School Composition and Improvements over Deferred Acceptance

Abstract

School choice mechanisms determine not only where students study but also who their classmates are. Deferred acceptance (DA) protects families in this regard through local non-bossiness: a student who keeps her school cannot alter its cohort by misreporting her ranking. This paper examines whether the protection persists under reforms designed to correct DA’s inefficiency, and concludes that it does not. Any mechanism that yields a Pareto improvement over DA whenever one exists fails to be locally non-bossy in every problem with a separating double rotation, a configuration of priorities and capacities that arises under random priorities in most large markets. Efficiency-adjusted deferred acceptance loses the protection once two identified students consent and, in large markets, with probability approaching one when a fixed fraction of students chosen independently of priorities consents. We also show how the consequences of this manipulation for segregation depend on how student types relate to priorities.