quadrant

Latest Coordinates and Compositions Country Year D1 USA 2017 0.52 Japan 2019 0.58

USA Japan

Time Span (years)

Trend Country

SacObe

D2 −0.46 −0.18 SacObe 0.25 0.24

Emancipated −0.13 Emancipated −0.02

Latest Quadrant 0.01 −0.07

SacEma SecObe 0.34 0.16 0.30 0.20

0.01 0.08

SacEma SecObe

SecEma 0.25 0.26

0.11 0.01

4.23 1.60

SecEma % World Population

Δ change in the country’s composition over the time span (latest–earliest)

Table 5.6  Converging trends for USA and Japan, but different processes of cultural change

15.67 3.68

% World GDP (PPP)

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Japan one of sacred emancipation. The drivers of these changes are thus likely to be uniquely different. We contend that the compositional approach makes these different processes of cultural change clear, whereas simple averages or an aggregate concept of emancipation would obscure them. Turning to the other two countries in Fig. 5.2, China remains relatively fixed in the Obedient quadrant and India in the Sacred quadrant over similar lengths of time to the USA and Japan. So, Fig. 5.2 suggests there is, in a sense, a two-speed world. Further analysis of the “long time span, small change” cell of the matrix in Chap. 4 (Table 4.8) reveals 14 countries that show little change, as we show in Table 5.7. These include several other large population countries which, like China and India, show little change over two or more decades, namely Indonesia, Nigeria, Philippines, and Russia. Then there is a second group of countries which is somewhat of a mixed bag. We have two countries, Belarus, and Peru, which also change little over similar time spans to the above, but then six countries where the time spans are possibly too short to reveal any changes. All 14 countries have change indices of less than 5% but they account for 47.5% of the Table 5.7  14 Countries with Little Changea Country China India Indonesia Nigeria Philippines Russia Belarus Cyprus Ecuador Ghana Iraq Kazakhstan Luxembourg Peru Totals

Time span (years)

Change index (%)

% World population

% World GDP (PPP)

28 22 17 28 23 27 28 13 5 5 5 7 9 22

3 4 3 2 3 2 3 1 4 2 1 4 3 2

18.35 17.71 3.51 2.69 1.41 1.85 0.12 0.02 0.23 0.40 0.52 0.24 0.01 0.42

18.61 6.96 2.43 0.79 0.69 3.26 0.14 0.03 0.14 0.13 0.29 0.37 0.06 0.32

47.48

34.22

Countries whose Change Index ranges from 1 to 4% compared to the 92-country mean of 14% and the maximum observed value of 45% (Norway, Chap. 4) a

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world population in 2021 and 34.2% of world GDP (PPP). Thus, close to half of our 92 country “world” is essentially static. At this point we have identified three “trends” on the map, (1) the USA to the east, (2) Japan to the south-southeast and then (3) 14 countries which are essentially static. But what about the other 76 countries in our world which also undergo larger magnitude changes like the USA and Japan? Remarkably, applying our eight broad compass heading categories from Chap. 4, we find each category contains at least one of the 76 countries, as we will illustrate through eight examples, one for each heading category. Here we start with the four countries displayed in Fig. 5.3 and which have “easterly” headings. The compass headings of these countries are ordered clockwise and the countries themselves selected as those with headings closest to the center line of their respective category (north-­ northeast, east-northeast, east-southeast, and south-southeast). Table 5.8 provides supporting details for these four countries and the four others to be discussed subsequently. At the top left of the Fig.  5.3, Rwanda moves from the Sacred to Obedient quadrant in a north-northeast direction, and in Table 5.8 we see this is associated with an increase of the proportion of SecObe in its composition and a decrease in the proportions of the two sacred elements. The proportion for SecEma also increases but to a much smaller extent than SecObe. Rwanda’s cultural change from 2007 to 2012 is therefore primarily one of a single element, SecObe, increasing with this increase drawn from sacred values in general. At the top right of Fig. 5.3, Chile moves from the Sacred to Secular quadrant in an east-northeast direction, which is associated with an increase in the proportions for both SecObe and SecEma, and a substantial decrease in the proportion of SacObe. Chile’s cultural change from 1990 to 2018 is therefore one of a general increase in secular values drawn from a single element of its composition. At the bottom left of Fig.  5.3, Northern Ireland moves from the Obedient to Secular quadrant in an east-southeast direction, associated with similar increases in the proportions for both SacEma and SecEma and, like Chile, a substantial decrease in the proportion for the traditional, SacObe element. However, unlike Chile, Northern Ireland’s cultural change from 1981 to 1999 is one of a general increase in both the emancipative elements. Note a linear extrapolation on Northern Ireland’s east-­ southeast trajectory suggests that by 2022 it may have moved to the

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Nor the rn I 1 re

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Fig. 5.3  Compasses for Rwanda, Chile, Northern Ireland, and Germany

Emancipated quadrant, a proposition that can be tested if and when another E&WVS survey becomes available. Finally, at the bottom-right of Fig.  5.3, Germany moves from the Secular to Emancipated quadrant in a south-southeast direction, associated with the greatest increase in a proportion we see in Table 5.8, here for SacEma, and substantial decreases in the proportions for both SacObe and SecObe. Germany’s cultural change from 1981 to 2018 is therefore one of a dramatic increase in a single element representing the joint configuration of sacred and emancipative values, drawn from a general decrease in obedient values.

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Table 5.8  Changes in the compositions of the eight example countries with easterly and westerly headings Δ change in the country’s composition over the time span (latest–earliest) Trend Representative country Easterly headings NNE Rwanda ENE Chile ESE Northern Ireland SSE Germany Westerly headings SSW Croatia WSW Bulgaria WNW Egypt NNW Bangladesh

Earliest quadrant

Latest quadrant

SacObe

SacEma SecObe SecEma

Sacred Sacred Obedient

Obedient Secular Secular

−0.06 −0.14 −0.11

−0.05 −0.01 0.05

0.09 0.06 −0.01

0.03 0.10 0.07

Secular

Emancipated

−0.10

0.22

−0.15

0.03

Secular Secular Sacred Sacred

Emancipated Secular Sacred Sacred

0.01 0.06 0.06 0.04

0.06 0.03 −0.05 −0.11

−0.04 −0.03 0.01 0.07

−0.04 −0.06 −0.01 0.01

Switching to the second set of examples, those for westerly headings (south-southwest, west-southwest, west-northwest, and north-­northwest), these are shown in Fig. 5.4, and paint a similarly rich and diverse picture of cultural change. At the top left of Fig.  5.4, Croatia moves from the Secular to Emancipated quadrant in a south-southwest direction, associated with, like Germany, an increase in the proportion for SacEma, albeit not as substantial. However, unlike Germany this is accompanied by a decrease in the proportions for both secular values, SecObe and SecEma rather than just SecObe as for Germany. Croatia’s cultural change from 1996 to 2017 is therefore one of an increase in the joint configuration of sacred and emancipated values, drawn from a general decrease in secular values. We might also extrapolate Croatia’s trajectory to enter the Sacred quadrant in time, but as we see no example of a country leaving the Emancipated quadrant in our four decades of data, to us this is unlikely. At the top right of Fig. 5.4, Bulgaria stays within the Secular quadrant but moves in a west-southwest direction. Bulgaria is also sufficiently close to the centre of the map that its trajectory may, in time, pass through the Obedient quadrant and on to the Sacred quadrant, propositions that also await future E&WVS surveys. For the moment, this movement is indeed

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Fig. 5.4  Compasses for Croatia, Bulgaria, Egypt, and Bangladesh

associated with an increase in the proportions of both sacred elements of Bulgaria’s composition, and a corresponding decrease in the proportions of both secular elements. Bulgaria’s cultural change from 1991 to 2017 is therefore a general switch from secular to sacred values. At the bottom left of Fig. 5.4, Egypt stays within the Sacred quadrant and while we classify its trajectory into our west-northwest category, it is the only country of the 76 we find in this category and its direction of movement is actually adjacent to north-west (314°). Similarly, at the bottom right of Fig. 5.4, Bangladesh also stays within the Sacred quadrant, is the only country moving in the north-northwest direction, and its

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direction of movement is almost north (358°). What can be said about these two unusual trends? The change in Egypt’s composition is almost entirely an increase in the proportion of SacObe and a corresponding decrease in the proportion of SacEma. Egypt’s cultural change from 2001 to 2018 is therefore a simple exchange between the two sacred elements of its composition. The change in Bangladesh’s composition also involves a (more substantial) decrease in the proportion of SacEma, but in this case a corresponding increase in the proportions for SacObe and SecObe. Bangladesh’s cultural change from 1996 to 2018 is therefore a decrease in a single sacred element translating to a general increase in obedience. In Table  5.9 we summarize the key elements of these eight change processes. As can be seen all eight are inherently different from each other. And while some of these countries converge to the same quadrant over time, for example Chile and Northern Ireland, similarly Germany and Croatia, the processes by which they arrive at that end state are also different, just as we saw earlier for the USA and Japan. The compositional approach reveals considerable diversity in direction and processes of cultural change. But which of these trends are important from a global perspective? This is the question we seek to answer in the next section.

Table 5.9  Summary of the eight cultural change processes around the compass Change in the country’s composition Country

Trend Earliest quadrant

Decreased proportions of…

Increased proportions of…

Rwanda Chile Northern Ireland Germany Croatia Bulgaria Egypt Bangladesh

NNE Sacred ENE Sacred ESE Obedient

SacObe, SacEma SacObe SacObe

SecObe Obedient SecObe, SecEma Secular SacEma, SecEma Secular

SSE SSW WSW NW N

SacObe, SecObe SecObe, SecEma SecObe, SecEma SacEma SacEma

SacEma SacEma SacObe, SacEma SacObe SacObe, SecObe

Secular Secular Secular Sacred Sacred

Latest quadrant

Emancipated Emancipated Secular Sacred Sacred

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5.4  How Did the “World” Change? It is important to restate that our “world” is not the actual world. The picture of global change we present above is based on the earliest and latest surveys for 92 countries, that is 184 observations from the 398 country-­waves of the common platform of compositions and coordinates. At the individual country level these estimates of change are valid but when we aggregate them into a “world” these estimates are not necessarily aligned in time, and neither do they present a complete picture of the cultural evolution of the actual world since the countries that participate in the E&WVS surveys vary from wave to wave. That said, this 92 country aggregation is the broadest available picture of global change and so is informative despite its limitations. So how does this “world” change? Table 5.10 summarizes the various trends from above, showing their importance in terms of the proportion of world population and GDP (PPP), where both these statistics are based on the actual world in 2021, as discussed in Chap. 4. Table 5.10 also provides the key takeaways from this chapter. The first row of the table shows those countries that are not changing, accounting for 47.5% of world population and 34.2% of world GDP. If we then focus on the countries which are changing, and if we set the USA aside for one moment, we see that the two emancipative trends east-­ southeast (ESE) and south-southeast (SSE) are the most important, particularly for GDP. These two trends are roughly equal in population at 8% of the world for ESE and 10% for SSE, but the SSE trend accounts for almost twice the proportion of GDP compared to the ESE trend, that is 19.6% versus 11.4%. In terms of the two emancipative elements of the country’s composition, while both are increasing their proportions over time, the SSE trend has larger increases in the proportion of SacEma than of SecEma, as for Germany and Japan, whereas the ESE trend has more equal increases of the two, as for Northern Ireland or, say, Brazil as the largest country with the ESE trend. The compositional approach thus makes a clear distinction between these two forms of emancipation and identifies the SSE trend towards the joint configuration of sacred and emancipative values, SacEma, as the more important in terms of GDP. Since this is the largest trend we identify, it is worth briefly discussing what a large proportion of SacEma in the composition implies. The Sac part of this archetype represents those who do not defy authority, hold religious beliefs of some form, respect social norms, and trust the

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Table 5.10  Key takeaways: Multiple trends in a two-speed world Trend

Number of countries

Countries

% World population 2021

% World GDP 2021a

Static

14

Belarus, China, Cyprus, Ecuador, Ghana, India, Indonesia, Iraq, Kazakhstan, Luxembourg, Nigeria, Peru, Philippines, Russia

47.48

34.22

Iran, Rwanda, Turkey 2.33 Algeria, Chile, Guatemala, Malaysia, Pakistan, 6.41 South Korea, Vietnam, Zimbabwe E 1 USA 4.23 Emancipative trends ESE 20 Australia, Bosnia & Herzegovina, Brazil, 8.28 Canada, Hong Kong, Jordan, Malta, Mexico, Northern Ireland, Poland, Puerto Rico, Serbia, Singapore, South Africa, Spain, Sweden, Switzerland, Taiwan, Tunisia, Uruguay SSE 25 Argentina, Austria, Colombia, Czechia, 8.24 Denmark, France, Germany, Hungary, Iceland, Ireland, Italy, Lithuania, Moldova, Morocco, Netherlands, New Zealand, North Macedonia, Norway, Portugal, Slovakia, Slovenia, Thailand, Ukraine, United Kingdom, Venezuela SSE 1 Japan 1.60 Sub-totals secular and emancipative trends 31.10 Sacred trends SSW 13 Albania, Armenia, Azerbaijan, Belgium, 0.92 Croatia, Estonia, Finland, Georgia, Latvia, Lebanon, Montenegro, Romania, Trinidad & Tobago WSW 5 Andorra, Bulgaria, Ethiopia, Greece, 1.80 Kyrgyzstan Obedient trends NW 1 Egypt 1.33 N 1 Bangladesh 2.11 Sub-totals sacred and obedient trends 6.16 Totals 92 84.74

1.79 4.89

Secular trends NNE 3 ENE 8

15.67 11.36

15.95

3.68 53.33 1.60

0.59

0.95 0.75 3.89 91.44

At the time of writing, 2021 estimates of GDP (PPP) were not available for Andorra, Iran, Northern Ireland, Puerto Rico, Taiwan, and Venezuela, so the numbers for the trends containing these countries are underestimates a

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country’s institutions. The Ema part represents those who are autonomous in their thinking, and believe in equality, the liberty of others to choose their lifestyle, and having a voice in political decisions. On the surface, SacEma might therefore reflect people who hold two conflicting sets of values. However, whether this is a conflict or not depends on the nature of the social and institutional context of the country. For example, Germany in 2018 is a highly developed, and liberal democracy, where the majority of citizens believe in religion of some form (Chap. 4). Hence there is no inherent conflict in 0.42 of Germany’s 2018 composition representing this joint set of values. Returning to the USA, this is an interesting and unusual case because the USA has a different trajectory to most other Western countries. As noted above, there is a 0.13 decrease in the proportion for SacObe and a corresponding 0.11 increase in the proportion for SecEma over time, with the other two elements remaining roughly constant. This gives the USA’s emancipating trend a distinctly secular flavour compared to countries following the ESE trend, and even more so to those following the SSE trend, both of which contain many other Western countries, as well as Japan. The compositional approach thus makes a distinction between the USA and the rest of the developed world. Finally, there are countries with secular, sacred or obedient trends which are relatively less important in terms of population or GDP but interesting nonetheless in that these are both different and also often contrary to the two major trends discussed above. Collectively 14.9% of the world’s population and 10.6% of the world’s GDP are changing in these opposing directions.

5.5  A Snapshot of the Current World Figure 5.5 put the latest estimates we have for our 92 countries onto a geographical map of the world. Countries are colour coded according to the quadrant of the cultural map in which their latest estimate places them,1 which reflects the relative emphasis of the four elements of their compositions. Countries which are not in the set of 92 are coloured white for “unknown.” 1  76 of the 92 estimates are within the last 5 years (2016–2021), 82 within the last 13 years (2008–2021) and only Ireland, Northern Ireland and Venezuela are earlier at 1999,1999 and 2000 respectively.

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Fig. 5.5  A geographical map of 92 country compositions

Figure 5.5 puts a fresh and final perspective on our results by showing the geographical dispersion of the four types of composition. Overall, the countries in North America, Western Europe and Oceania are emancipated, those in South Asia and Middle East are sacred, China is obedient, Russia and parts of Eastern Europe are secular, whereas Latin America includes a mixture of all four types.

5.6  Concluding Thoughts We hope we have demonstrated that an approach based on archetypes and archetypal compositions is valuable for understanding the heterogeneity of secular and emancipative values between and within countries, and for identifying the trends in the evolution of these values over time. Our results reveal that the global matrix of country compositions has unity in that all archetypes are represented in all countries, but also diversity in that the proportions of the four elements vary over countries and evolve over time. An evolution which has two speeds, in that some countries change radically over a decade, while others show little change over several decades. There is also diversity in the direction in which these cultural compositions are evolving, and, while there are two major trends towards emancipation, one balancing the secular and sacred forms, the

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other accentuating the sacred form, there are also many countries that follow neither of these paths, including the USA. Our finding of a rich, complex, and constantly changing global matrix provides a novel and useful perspective for culture scholars and business practitioners into the size, shape, and direction of culture evolution around the world. We hope our research has made a small but important contribution to enriching our understanding of the diversity in culture states and changes across countries worldwide. Finally, while we illustrate our approach here with cultural values, it can clearly be extended to other social and psychological phenomena, and we urge researchers to consider adopting these methods. A quote attributed to Stewart Brand, founder of the Long Now Foundation, aptly captures the essence of this approach when he said “you look at the edges to see where the center is going” [1]. For understanding social change, archetypes provide these edges.

Reference 1. Sykes, C. (Ed) 1994. No ordinary genius: The illustrated Richard Feynman. New York: Norton, p179.

Technical Appendix A

Imputation of Missing Data The WVS website suggests that researchers should downweight cases where a respondent did not provide answers to one or more of the 24 questions that form the basis for the two meta-values [1]. We did not use this procedure for three reasons. First, according to best practice in handling missing data, downweighting is not recommended. Placing less weight on these cases is potentially increasing non-response biases if, as likely, these respondents have different characteristics to those who provided complete answers. The correct procedure is to use imputation to estimate these missing values, which Welzel does through the methods discussed in his online appendix [2], and then to give equal weight to imputed and complete cases in any subsequent analysis, which we do here. Second, while it is true there are a few individual questions with high levels of missing data (~33%), the mean proportion of missing data is only 9% across the 24 items used to construct the meta-values. Many respondents also provided complete data, and the majority of those who did not typically only miss one, two or three of these 24 items. Effective imputation is therefore practicable as there is far more complete than incomplete information for those respondents with missing entries.

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Third, Welzel employed regression-based methods for his imputation, inventing a two-step procedure specifically for the nature of the E&WVS data. In step one, various combinations of complete information are used to impute missing values for the sub-indices of the meta-values, where possible. In step two, and where one sub-index of the four relating to each meta-value still remains missing, the other three are used to estimate the meta-value. Since this is not a standard procedure, we ran a validity check where we imputed the missing values at the level of the 24 items with a more general and recent method (random forests), constructed the two meta-values from these, and found that the correlations between these meta-values and those imputed by Welzel were high (0.98 for secular values and 0.97 for emancipative values). This result validates Welzel’s imputation, so in our work here we use the original meta-values as supplied in the E&WVS datasets. Best practice in imputation also typically involves using multiple sets of imputations to generate and understand variability rather than one imputation as provided in these datasets. Here we use subsampling to achieve this objective, generating 100 random mixtures of complete and imputed cases.



References [1] C. Welzel, ‘Construction of Indices for Secular and Emancipative Values’. https://www.worldvaluessurvey.org/WVSContents.jsp (accessed Oct. 27, 2022). [2]  ‘Freedom Rising Online’, Cambridge University Press. https://www. cambridge.org/fr/ academic/subjects/politics-­international-­relations/ c o m p a r a t i v e -­p o l i t i c s / f r e e d o m -­r i s i n g -­h u m a n -­e m p o w e r m e n t ­and-­quest-­emancipation, https://www.cambridge.org/fr/academic/ subjects/politics-­international-­relations/comparative-­politics (accessed Sep. 07, 2022).

Technical Appendix B

The Means of Sets of Compositions Also Sum to 1 Lemma Let A be a row stochastic matrix Anxk. Then the vector of column means is also a stochastic vector. Proof Let the matrix be



 a1,1  A …  a  n,1

a1, j

a1,2

…

… an , 2

… ai , j … an , j

… a1, k   … …  … an, k 

Then we create the vector V of column means with its arbitrary component j ∈ {1, 2, …, k} being Vj 

1 n ai, j n i 1

By adding we find directly

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. Midgley et al., A New Theory of Cultural Archetypes, https://doi.org/10.1007/978-3-031-24482-7

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k

k

1

n

V   n a

i, j

j

j 1



j 1

i 1



1 n k 1 n 1 ai , j   1  n  1  n i 1 j 1 n i 1 n

because A is row stochastic, and it always holds k

a

i, j



j 1

 1, i  1,2,,n



Technical Appendix C



R Packages Used in Our Work

Package

Citation

archetypal

Christopoulos D (2022). _archetypal: Finds the Archetypal Analysis of a Data Frame_. R package version 1.3.0, https:// CRAN.R-­project.org/package=archetypal. Plate T, Heiberger R (2016). _abind: Combine Multidimensional Arrays_. R package version 1.4–5, https://CRAN.R-­project.org/ package=abind. Arel-Bundock V, Enevoldsen N, Yetman C (2018). “countrycode: An R package to convert country names and country codes.” _Journal of Open Source Software_, *3*(28), 848. https://doi.org/10.21105/ joss.00848. Corporation M, Weston S (2022). _doParallel: Foreach Parallel Adaptor for the ‘parallel’ Package_. R package version 1.0.17, https://CRAN.R-­project.org/package=doParallel. Wickham H, François R, Henry L, Müller K (2022). _dplyr: A Grammar of Data Manipulation_. R package version 1.0.10, https:// CRAN.R-­project.org/package=dplyr.

abind

countrycode

doParallel

dplyr

(continued)

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(continued) Package

Citation

GDAtools

Robette N (2022). _GDAtools: A Toolbox for Geometric Data Analysis and More_. R package version 1.7.2, https:// CRAN.R-­project.org/package=GDAtools. geometry Habel K, Grasman R, Gramacy R, Mozharovskyi P, Sterratt D (2022). _geometry: Mesh Generation and Surface Tessellation_. R package version 0.4.6.1, https://CRAN.R-­project.org/ package=geometry. ggplot2 Wickham H (2016). _ggplot2: Elegant Graphics for Data Analysis_ Springer-­Verlag New York. ISBN 978-3-319-24277-4, https:// ggplot2.tidyverse.org. haven Wickham H, Miller E, Smith D (2022). _haven: Import and Export ‘SPSS’, ‘Stata’ and ‘SAS’ Files_. R package version 2.5.1, https:// CRAN.R-­project.org/package=haven. magick Ooms J’ (2021). _magick: Advanced Graphics and Image-Processing in R_. R package version 2.7.3, https://CRAN.R-­project.org/ package=magick. maps Becker RA, Minka,T, Deckmyn. A (2021). _maps: Draw Geographical Maps_. R package version 3.4.0, https:// CRAN.R-­project.org/package=maps. MatrixCorrelation Indahl UG, Næs T, Liland KH (2018). “A similarity index for comparing coupled matrices.” _Journal of Chemometrics_, *e3049*. missRanger Mayer M (2021). _missRanger: Fast Imputation of Missing Values_. R package version 2.1.3, https://CRAN.R-­project.org/ package=missRanger. openxlsx Schauberger P, Walker A (2022). _openxlsx: Read, Write and Edit xlsx Files_. R package version 4.2.5.1, https://CRAN.R-­project.org/ package=openxlsx. pracma Borchers H (2022). _pracma: Practical Numerical Math Functions_. R package version 2.3.8, https://CRAN.R-­project.org/ package=pracma. ptinpoly Maisog JM, Wang Y, Luta G, Liu J (2020). _ptinpoly: Point-in-­ Polyhedron Test (2D and 3D)_. R package version 2.8, https:// CRAN.R-­project.org/package=ptinpoly. robCompositions Templ M, Hron K, Filzmoser P (2011). _robCompositions: an R-package for robust statistical analysis of compositional data_. John Wiley and Sons. ISBN 978-0-470-71135-4. shape Soetaert K (2021). _shape: Functions for Plotting Graphical Shapes, Colors_. R package version 1.4.6, https://CRAN.R-­project.org/ package=shape. (continued)

  TECHNICAL APPENDIX C 

115

(continued) Package

Citation

smacof

Patrick Mair, Patrick J. F. Groenen, Jan de Leeuw (2022). More on multidimensional scaling in {R}: smacof version 2. Journal of Statistical Software, 102(10), 1–47 URL https://doi. org/10.18637/jss.v102.i10 Müller K, Wickham H (2022). _tibble: Simple Data Frames_. R package version 3.1.8, https://CRAN.R-­project.org/package=tibble. Wickham H, Averick M, Bryan J, Chang W, McGowan LD, François R, Grolemund G, Hayes A, Henry L, Hester J, Kuhn M, Pedersen TL, Miller E, Bache SM, Müller K, Ooms J, Robinson D, Seidel DP, Spinu V, Takahashi K, Vaughan D, Wilke C, Woo K, Yutani H (2019). “Welcome to the tidyverse.” _Journal of Open Source Software_, *4*(43), 1686. doi:10.21105/joss.01686 https://doi. org/10.21105/joss.01686. Schwartz M, file. vafPmlie. (2022). _WriteXLS: Cross-Platform Perl Based R Function to Create Excel 2003 (XLS) and Excel 2007 (XLSX) Files_. R package version 6.4.0, https://CRAN.R-­project. org/package=WriteXLS.

tibble tidyverse

WriteXLS

Technical Appendix D

Future Roadmap for the Archetypal Analysis of Culture There is much that can be done to extend our approach in the future, in three main areas. First, from a methodological perspective the main hurdle to our approach is the combination of subsampling and archetypal analysis. The former is necessary to ensure the equality of country samples and to estimate confidence intervals, but the latter is computer intensive. At the moment we generate 100 subsamples to establish two sigma confidence limits, and we then apply archetypal analysis to each subsample, where each such analysis takes considerable time to complete. Estimating confidence limits at three, four or five sigma is desirable but currently not feasible as the thousands of archetypal analyses needed would be prohibitively expensive in time. We believe there is potential in investigating whether subsampling can be used to build a representation of the population distribution, possibly by data “binning” techniques, where applying archetypal analysis to this representation might then require fewer runs to obtain the final estimates. Second, a country is an important but high level unit of analysis and there may be merit in looking at more granular regional analyses, as the values individuals regard as important may vary by region within a

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country. The E&WVS survey data contains regional categorizations for many countries, so this is feasible for countries where the samples are large enough to provide robust results for each region. However, given these will be the larger sample sizes, it is possible the methodological developments mentioned above will be necessary to make regional analyses practical. Third, in theory the country-wave compositions and coordinates are amenable to time series analysis techniques, possibly incorporating other data on the countries selected, and to better understand both trends and causality. However, we are currently limited by the fact that only six countries have all seven waves of E&WVS data available, and many countries only three or four waves. Clearly more waves of data would help here, as might the regional analysis proposed above as this would increase the degrees of freedom for time series modelling.

Index

A Archetypal analysis algorithm definition, 16 archetypal spanning hull, 18 archetype matrix, 16 choice of the number of archetypes, 17 composition matrix, 16 identifying points on the convex hull, 17 independence of the dimensions, 19 measurement requirements, 21 Principal Convex Hull Analysis, 16 R package “archetypal,” 17 Archetypes found at the edges, 4 global archetypes, 5, 41, 91 global, confidence intervals for, 41 global, definition of, 9 theory of, 3 C Compositions are more subtle than averages, 93

beyond simple stereotypes, 7 country, confidence intervals for, 44 country, definition of, 9 example country compositions, 42 metal alloy analogy, 6 Compositions and coordinates Australia, 84 Bangladesh, 79 Brazil, 83 Chile, 59 China, 72 countries on the Wave 7 convex hull, 50 country-waves on the complete data convex hull, 56 Ethiopia, 77 Germany, 81 Greece, 83 India, 73 Japan, 75 South Africa, 77 USA, 76

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INDEX

Countries Argentina, 40 Australia, 84 Bangladesh, 41, 79, 102 Belarus, 56, 97 Bosnia & Herzegovina, 48 Brazil, 83 Bulgaria, 48, 100 Canada, 61 Chile, 58, 59, 61, 98 China, 43, 69, 72 Croatia, 40, 100 Czechia, 56 Denmark, 44, 50, 56, 91 Egypt, 42, 44, 50, 56, 101 Estonia, 56, 91 Ethiopia, 12, 41, 69, 77 France, 92 Germany, 40, 69, 81, 99, 105 Greece, 83 Iceland, 44, 56 India, 41, 69, 73 Indonesia, 97 Iraq, 44 Italy, 40, 94 Japan, 41, 43, 69, 74, 92 Jordan, 44, 56, 91 Malaysia, 50 Mongolia, 50 Montenegro, 23, 48 Netherlands, 94 New Zealand, 67 Nigeria, 44, 69, 97 Northern Ireland, 98 North Macedonia, 40 Norway, 44, 66 Peru, 97 Philippines, 71, 97 Qatar, 56 Russia, 71, 97 Rwanda, 98

Singapore, 40 South Africa, 77 Spain, 11 Sweden, 42, 44, 50, 56, 91 Switzerland, 44 Thailand, 48 Trinidad and Tobago, 61 Turkey, 23, 71 USA, 43, 69, 76, 105 Venezuela, 61 Vietnam, 69 Yemen, 56 Cultural change, compasses China, India, Japan and the USA, 94 contrast Ethiopia and Spain, 12 easterly Rwanda, Chile, Northern Ireland and Germany, 98 westerly Croatia, Bulgaria, Egypt and Bangladesh, 100 Cultural change, examples of Australia, 84 Bangladesh, 79 Brazil, 83 Chile, 59 China, 73 Ethiopia, 77 Germany, 81 Greece, 83 India, 73 Japan, 74 New Zealand, 67 Norway, 66 South Africa, 77 USA, 76 Cultural change, major trends convergence of the USA and Japan, 94 countries changing in short time spans, 69

 INDEX 

countries changing over long time spans, 69 examples of easterly headings, 98 examples of westerly headings, 100 the largest trend (south-south-­ east), 103 the second largest trend (east-south-­east), 103 static countries, 69, 97 two-speed world, 68, 97 the USA’s secular trend, 105 Cultural change, measurement of calibrating the magnitude of changes, 66 change index, 65 change metrics for 92 countries, 61 compass, 11 compass heading, 65 earliest and latest quadrants, 61 five aspects, 61 magnitude by time span, 70 time span, 61 Cultural map based on 398 country-wave compositions, 56, 91 confidence intervals for coordinates, 52 convex hull for 398 country-­ waves, 56 convex hull for Wave 7, 50 coordinates for Wave 7 countries, 50 definition of, 11 geographical map of the current world, 105 quadrants, 11, 56, 91, 94 used as a common platform across results, 59

121

E European & World Value Surveys available data, 8 calibration weights, 22 coverage of the globe, 22 integrated database, 21 survey samples by waves, 24–26 G Global matrix definition of, 9 unity, diversity and evolution of, 106 for Wave 7 countries, 44 H Heterogeneity both within and between are substantial, 44 represented through archetypes and compositions, 2 within and between countries, 2, 92 K Key takeaways chapter five, 103 chapter four, 85 chapter three, 53 M Multidimensional scaling Aitcheson distance, 29 common system of coordinates, 30 dimensions as contrasts, 50 two-dimensional solution, 48

122 

INDEX

S Subsampling aggregation to countries, 28 alignment of outputs, 28 comparison of random and weighted random, 37 determining the number of archetypes, 35 estimated rates of convergence, 37 experiments with varying subsample sizes, 34

indices of resampling variability, 29 population estimates for the meta-values, 35 rate of convergence, 27 technique of, 27 W Welzel meta-values definition and measurement, 7 secular and emancipative, 4