Evaluating ordinal inequalities between groups

Abstract

We explore the inequality measurement of a discrete ordinal variable between social groups. We provide an axiomatic characterization for the Net Difference Index (Lieberson: Sociol. Methodol. 7, 276–291 1976), that makes use of rank-domination to evaluate the discrepancy between the distributions of two social groups over ordered categories. Adapting well-known principles of cardinal inequality measurement to the between-group ordinal inequality setting, we show that the Net Difference Index mimics the Gini Index in terms of its relationship to the Lorenz curve, in our setting.