Ulric B. and Evelyn L. Bray Social Sciences Seminar
Abstract: We approach the problem of efficient matching in school choice by enforcing only priorities that can improve a student's match. A set of matchings is an admissible set iff it includes precisely those matchings with the property that any student whose priority is violated has no better matching in the set. It is shown that there is a unique admissible set, and so each matching in this set can be called admissible. Every stable matching (i.e., any matching without priority violations) is admissible and the admissible matchings form a lattice under the coordinatewise partial order defined by the students' preferences. So among all the admissible matchings, there is one that all of the students agree is best. Importantly, this student-optimal admissible matching is Pareto efficient. We also consider an alternative approach to efficient matching in school choice by defining a matching µ to be priority-neutral iff it is not possible to make any student whose priority is violated by µ better off without violating the priority of some student who is made worse off. It is shown that there is a unique Pareto efficient priority-neutral matching and that it in fact coincides with the unique student-optimal admissible matching.
Professor Reny will be joined by guests Tayfun Sönmez and Utku Ünver.