Dynamic Matching in School Choice: Efficient Seat Reassignment after Late Cancellations

68 Pages Posted: 28 Jun 2017 Last revised: 27 Feb 2019

See all articles by Itai Feigenbaum

Itai Feigenbaum

CUNY Lehman College

Yash Kanoria

Columbia Business School - Decision Risk and Operations

Irene Lo

Stanford

Jay Sethuraman

Columbia University

Date Written: June 27, 2017

Abstract

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 reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from NYC high school admissions support our theoretical findings.

Keywords: dynamic matching, matching markets, school choice, deferred acceptance, tie-breaking, cancellations, reassignments

JEL Classification: C78, C73, D47, D82, I28

Suggested Citation

Feigenbaum, Itai and Kanoria, Yash and Lo, Irene and Sethuraman, Jay, Dynamic Matching in School Choice: Efficient Seat Reassignment after Late Cancellations (June 27, 2017). Columbia Business School Research Paper No. 17-68. Available at SSRN: https://ssrn.com/abstract=2993375 or http://dx.doi.org/10.2139/ssrn.2993375

Itai Feigenbaum

CUNY Lehman College ( email )

Bronx, NY 10468
United States

Yash Kanoria

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Irene Lo (Contact Author)

Stanford ( email )

United States

Jay Sethuraman

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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