The High Cost of Stability in Two-Sided Matching: How Much Social Welfare Should be Sacrificed in the Pursuit of Stability?

New results on a class of distributed two-sided matching algorithms are described. In particular, these algorithms can dominate the matches produced by the Gale-Shapley algorithm in terms of both average social welfare and fairness. However, stability is not guaranteed and therefore a natural tradeoff arises between stability and social welfare. At one extreme, stability is ‘purchased’ in Gale-Shapley by significant welfare losses. At the other extreme, matches yielding high social welfare are vulnerable to unraveling when information costs—basically, the cost of acquiring others’ ranks—are small. In the face of either large information costs or a ‘veil of ignorance’ for match participants, it may be easy to justify matches that are not stable. Computational evidence is provided that these extreme Gale-Shapley matchings are brittle in the sense of being not robust to ostensibly minor perturbations. We argue that the nearly universal focus on stable matchings in this literature is misguided at best. As a positive description of any human social process, such as marriage matching or college admissions, Gale-Shapley and related centralized, synchronized algorithms are hopelessly flawed. As normative devices for achieving social good they explore only a tiny part of the Pareto frontier that trades-off stability for welfare, and so do not serve as robust design tools.