The decomposition of inequality reconsidered: Weakly decomposable measures

The paper characterizes the class of weakly decomposable (aggregable) inequality measures which satisfy a new (weak) decomposition (and aggregation) property. These measures can be decomposed into the sum of the usual within-group and a between-group term which is based on the inequality between all pairs of individuals belonging to the groups involved. The measures therefore depend on the inequality index for two-person distributions and are proportional to the total sum of the inequality values between all pairs of individuals. Extending Gini's mean difference, the Gini coefficient, and the variance of logarithms we characterize three families of measures. By choosing other basic measures further (families of) weakly decomposable measures can be defined.