Strategyproofness Versus Efficiency in Matching With Indifferences: Redesigning the NYC High School Match
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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 strategyproof 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.
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