IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2504.09357.html

A Unified Theory of School Choice

Author

Listed:
  • Peter Doe

Abstract

In school choice, policymakers consolidate a district's objectives for a school into a priority ordering over students. They then face a trade-off between respecting these priorities and assigning students to more-preferred schools. However, because priorities are the amalgamation of multiple policy goals, some may be more flexible than others. This paper introduces a model that distinguishes between two types of priority: a between-group priority that ranks groups of students and must be respected, and a within-group priority for efficiently allocating seats within each group. The solution I introduce, the unified core, integrates both types. I provide a two-stage algorithm, the DA-TTC, that implements the unified core and generalizes both the Deferred Acceptance and Top Trading Cycles algorithms. This approach provides a method for improving efficiency in school choice while honoring policymakers' objectives.

Suggested Citation

  • Peter Doe, 2025. "A Unified Theory of School Choice," Papers 2504.09357, arXiv.org.
    • Handle: RePEc:arx:papers:2504.09357
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2504.09357
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    2. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    3. Dur, Umut & Paiement, Scott, 2024. "A characterization of the top trading cycles mechanism for the school choice problem," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 93-100.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Onur Kesten, 2012. "On two kinds of manipulation for school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 677-693, November.
    2. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    3. Yao Cheng & Zaifu Yang, "undated". "Stable Matching Mechanisms under Distributional Constraints," Discussion Papers 23/03, Department of Economics, University of York.
    4. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    5. Haeringer, Guillaume & Iehlé, Vincent, 2021. "Gradual college admission," Journal of Economic Theory, Elsevier, vol. 198(C).
    6. Siwei Chen & Yajing Chen & Chia‐Ling Hsu, 2023. "New axioms for top trading cycles," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1064-1077, October.
    7. Jiarui Xie, 2024. "Games under the Tiered Deferred Acceptance Mechanism," Papers 2406.00455, arXiv.org, revised Oct 2024.
    8. Bando, Keisuke, 2014. "On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 87(C), pages 269-287.
    9. Mustafa Oǧuz Afacan, 2024. "Dorm augmented college assignments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(3), pages 609-627, May.
    10. Turhan, Bertan, 2019. "Welfare and incentives in partitioned school choice markets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 199-208.
    11. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    12. Ortega, Josué & Klein, Thilo, 2023. "The cost of strategy-proofness in school choice," Games and Economic Behavior, Elsevier, vol. 141(C), pages 515-528.
    13. Arribillaga, R. Pablo & Pepa Risma, Eliana, 2025. "Obvious manipulations in matching with and without contracts," Games and Economic Behavior, Elsevier, vol. 151(C), pages 70-81.
    14. Li, Mengling, 2020. "Ties matter: Improving efficiency in course allocation by allowing ties," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 354-384.
    15. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    16. Vincent Iehlé, 2016. "Gradual College Admisssion," Post-Print halshs-02367006, HAL.
    17. Benoit Decerf & Guillaume Haeringer & Martin Van der Linden, 2024. "Incontestable Assignments," Papers 2401.03598, arXiv.org, revised Feb 2024.
    18. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    19. Cai, Zhengyang, 2025. "The manipulability of the deferred acceptance mechanism without outside options," Economics Letters, Elsevier, vol. 254(C).
    20. Muriel Niederle & Alvin E. Roth, 2009. "The Effects of a Centralized Clearinghouse on Job Placement, Wages, and Hiring Practices," NBER Chapters, in: Studies of Labor Market Intermediation, pages 235-271, National Bureau of Economic Research, Inc.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2504.09357. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.