The single parameter family of Gini Bonferroni welfare functions and the binomial decomposition, transfer sensitivity and positional transfer sensitivity

We consider the binomial decomposition of generalized Gini welfare functions in terms of the binomial welfare functions Cj, j = 1,...,n and we examine the weighting structure of the latter, which progressively focus on the poorest part of the population. In relation with the generalized Gini welfare functions, we introduce measures of transfer sensitivity and positional transfer sensitivity and we illustrate the behaviour of the binomial welfare functions Cj, j = 1,...,n with respect to these measures. We investigate the binomial decomposition of the Gini Bonferroni welfare functions and we illustrate the dependence of the binomial decomposition coefficients in relation with the single parameter which describes the family. Moreover we examine the family of Gini Bonferroni welfare functions with respect to the transfer sensitivity and positional transfer sensitivity principles.