Peer Preferences in Centralized School Choice Markets

School-choice clearinghouses often advise students to "rank their true preferences" despite not allowing students to express preferences over peers. We evaluate the consequences of doing so. Empirically, we find students have preferences over relative peer ability in the college admissions market in New South Wales, Australia. Theoretically, we show stable matchings exist even with peer preferences under mild conditions, but finding one via one-shot mechanisms is unlikely. The status quo procedure frequently employed by clearinghouses is to inform applicants about the assignment of students in the previous cohort, inducing a tâtonnement process which potentially provides useful information about likely peers in the current cohort. We theoretically argue this process likely leads to an unstable outcome, and we find instability in our empirical setting. We propose a mechanism that yields stability and incentivizes truthful reporting in the presence of peer preferences.