A social-psychological reconstruction of Amartya Sen's measures of inequality and social welfare

The Gini coefficient features prominently in Amartya Sen's 1973 and 1997 seminal work on income inequality and social welfare. We construct the Gini coefficient from social-psychological building blocks, reformulating it as a ratio between a measure of social stress and aggregate income. We determine when as a consequence of an income gain by an individual, an increase in the social stress measure dominates a concurrent increase in the aggregate income, such that the magnitude of the Gini coefficient increases. By integrating our approach to the construction of the Gini coefficient with Sen's social welfare function, we are able to endow the function with a social-psychological underpinning, showing that this function, too, is a composite of a measure of social stress and aggregate income. We reveal a dual role played by aggregate income as a booster of social welfare in Sen's social welfare function. Quite surprisingly, we find that a marginal increase of income for any individual, regardless of the position of the individual in the hierarchy of incomes, improves welfare as measured by Sen's social welfare function.