Fair Resource Allocation by Gini Index Minimization

Abstract

In many resource allocation problems there is a need to minimize inequity to respect some fairness rules while looking for the overall efficiency. The Gini index representing the relative mean absolute difference of outcomes is the classical measure of inequity in outcome distribution. It was empirically found in real-life applications that the Gini index minimization while equalizing the outcomes it may simultaneously support their maximization (allocation efficiency). However, it depends on the feasible set structure and there is no guarantee to achieve good equitable and efficient allocation scheme. We show that with appropriate outcome shift the Gini index minimization is consistent both with inequity minimization and with outcomes maximization thus guaranteeing equitable allocation schemes. The interval of appropriate target values depends on the problem structure (feasible set). Although it can be found or adjusted during the optimization process without necessity of a special feasible set analysis.