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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.

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  • 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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    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. Daniel Kornbluth & Alexey Kushnir, 2024. "Undergraduate Course Allocation through Competitive Markets," Papers 2412.05691, arXiv.org.
    4. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    5. Basteck, Christian, 2024. "An axiomatization of the random priority rule," Discussion Papers, Research Unit: Market Behavior SP II 2024-201, WZB Berlin Social Science Center.
    6. Basteck, Christian & Ehlers, Lars, 2024. "On (constrained) Efficiency of strategy-proof random assignment," VfS Annual Conference 2024 (Berlin): Upcoming Labor Market Challenges 302429, Verein für Socialpolitik / German Economic Association.
    7. Alex Rees-Jones & Ran Shorrer & Chloe Tergiman, 2024. "Correlation Neglect in Student-to-School Matching," American Economic Journal: Microeconomics, American Economic Association, vol. 16(3), pages 1-42, August.
    8. Allman, Maxwell & Ashlagi, Itai & Nikzad, Afshin, 2023. "On rank dominance of tie-breaking rules," Theoretical Economics, Econometric Society, vol. 18(2), May.
    9. 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.
    10. Nick Arnosti, 2022. "A Continuum Model of Stable Matching With Finite Capacities," Papers 2205.12881, arXiv.org.
    11. 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.
    12. Nick Arnosti, 2023. "Lottery Design for School Choice," Management Science, INFORMS, vol. 69(1), pages 244-259, January.
    13. Han, Xiang, 2024. "On the efficiency and fairness of deferred acceptance with single tie-breaking," Journal of Economic Theory, Elsevier, vol. 218(C).
    14. Ashlagi, Itai & Nikzad, Afshin, 2020. "What matters in school choice tie-breaking? How competition guides design," Journal of Economic Theory, Elsevier, vol. 190(C).
    15. 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.
    16. 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.
    17. Christian Basteck, 2024. "An Axiomatization of the Random Priority Rule," Rationality and Competition Discussion Paper Series 502, CRC TRR 190 Rationality and Competition.
    18. Kenny Peng & Nikhil Garg, 2023. "Monoculture in Matching Markets," Papers 2312.09841, arXiv.org.
    19. 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.
    20. 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.
    21. Peng Shi, 2022. "Optimal Priority-Based Allocation Mechanisms," Management Science, INFORMS, vol. 68(1), pages 171-188, January.

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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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