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Linear Measures, the Gini Index and the Income-Equality Tradeoff

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Elchanan Ben Porath
Itzhak Gilboa

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Abstract

The paper provides an axiomatization of linear inequality measures as a representation of a binary relation on the subspace of income profiles having the same total income. Interpreting the binary relation as a preferences (of, say, a policymaker), we extend the axioms to the whole space of income profiles, and find that they characterize linear social evaluation functions. The axiomatiziation seems to suggest that a policymaker who has a linear measure of inequality on a subspace should have a linear evaluation on the whole space. In particular, we find that an extension of the preferences reflected in the Gini index to the whole space is represented by a linear combination of total income and the Gini index.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 944.

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Date of creation: Jul 1991
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Handle: RePEc:nwu:cmsems:944

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  1. Sheshinski, Eytan, 1972. "Relation between a social welfare function and the gini index of income inequality," Journal of Economic Theory, Elsevier, vol. 4(1), pages 98-100, February. [Downloadable!] (restricted)
  2. Ebert, Udo, 1987. "Size and distribution of incomes as determinants of social welfare," Journal of Economic Theory, Elsevier, vol. 41(1), pages 23-33, February. [Downloadable!] (restricted)
  3. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  5. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Luis José Imedio Olmedo & Elena Bárcena Martín, 2007. "Dos familias numerables de medidas de desigualdad," Investigaciones Economicas, Fundación SEPI, vol. 31(1), pages 191-217, January. [Downloadable!]
  2. Ok, Efe A. & Zhou, Lin, 1997. "The Choquet Bargaining Solutions," Working Papers 97-36, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
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  3. Duclos, Jean-Yves & Jalbert, Vincent & Araar, Abdelkrim, 2003. "Classical Horizontal Inequity and Reranking: an Integrating Approach," Cahiers de recherche 0306, CIRPEE. [Downloadable!]
  4. Abdelkrim Araar & Jean-Yves Duclos, 2001. "An Atkinson-Gini Family of Social Evaluation Functions," UFAE and IAE Working Papers 476.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
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  5. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559. [Downloadable!]
  6. De Waegenaere, A. & Wakker, P., 1997. "Choquet integrals with respect to non-monotonic set functions," Discussion Paper 44, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Jean-Yves Duclos & Vincent Jalbert & Abdelkrim Araar, 2001. "Classical Horizontal Inequity and Reranking: an Integrated Approach," UFAE and IAE Working Papers 478.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
    Other versions:
  8. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research. [Downloadable!]
  9. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497. [Downloadable!]
  10. Rolf Aaberge & Steinar Bjerve & Kjell Doksum, 2005. "Decomposition of rank-dependent measures of inequality by subgroups," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 493-503. [Downloadable!]
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  11. Thibault Gajdos, 2002. "Measuring Inequalities without Linearity in Envy Through Choquet Integral with Symmetric Capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085888_v1, HAL. [Downloadable!]
  12. Pedro Miranda & Michel Grabisch & Pedro Gil, 2006. "Dominance of capacities by k-additive belief functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00186905_v1, HAL. [Downloadable!]
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  13. Aaberge, Rolf & Flood, Lennart, 2008. "Evaluation of an In-Work Tax Credit Reform in Sweden: Effects on Labor Supply and Welfare Participation of Single Mothers," IZA Discussion Papers 3736, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  14. Yoram Amiel & Frank A Cowell, 1997. "Inequality, Welfare and Monotonicity," STICERD - Distributional Analysis Research Programme Papers 29, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  15. Ok, E.A., 1996. "Inequality Averse Collective Choice," Working Papers 96-36, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    Other versions:
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