An Axiomatic Theory of Fairness in Network Resource Allocation

TL;DR

This paper develops an axiomatic framework for fairness in network resource allocation, unifying existing measures and providing new insights into their properties and implications.

Contribution

It introduces five axioms for fairness measures, unifies well-known fairness concepts, and explores their properties and engineering implications.

Findings

Well-known fairness measures are special cases of the axiomatic framework.

A generalized Jain's index with adjustable resolution is proposed.

An interpretation of 'larger alpha is more fair' is provided.

Abstract

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.