A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality

We investigate several properties of the Bonferroni inequality index, including its welfare theoretic interpretation. We also interpret and characterize the absolute Bonferroni index as the average of subgroup average depression indices, where to each income we associate a subgroup containing all persons whose incomes are not higher than this income. An aggregate depression index for a subgroup has been derived axiomatically as the sum of gaps between the subgroup highest income and all incomes not higher than that.