The binomial Gini inequality indices and the binomial decomposition of welfare functions

Silvia Bortot () and Ricardo Alberto Marques Pereira ()
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Silvia Bortot: Department of Economics and Management, University of Trento
Ricardo Alberto Marques Pereira: Department of Economics and Management, University of Trento

No 305, Working Papers from ECINEQ, Society for the Study of Economic Inequality

Abstract: In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the generalized Gini welfare functions and inequality indices for populations of n>=2 individuals, and on the other hand, the Mobius representation framework for Choquet integration, particularly in the case of k-additive symmetric capacities. We recall the binomial decomposition of OWA functions due to Calvo and De Baets [14] and we examine it in the restricted context of generalized Gini welfare functions, with the addition of appropriate S-concavity conditions. We show that the original expression of the binomial decomposition can be formulated in terms of two equivalent functional bases, the binomial Gini welfare functions and the Atkinson-Kolm-Sen (AKS) associated binomial Gini inequality indices, according to Blackorby and Donaldson's correspondence formula. The binomial Gini pairs of welfare functions and inequality indices are described by a parameter j = 1,...,n, associated with the distributional judgements involved. The j-th generalized Gini pair focuses on the (n - j + 1)/n poorest fraction of the population and is insensitive to income transfers within the complementary richest fraction of the population.

Keywords: Social welfare; Generalized Gini welfare functions and inequality indices; symmetric capacities and Choquet integrals; OWA functions; Binomial decomposition and k-additivity. (search for similar items in EconPapers)
JEL-codes: D31 D63 I31 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2013-09
New Economics Papers: this item is included in nep-dem
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