Fairness as a Robust Utilitarianism

Abstract

This article focuses on the social choice problem in which decisions are based on the utility of multiple stakeholder types. The sum of these utilities—Utilitarian welfare—is one of the most important objectives in solving the social choice problem. While it is the most efficient solution, maximizing Utilitarian welfare may lead to unfair outcomes. However, Encouraging a Utilitarian decision-maker to adopt a fair decision is challenging due to the associated efficiency loss. This article takes a novel perspective by motivating a Utilitarian decision-maker to make fair decisions from an uncertainty-averse standpoint. We study the problem where the proportions of stakeholder types are uncertain and propose a distributionally robust optimization (DRO) model that maximizes the worst-case Utilitarian welfare over an $\varphi$ -divergence-based uncertainty set. We provide three aspects of the relationship between fairness and the uncertain-averse Utilitarian welfare maximization. First, we establish that the worst-case Utilitarian welfare adheres to all five axioms of unfairness-averse cardinal welfare functions with two stakeholder types and satisfies four of these when this number exceeds two. Second, we demonstrate that with the maximal extent of uncertainty aversion, the DRO model identifies the Egalitarian welfare maximizer, which prioritizes fairness. Furthermore, given several conventional assumptions, the proposed model selects the Nash welfare maximizer, an objective trade-off between efficiency and fairness, with moderate levels of uncertainty aversion. Lastly, we present numerical studies of two specific instances of the social choice problem—resource allocation and facility location—to show that, as uncertainty aversion increases, our model increasingly emphasizes fairness.