Fairness in Matching under Uncertainty

TL;DR

This paper introduces a fairness framework for two-sided marketplaces that accounts for uncertainty in individual merits, using axioms and linear programming to ensure fair and robust allocations.

Contribution

It axiomatizes a notion of individual fairness considering merit uncertainty and develops a linear programming method for fair, utility-maximizing, and robust allocations.

Findings

The linear program effectively finds fair distributions under uncertain merits.

The approach is robust to parameter estimation errors.

It integrates well with machine learning for merit inference.

Abstract

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always \emph{uncertain}, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.