School Choice Mechanism with Partial Preferences

Abstract

The traditional two-sided matching problems assume that all agents fully know their own preferences. As markets grow large, however, it becomes impractical for agents to precisely assess their rankings over all agents on the other side of the market. In this paper, we consider a school choice problem with partial preferences which are not strictly orderings. The complete preferences are learned through interviews, revealing the pairwise rankings among all interviewed agents. In many real-world settings, however, it is natural to consider that it will cost to perform interviews. Therefore, we require the policy that guarantees the student-optimal matching and minimizes the number of interviews. In the one-to-one matching problem, there exists a mechanism which works when all schools have the same partial preference. We relax that requirement and then extend to the many-to-one matching problems. Under that settings, we develop Lazy Deferred Acceptance mechanism (LDA) which yields the student-optimal matching with minimum interviews.