We present a set of five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Well-known notions such as alpha-fairness, Jain's index  and entropy are shown to be special cases. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a  new understanding of alpha-fair utility functions  and an interpretation of "larger alpha is more fair"  .
We present a set of five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Well-known notions such as alpha-fairness, Jain's index , and entropy are shown to be special cases. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a generalized Jain's index that tunes the resolution of the fairness measure, a new understanding of alpha-fair utility functions , and an interpretation of "larger alpha is more fair" . We also construct an alternative set of four axioms to capture efficiency objectives and feasibility constraints .
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generalized Jain's index that tunes the resolution of the fairness measure, a
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. We also construct an alternative set of four axioms to capture efficiency objectives and feasibility constraints