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In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful, and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the permuted lottery deferred acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used deferred acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second-round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare and that reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from New York City high school admissions support our theoretical findings. This paper was accepted by Gad Allon, operations management.

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esidency and fellowship candidates are applying to more programs to enhance their chances of securing interviews and matching favorably. The COVID-19 pandemic has shifted interviews to video formats, which lowers interviewassociated costs for applicants but may further increase application numbers. 1 While a candidate's application to a training program communicates some interest in the program, the relative amount of interest is obscured when candidates apply to large numbers of programs. We suspect that, as a result, programs host large numbers of low-yield interviews.The number of interviews is steadily increasing, and there is widespread agreement on the need to ease congestion in the pre-Match evaluation process. 2 Proposals to reduce this burden include signaling (organized, centrally-controlled protocol for limited communication of interest), [3][4][5] capping the number of applications or the number of interviews, 6,7 and an early acceptance matching program as in college admissions. 8,9 We propose another solution, an ''interview match'' to address the expanding number of interviews. 10 An interview match enables candidates and programs to express preferences privately by ranking their interview choices individually or in tiers. This may ease congestion in the ''marketplace,'' reduce costs for candidates, favor interviews that are more likely to lead to a match in the final Match, and avoid interviews unlikely to convert to a match. An interview match algorithm would match based on the same ''deferred-acceptance'' algorithm currently used by the National Resident Matching Program but adapted to a ''many-to-many'' setting where candidates and programs receive multiple interviews. 11,12 In brief, the algorithm assigns candidates to their top preference interview positions, and the programs temporarily retain those assigned candidates who coincide with their preferred (top) candidates, while rejecting those candidates who exceed the program's interview capacity. The ''rejected'' interview match candidates are then assigned to their next most preferred program on their interview match ranking lists, and so on.In this Perspective, we present 2 simplified scenarios to illustrate the potential to minimize low-yield interviews and some of the challenges to be considered when implementing an interview match. We then briefly discuss the advantages of an interview match over other proposals.

This paper develops a tractable theoretical framework for the Top Trading Cycles (TTC) mechanism for school choice that allows quantifying welfare and optimizing policy decisions. We compute welfare for TTC and Deferred Acceptance (DA) under different priority structures, and find that the choice of priorities can have larger welfare implications than the choice of mechanism. We solve for the welfare-maximizing distributions of school quality for parametrized economies, and find that optimal investment decisions can be very different under TTC and DA. Our framework relies on a novel characterization of the TTC assignment in terms of a cutoff for each pair of schools. These cutoffs parallel prices in competitive equilibrium, with students’ priorities serving the role of endowments. We show that these cutoffs can be computed directly from the distribution of preferences and priorities in a continuum model, and derive closed-form solutions and comparative statics for parameterized settings. The TTC cutoffs clarify the role of priorities in determining the TTC assignment, but also demonstrate that TTC is more complicated than DA.