Contents

3.1. Introduction 142

3.1.1 HistoricalDevelopmentsandMainThemes 145

3.2. Preliminaries: Dimensions, Indicators, and Weights 148

3.2.1 SelectionofDimensions 148

3.2.2 Indicators 150

3.2.3 Weighting of Dimensions 152

3.3.

3.3.1 The Composite Index Approach 158

3.3.2 The Counting Approach 160

3.3.2.1 PartialOrderings 161

3.3.2.2 Complete Orderings: The Independence Axioms 164

3.3.2.3 Complete Orderings: The Dual Approach 167

3.3.2.4 Complete Orderings: The Primal Approach 169

3.3.2.5 Association Rearrangements 173

3.3.2.6 Counting Deprivations versus Measuring Poverty 179

3.3.3 PovertyMeasurementBasedonContinuousVariables 183

3.3.3.1 MeasuresofMultidimensionalPoverty 184

3.3.3.2 Partial Orderings 187

3.4. MultidimensionalInequalityMeasurement 189

3.4.1 Multidimensional Extensions of the Pigou-Dalton Transfers Principle 190

3.4.2 Partial Orderings and Sequential Dominance Criteria 192

3.4.3 Measures of Multidimensional Inequality 193

3.4.3.1 Two-Stage Approaches: First Aggregating Across Individuals 194

3.4.3.2 Two-Stage Approaches: First Aggregating Across Attributes 195

3.4.3.3 Indices for Binary Variables 198

3.5. Summary and Conclusions 200

Acknowledgments 203

References 203