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What Matters in School Choice Tie-breakings?: How Competition Guides Design

Published: 21 July 2016 Publication History

Abstract

School districts that adopt the Deferred Acceptance (DA) mechanism to assign students to schools face the tradeoff between fairness and efficiency when selecting how to exogenously break ties among equivalent students. We analyze a model with random generated preferences for students and compare two tie-breaking rules: a single lottery (STB) and DA with a separate lottery for each school (MTB). We consider three different notions for this comparison: stochastic dominance of rank distributions, variance of students' ranks, and number of Pareto improving pairs (pairs of students whom would be better off by swapping their positions).
We identify that the balance between supply and demand is the determinant factor in these comparisons. When there is a shortage of seats, the rank distribution under STB stochastically dominates the rank distribution under MTB, and also, has a smaller variance. In addition, MTB creates ``many'' Pareto improving pairs, while STB creates none.
When there is a surplus of seats, we show that neither random assignment under these mechanisms stochastically dominates the other, variance of the rank distribution is lower under MTB, and MTB generates few Pareto improving pairs. Our findings imply that ``popular" schools should use a single common lottery to break ties. Finally, numerical experiments using NYC school choice data confirm our predictions.

References

[1]
Atila Abdulkadiro\uglu and Tayfun Sönmez. School choice: A mechanism design approach. The American Economic Review, 93 (3): 729--747, 2003. ISSN 00028282.
[2]
Atila Abdulkadiro\uglu, Parag A Pathak, and Alvin E Roth. Strategy-proofness versus efficiency in matching with indifferences: Redesigning the nyc high school match. The American Economic Review, pages 1954--1978, 2009.
[3]
Monique De Haan, Pieter A Gautier, Hessel Oosterbeek, Bas Van der Klaauw, et al. The performance of school assignment mechanisms in practice. Technical report, CEPR Discussion Papers, 2015.

Cited By

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  • (2023)On rank dominance of tie‐breaking rulesTheoretical Economics10.3982/TE476218:2(707-748)Online publication date: 2023
  • (2021)In which matching markets does the short side enjoy an advantage?Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458147(1374-1386)Online publication date: 10-Jan-2021
  • (2020)Dynamic Matching in School Choice: Efficient Seat Reassignment After Late CancellationsManagement Science10.1287/mnsc.2019.3469Online publication date: 8-May-2020
  • Show More Cited By

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cover image ACM Conferences
EC '16: Proceedings of the 2016 ACM Conference on Economics and Computation
July 2016
874 pages
ISBN:9781450339360
DOI:10.1145/2940716
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Publication History

Published: 21 July 2016

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  1. galton watson multitype branching process
  2. random graphs

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EC '16
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EC '16: ACM Conference on Economics and Computation
July 24 - 28, 2016
Maastricht, The Netherlands

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EC '16 Paper Acceptance Rate 80 of 242 submissions, 33%;
Overall Acceptance Rate 664 of 2,389 submissions, 28%

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Cited By

View all
  • (2023)On rank dominance of tie‐breaking rulesTheoretical Economics10.3982/TE476218:2(707-748)Online publication date: 2023
  • (2021)In which matching markets does the short side enjoy an advantage?Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458147(1374-1386)Online publication date: 10-Jan-2021
  • (2020)Dynamic Matching in School Choice: Efficient Seat Reassignment After Late CancellationsManagement Science10.1287/mnsc.2019.3469Online publication date: 8-May-2020
  • (undefined)'Strategic' Behavior in a Strategy-Proof EnvironmentSSRN Electronic Journal10.2139/ssrn.2784659

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