Fair and Efficient Resource Allocation - Bicriteria Models for Equitable Optimization

Resource allocation problems are concerned with the allocation of limited resources among competing activities so as to achieve the best performances. In systems which serve many usersthere is a need to respect some fairness rules while looking for the overall efficiency. The so-called Max-Min Fairness is widely used to meet these goals. However, allocating the resource to optimize the worst performance may cause a dramatic worsening of the overall system efficiency. Therefore, several other fair allocation schemes are searched and analyzed. In this paper we focus on mean-equity approaches which quantify the problem in a lucid form of two criteria: the mean outcome representing the overall efficiency and a scalar measure of inequality of outcomes to represent the equity (fairness) aspects. The mean-equity model is appealing to decision makers and allows a simple trade-off analysis. On the other hand, for typical dispersion indices used as inequality measures, the mean-equity approach may lead to inferior conclusions with respect to the outcomes maximization (system efficiency). Some inequality measures, however, can be combined with the mean itself into optimization criteria that remain in harmony with both inequality minimization and maximization of outcomes. In this paper we introduce general conditions for inequality measures sufficient to provide such an equitable consistency. We verify the conditions for the basic inequality measures thus showing how they can be used not leading to inferior distributions of system outcomes.