Abstract
In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the classical Gini inequality index for populations of n ≥ 2 individuals, including the associated Lorenz area formula, and on the other hand, 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 multiplicity 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.
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Bortot, S., Marques Pereira, R.A. (2013). The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration. In: Ventre, A., Maturo, A., Hošková-Mayerová, Š., Kacprzyk, J. (eds) Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences. Studies in Fuzziness and Soft Computing, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35635-3_2
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