Anderson Multilateral Wellbeing Comparison in a Many Dimensioned World

Ordering and Ranking Collections of Groups
1. Auflage 2019
ISBN: 978-3-030-21130-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 205 Seiten

Reihe: Progress in Mathematics

This book addresses the disparities that arise when measuring and modeling societal behavior and progress across the social sciences. It looks at why and how different disciplines and even researchers can use the same data and yet come to different conclusions about equality of opportunity, economic and social mobility, poverty and polarization, and conflict and segregation. Because societal behavior and progress exist only in the context of other key aspects, modeling becomes exponentially more complex as more of these aspects are factored into considerations. The content of this book transcends disciplinary boundaries, providing valuable information on measuring and modeling to economists, sociologists, and political scientists who are interested in data-based analysis of pressing social issues.

Autoren/Hrsg.

Anderson, Gordon

Inhaltsverzeichnis

1;Acknowledgments;7
2;Contents;8
3;List of Figures;11
4;List of Tables;13
5;Introduction;15
6;Chapter 1: Measuring the Wellbeing of Groups;19
6.1;1.1 Introduction;19
6.2;1.2 An Outline of What Follows;21
6.3;1.3 Measuring Wellbeing: The Social Welfare Function;24
6.4;1.4 Measuring Wellbeing: The Benthamite Tradition;28
6.5;1.5 The Pigou-Dalton Principle: “Inequality Is a Bad Thing”;29
6.6;1.6 Polarization;30
6.7;1.7 Social Exclusion;31
6.8;1.8 Equality of Opportunity and Social Mobility;34
6.9;1.9 The Rawlsian Principle and the Focus on Poverty;36
6.10;1.10 What to Do Now?;36
6.11;References;37
7;Chapter 2: Statistical Matters;40
7.1;2.1 Introduction;40
7.2;2.2 Probability Distributions;41
7.2.1;Multivariate Considerations;43
7.2.2;Statistical Independence;45
7.2.3;Independence and Random Samples;47
7.2.4;Independence and Groups;47
7.2.5;Measures of Location and Dispersion;48
7.2.6;Means and Variances and the Expectations Operator;48
7.2.7;Location Measures;51
7.2.8;Inequality Measures;51
7.2.9;Some Unit Free Inequality Measures;51
7.3;2.3 Parametric and Non-Parametric Distributions;54
7.3.1;An Example of a Discrete Probability Density Function: The Poisson Distribution;54
7.3.2;An Example of Continuous Probability Density Function: The Normal Distribution;56
7.3.3;Multidimensional Considerations;58
7.3.4;A Note of Caution;58
7.3.5;The Normal Distribution and Central Limit Theorems;59
7.3.6;Estimation of Unknown Parameters;60
7.4;2.4 Kernel Estimation;60
7.4.1;Non-Parametric Distributions;60
7.4.2;The Kernel Function;61
7.4.3;Choosing the “H” and the Kernel;62
7.4.4;Choosing “H”;63
7.4.5;Least Squares Cross Validation;64
7.4.6;Likelihood Cross Validation;64
7.4.7;A Variable Bandwidth H: The Adaptive Kernel;65
7.4.8;Consistency of the Kernel Estimator;66
7.5;2.5 Stochastic Dominance Relations;66
7.6;2.6 Comparing Distributions;67
7.6.1;Tests for Similarity of Two Distributions;68
7.7;2.7 The Test Inconsistency Problem;70
7.7.1;Test Inconsistency for Smooth Continuous Alternatives;72
7.7.2;Maximizing the Power of a Test;74
7.8;References;76
8;Chapter 3: Complete Orderings: Index Types and the Ambiguity Problem;78
8.1;3.1 Chapter Outline;78
8.2;3.2 Introduction;79
8.3;3.3 Indices for the Level of Wellbeing;81
8.4;3.4 Some Unit Free Inequality Measures;82
8.5;3.5 Inequality Adjusted Wellbeing Levels;86
8.6;3.6 Polarization Measures;89
8.7;3.7 Multivariate Polarization Indices;95
8.7.1;Three Measures of Multivariate Bipolarization;96
8.8;3.8 Poverty Measurement;99
8.8.1;Multivariate Poverty, Deprivation and Exclusion Indices;100
8.9;3.9 Equal Opportunity and Mobility Indices;104
8.10;3.10 Exploring the Impact of Ambiguity;106
8.11;References;109
9;Chapter 4: Partial Orderings;113
9.1;4.1 Introduction;114
9.2;4.2 Stochastic Dominance Criteria;117
9.2.1;Some Preliminaries;117
9.2.2;Stochastic Dominance Relations;120
9.2.3;What Does for Different “I” Imply for Societal Preferences?;121
9.3;4.3 On Restricting the Criterion Space;123
9.4;4.4 Stochastic Dominance and Inequality Orderings;125
9.5;4.5 Stochastic Dominance and Poverty Orderings;126
9.6;4.6 Stochastic Dominance and Polarization;127
9.7;4.7 The Problem of Ambiguity and Conditions for its Absence;131
9.7.1;The Case of Perfect Segmentation;132
9.7.2;Dealing with Ambiguity When K = 2;133
9.7.3;Restricting the Preference Space Reduces Ambiguity;133
9.7.4;Ambiguity in Inequality Measures;134
9.8;4.8 Determination of Ambiguity Groupings: Non-Ambiguity Cuts and Groups;137
9.9;4.9 Tools for Ordering Groups and Quantifying their Differences;139
9.9.1;Ordering Groups, the Utopia-Dystopia Index;139
9.9.2;Measures of Discrepancies Between Distributions;141
9.9.3;Multilateral Transvariation;142
9.9.4;A Distributional Gini Coefficient;142
9.9.5;Multivariate Considerations;143
9.9.6;Inference for Multilateral Transvariation and Distributional Gini Coefficients;143
9.9.7;Multilateral Transvariation;144
9.9.8;The Distributional Gini;146
9.10;References;148
10;Chapter 5: Comparing Latent Subgroups;151
10.1;5.1 Introduction;151
10.2;5.2 Semi-Parametric Mixture Distributions;155
10.3;5.3 The Probability of Class Membership of an Agent with an Income x;157
10.4;5.4 Estimating the Model;159
10.5;5.5 Determining the Number of Classes;160
10.6;5.6 Studying the Probability of Class Membership;161
10.7;5.7 Comparing the Subgroups;162
10.8;5.8 An Example: The Eurozone Income Distribution;162
10.9;References;165
11;Chapter 6: Ambiguity, Comparability, Segmentation and All That;168
11.1;6.1 Introduction;168
11.2;6.2 An “Absence of Ambiguity” Criteria;173
11.2.1;The Case of Complete Segmentation;173
11.3;6.3 Dealing with Ambiguity within Two Groups;175
11.3.1;Restricting the Preference Space Reduces Ambiguity;176
11.4;6.4 Two Ambiguity Indices;177
11.4.1;A Leshno–Levy Based Index;177
11.4.2;A Transvariation Based Index;179
11.5;6.5 Ambiguity in Inequality Measures;180
11.5.1;Assessing the Extent of Incoherent Ranking;183
11.6;6.6 Determination of Ambiguity Groupings: Unambiguous Cuts and Groups;183
11.7;6.7 An Empirical Application;185
11.7.1;The Data;185
11.7.2;Exploring the Impact of Ambiguity;186
11.7.3;Partition Analysis;190
11.8;6.8 Conclusions;194
11.9;References;194
12;Chapter 7: Some Applications;196
12.1;7.1 Introduction;196
12.2;7.2 An Example of Canadian Unidimensional Income Distribution Analysis;197
12.3;7.3 A Multidimensional Equal Opportunity Example: German Educational Attainment;199
12.4;7.4 An Example in Portfolio Choice;202
12.5;7.5 Gender Equality in Sub Saharan Africa Irrigation Schemes;204
12.6;7.6 A Multidimensional Human Development Example;210
12.7;References;214
13;Index;218