Optimal matchings with one-sided preferences: fixed and cost-based quotas

Santhini K. A., Govind S. Sankar, Meghana Nasre

Abstract: We consider the well-studied many-to-one bipartite matching problem of assigning applicants \({\varvec{\mathcal {A}}}\) to posts \({\varvec{\mathcal {P}}}\) where applicants rank posts in the order of preference. This setting models many important real-world allocation problems like assigning students to courses, applicants to jobs, amongst many others. In such scenarios, it is natural to ask for an allocation that satisfies guarantees of the form “match at least 80% of applicants to one of their top three choices” or “it is unacceptable to leave more than 10% of applicants unassigned”. The well-studied notions of rank-maximality and fairness fail to capture such requirements due to their property of optimizing extreme ends of the signature of a matching. We, therefore, propose a novel optimality criterion, which we call the “weak dominance ” of ranks.