From social choice to inequality-decomposition: in the spirit of Arrow and Atkinson by way of Sen and Shorrocks

Abstract

ABSTRACT This article forges connections between social choice theory and inequality-measurement to deliver a series of advances to the latter. It discusses the ethical and formal aspects connecting the fields, linking the roles played by the intensity of preferences and interpersonal comparability (in social choice) and, respectively, inequality-aversion and interpersonal comparability (in inequality-measurement). This extends naturally to relaxing the assumption of symmetry in group-wise inequality-decompositions, allowing a measure capable of unambiguous decomposition that, overcoming well-known limitations of existing measures, still incorporates different degrees of inequality-aversion through the use of its demonstrated duality with inter-group comparability. The framework is then applied to inequality in Brazil and the changes it underwent between 2003 and 2015, focusing on labour-market incomes of white men and non-white women. We show how sensitive are measures of (changes in) inequality to assumptions regarding the interpersonal comparability of the groups’ income and inequality-aversion, pinpointing the precise trade-offs between the two. The results indicate that, for a reasonable range of parameters, overall inequality changed by between −28.6% and −12.2% over the period. This highlights the analysis of the trade-off between interpersonal comparability and inequality-aversion warrants being addressed explicitly in empirical measurements of, or judgements over, levels and variations of inequality.