Welfare functions and inequality indices in the binomial decomposition of OWA functions

In the context of Choquet integration with respect to symmetric capacities, we consider the binomial decomposition of OWA functions in terms of the binomial Gini welfare functions Cj , j = 1, ...,n, and the associated binomial Gini inequality indices Gj , j = 1, ...,n, which provide two equivalent descriptions of k-additivity. We illustrate the weights of the binomial Gini welfare functions Cj , j = 1, ...,n, and the coefficients of the associated binomial Gini inequality indices Gj , j = 1, ...,n, which progressively focus on the poorest part of the population. Moreover, we investigate the numerical behavior of the binomial Gini welfare functions and inequality indices in relation to a family of income distributions described by a parameter related with inequality.