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

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  • Silvia Bortot
  • Ricardo Alberto Marques Pereira

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

Suggested Citation

  • Silvia Bortot & Ricardo Alberto Marques Pereira, 2012. "The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration," DISA Working Papers 2012/04, Department of Computer and Management Sciences, University of Trento, Italy, revised May 2012.
  • Handle: RePEc:trt:disawp:2012/04
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    Keywords

    Social Welfare; Gini Inequality Index; Symmetric Capacities and Choquet Integrals; OWA Functions; 2-Additivity and Equidistant Weights;

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