Classical inequality indices, welfare functions, and the dual decomposition

Oihana Aristondo, José Luis García-Lapresta, Casilda Lasso de la Vega, Ricardo Alberto Marques Pereira
Discussion papers: Department of Applied Economics IV. Basque Country University, No.99, April 2012.

Abstract
We consider the classical inequality measures due to Gini, Bonferroni, and De Vergottini and we present a brief review of the three inequality indices and the associated welfare functions, in the correspondence scheme introduced by Blackorby and Donaldson, and Weymark. The three classical inequality indices incorporate di®erent value judgments in the measurement of inequality, leading to di®erent behavior under income transfers between individuals in the population. The welfare functions associated with the Gini, Bonferroni, and (normalized) De Vergottini indices are Schur-concave OWA functions, with larger weights for lower incomes. We examine the dual decomposition and the orness degree of the three welfare functions in the standard framework of aggregation functions on the [0; 1]n domain, and show that it others interesting insight on the distinct and complementary nature of the classical inequality indices.
Keywords: income inequality and social welfare, classical Gini, Bonferroni, and De Vergottini inequality indices, welfare functions, aggregation functions, WA and OWA functions, dual decomposition, orness.
JEL Classification: D63, I32.

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