Measuring Inequalities without Linearity in Envy Through Choquet Integral with Symmetric Capacities

Thibault Gajdos ()
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Thibault Gajdos: EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: The (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari's model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where the welfare of a coalition is defined as the income of the worst-off member of that coalition. We provide a set of axioms (Ak) and prove that the three following statements are equivalent: (i) the decision maker respects (Ak); (ii) f is a polynomial of degree k; (iii) the weight of all coalitions withmore than k members is equal to zero.

Keywords: Inequality measurement; Choquet integral; Symmetric capacities (search for similar items in EconPapers)
Date: 2002
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00085888
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Published in Journal of Economic Theory, 2002, 106 (1), pp.190-200

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