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

Silvia Bortot and Ricardo Alberto Marques Pereira

No 2012/04, DISA Working Papers from Department of Computer and Management Sciences, University of Trento, Italy

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 multi- plicative 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

Keywords: Social Welfare; Gini Inequality Index; Symmetric Capacities and Choquet Integrals; OWA Functions; 2-Additivity and Equidistant Weights (search for similar items in EconPapers)
Date: 2012-05, Revised 2012-05
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