Contents

5.1. Introduction 302

5.1.1 IncomePolarization 303

5.1.2 Bipolarization 304

5.1.3 Social Polarization 305

5.1.4 SocioeconomicandMultidimensionalPolarization 305

5.2.

5.3. Notation 309

5.4. Income Polarization 310

5.4.1 Discrete Income Polarization 310

5.4.2 Continuous Income Polarization 314

5.4.3 DiscreteIncomePolarizationwithEndogenousGrouping 317

5.5. Bipolarization 318

5.5.1 MeasuresoftheSizeoftheMiddleClass 318

5.5.2 Two Basic Properties of Bipolarization Indices 322

5.5.3 Bipolarization Dominance 326

5.5.3.1 First-Order Bipolarization Dominance 326

5.5.3.2 First-Order Symmetric Bipolarization Dominance 327

5.5.3.3 Second-Order Bipolarization Dominance 328

5.5.3.4 Second-Order Symmetric Bipolarization Dominance 328

5.5.4 Bipolarization Indices 328

5.5.5 Income Polarization and Bipolarization 332

5.5.6 Extensions 333

5.5.7 Absolute and Relative Bipolarization Indices 335

5.5.8 Bipolarization with Ordinal Data 336

5.6. Social Polarization 337

5.6.1 Concepts and Motivation 337

5.6.2 Measurement 338

5.7. Socioeonomic Polarization 341

5.7.1 Between- and Within-Group Income Inequality 341

5.7.2 Identification/Alienation Hybrids 342

5.8. Multidimensional Polarization 348

5.9. Polarization in Practice 351

5.9.1 Polarization and Inequality 351

5.9.2 Empirical Polarization Comparisons 353

5.9.3 Polarization and Conflict 354

Handbook of Income Distribution, Volume 2A

301

ISSN 1574-0056, http://dx.doi.org/10.1016/B978-0-444-59428-0.00006-0

5.10. Conclusion

355

355

355

Acknowledgments

References