An Axiomatic Theory of Fairness

Abstract

The tradeoff between fairness and throughput has been widely observed in network analysis and protocol design. Despite many existing fairness metrics (from simple ones like Jain’s index to more complex ones like α-fair utility), the meaning of fairness is largely based on problemoriented interpretations and judgments, with no well-established framework. To tackle this challenging problem, we presented a set of five axioms for fairness, and showed that a wide range of fairness measures satisfying the axioms can be constructed in a unifying framework. The construction incorporates as special cases many existing metrics, such as Jain’s index, entropy, and α-fair utility, and also reveals a new family of fairness measures. Our axiomatic theory illuminates many issues in network resource allocation research, among which is a novel tradeoff between efficiency and fairness. The parallelism of our framework and well-known theories in other fields, e.g., Renyi Entropy, Lorenz Curve, Nash Bargaining Solutions, and Rawls’ Theory of Justice, greatly sharpens our understanding of the notion of fairness.