On a transformation of the Gini coefficient into a well-behaved social welfare function

Following Sen's (1973) characterization of the Gini coefficient as a ratio between a measure of aggregate income-based stress ("depression" in Sen's terminology) and aggregate income, we transform the Gini coefficient into a social welfare function rather than having the Gini coefficient feature as an input in a social welfare function as in Sen (1973 and 1997), Sen (1976), and Sen (1982). The "Gini social welfare function" assigns weights that reflect preferences to aggregate income and to aggregate income-based stress (income inequality), a desirable property that a social welfare function in which the Gini coefficient features as an input does not have. The transformation bears on the formation of public policy and on the welfare analysis of policy interventions.