Measuring fairness: Axioms and applications

We present a set of five axioms for fairness measures and prove that there is a unique family of fairness measures satisfying the axioms. This unique family is constructed in closed form and shown to include both symmetric and asymmetric ones as special cases. The results are further extended to quantify fairness of continuous dimension inputs, where resource allocations vary over time. We demonstrate the applications of the axiomatic theory in congestion control, routing, and spectrum management problems.