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

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