Measuring Inequalities without Linearity in Envy Through Choquet Integral with Symmetric Capacities
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 with
more than k members is equal to zero.
more than k members is equal to zero.
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