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

n 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.