On Fairness and Stability in Two-Sided Matchings

Abstract

There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in the context of a two-sided market, where there are two sets of agents, and each agent has preferences over the other set. The goal is producing a matching between the sets. Throughout this work, we use the example of matching medical residents (who we call "doctors") to hospitals. This setting has been the focus of a rich body of work. The seminal work of Gale and Shapley formulated a stability desideratum, and showed that a stable matching always exists and can be found in polynomial time.With fairness concerns in mind, it is natural to ask: might a stable matching be discriminatory towards some of the doctors? How can we obtain a fair matching? The question is interesting both when hospital preferences might be discriminatory, and also when each hospital's preferences are fair.We study this question through the lens of metric-based fairness notions (Dwork et al. [ITCS 2012] and Kim et al. [ITCS 2020]). We formulate appropriate definitions of fairness and stability in the presence of a similarity metric, and ask: does a fair and stable matching always exist? Can such a matching be found in polynomial time? Can classical Gale-Shapley algorithms find such a matching? Our contribution are as follows: