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

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  • Elchanan Ben Porath
  • Itzhak Gilboa

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. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
  3. 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.
  4. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  5. 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.
  6. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  7. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
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