Fair Public Decision Making

TL;DR

This paper extends fair division concepts to public decision making across multiple issues, introducing new fairness relaxations and analyzing the fairness and computational aspects of the Maximum Nash Welfare solution.

Contribution

It generalizes proportionality to a multi-issue setting, introduces three new fairness relaxations, and analyzes the fairness and computational properties of the Maximum Nash Welfare solution.

Findings

Maximum Nash Welfare satisfies or approximates all three relaxations.

Polynomial algorithms are provided for finding fair allocations.

Hardness results are established for certain fairness constraints.

Abstract

We generalize the classic problem of fairly allocating indivisible goods to the problem of \emph{fair public decision making}, in which a decision must be made on several social issues simultaneously, and, unlike the classic setting, a decision can provide positive utility to multiple players. We extend the popular fairness notion of proportionality (which is not guaranteeable) to our more general setting, and introduce three novel relaxations --- \emph{proportionality up to one issue, round robin share, and pessimistic proportional share} --- that are also interesting in the classic goods allocation setting. We show that the Maximum Nash Welfare solution, which is known to satisfy appealing fairness properties in the classic setting, satisfies or approximates all three relaxations in our framework. We also provide polynomial time algorithms and hardness results for finding allocations satisfying these axioms, with or without insisting on Pareto optimality.