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Assigning more students to their top choices: A comparison of tie-breaking rules

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  • Ashlagi, Itai
  • Nikzad, Afshin
  • Romm, Assaf

Abstract

School districts that implement stable matchings face various decisions that affect students' assignments to schools. We study the properties of the rank distribution of students with random preferences when schools use different tie-breaking rules to rank equivalent students. Under a single tie-breaking rule, where all schools use the same ranking, a constant fraction of students are assigned to one of their top choices. In contrast, under a multiple tie-breaking rule, where each school independently ranks students, a vanishing fraction of students are matched with one of their top choices. However, if students are allowed to submit only relatively short preference lists under a multiple tie-breaking rule, a constant fraction of students will be matched with one of their top choices, while only a “small” fraction of students will remain unmatched.

Suggested Citation

  • Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.
    • Handle: RePEc:eee:gamebe:v:115:y:2019:i:c:p:167-187
    DOI: 10.1016/j.geb.2019.02.015
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Amel Awadelkarim & Arjun Seshadri & Itai Ashlagi & Irene Lo & Johan Ugander, 2023. "Rank-heterogeneous Preference Models for School Choice," Papers 2306.01801, arXiv.org.
    2. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    3. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    4. Alex Rees-Jones & Ran Shorrer & Chloe J. Tergiman, 2020. "Correlation Neglect in Student-to-School Matching," NBER Working Papers 26734, National Bureau of Economic Research, Inc.
    5. Allman, Maxwell & Ashlagi, Itai & Nikzad, Afshin, 2023. "On rank dominance of tie-breaking rules," Theoretical Economics, Econometric Society, vol. 18(2), May.
    6. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    7. Nick Arnosti, 2022. "A Continuum Model of Stable Matching With Finite Capacities," Papers 2205.12881, arXiv.org.
    8. Yeon-Koo Che & Olivier Tercieux, 2019. "Efficiency and Stability in Large Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 2301-2342.
    9. Nick Arnosti, 2023. "Lottery Design for School Choice," Management Science, INFORMS, vol. 69(1), pages 244-259, January.
    10. Ashlagi, Itai & Nikzad, Afshin, 2020. "What matters in school choice tie-breaking? How competition guides design," Journal of Economic Theory, Elsevier, vol. 190(C).
    11. Itai Feigenbaum & Yash Kanoria & Irene Lo & Jay Sethuraman, 2020. "Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations," Management Science, INFORMS, vol. 66(11), pages 5341-5361, November.
    12. 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.
    13. Kenny Peng & Nikhil Garg, 2023. "Monoculture in Matching Markets," Papers 2312.09841, arXiv.org.
    14. Mustafa Oğuz Afacan & Umut Dur, 2023. "Strategy‐proof size improvement: is it possible?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 321-338, April.
    15. Carmelo Rodríguez-Álvarez & Antonio Romero-Medina, 2023. "The implicit (un)healthy life expectancy used for pricing long-term care insurance and life care annuities," Documentos de Trabajo del ICAE 2023-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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    More about this item

    Keywords

    School choice; Tie-breaking rule; Deferred acceptance; Stable matching;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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