On Achieving Leximin Fairness and Stability in Many-to-One Matchings

The past few years have seen a surge of work on fairness in allocation problems where items must be fairly divided among agents having individual preferences. In comparison, fairness in matching settings with preferences on both sides, that is, where agents have to be matched to other agents, has received much less attention. Moreover, the two-sided matching literature has largely focused on ordinal preferences. We study leximin optimality over stable many-to-one matchings under cardinal preferences. We first investigate matching problems with ranked valuations for which we give efficient algorithms to find the leximin optimal matching over the space of stable matchings. We complement these results by showing that relaxing the ranked valuations condition in any way, makes finding the leximin optimal stable matching intractable.