Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match
Executive Summary — One of the goals of school matching systems is to limit the extent to which students and parents feel it necessary to "game the system" to be accepted at a favored school. Several years ago, the authors of this paper assisted the New York City Department of Education in redesigning the way it matched over 90,000 students entering public high schools each year. The situation in New York City is a hybrid: Some schools actively rank potential students, others have no preferences, and still others fall in between. This paper concentrates on the welfare considerations and incentives that arise in school choice due to the fact that many students are regarded by schools as equivalent. The research develops and expands on economic theory demanded by the design of school choice mechanisms. Key concepts include:
- As economists are more often asked to design practical markets and allocation mechanisms, they will increasingly navigate two-way feedback between theory and design.
- The paper raises new theoretical questions. It would be helpful to have answers before the next major design or redesign of school matching systems.
The design of the New York City (NYC) High School match involved tradeoffs between incentives and efficiency, because some schools are strategic players that rank students in order of preference, while others order students based on large priority classes. Therefore it is desirable for a mechanism to produce stable matchings (to avoid giving the strategic players incentives to circumvent the match), but is also necessary to use tie-breaking for schools whose capacity is sufficient to accommodate some but not all students of a given priority class. We analyze a model that encompasses one-sided and two-sided matching models. We first observe that breaking indifferences the same way at every school is sufficient to produce the set of student optimal stable matchings. Our main theoretical result is that a student-proposing deferred acceptance mechanism that breaks indifferences the same way at every school is not dominated by any other mechanism that is strategy- proof for students. Finally, using data from the recent redesign of the NYC High School match, which places approximately 90,000 students per year, we document that the extent of potential efficiency loss is substantial. Over 6,800 student applicants in the main round of assignment could have improved their assignment in a (non strategy-proof) student optimal mechanism, if the same student preferences would have been revealed.