The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration

Abstract

In the context of Social Welfare and Choquet integration, we briefly review the classical Gini inequality index for populations of n ≥ 2 individuals, including the associated Lorenz area formula, plus the k-additivity framework for Choquet integration introduced by Grabisch, particularly in the additive and 2-additive symmetric cases. We then show that any 2-additive symmetric Choquet integral can be written as the difference between the arithmetic mean and a multiple of the classical Gini inequality index, with a given interval constraint on the multiplicative parameter. In the special case of positive parameter values, this result corresponds to the well-known Ben Porath and Gilboa's formula for Weymark's generalized Gini welfare functions, with linearly decreasing (inequality averse) weight distributions.

SUOWA operators: An analysis of their conjunctive/disjunctive character

“…Notice that nondecreasing sequence of weights appear frequently in the literature; for instance, when the weights form a (nondecreasing) arithmetic progression, which arise in the 2-additive symmetric normalized capacities (see Beliakov et al [40,p. 86] and Bortot and Marques Pereira [41]) and in some models proposed in the literature to determine the OWA weighting vector 5 (see Liu [45]). Likewise, nondecreasing weights allow to characterize the Schur-concavity of OWA operators (see 2.…”