Linear Measures, the Gini Index, and The Income-Equality Trade-off
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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- Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
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- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
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