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Median Stable Matching for College Admission

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  • Bettina Klaus
  • Flip Klijn

Abstract

We give a simple and concise proof that so-called generalized median stable matchings are well-defined for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings.

Suggested Citation

  • Bettina Klaus & Flip Klijn, 2004. "Median Stable Matching for College Admission," Working Papers 165, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:165
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    References listed on IDEAS

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    11. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
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    13. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
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    Cited by:

    1. Chen, Peter & Egesdal, Michael & Pycia, Marek & Yenmez, M. Bumin, 2016. "Median stable matchings in two-sided markets," Games and Economic Behavior, Elsevier, vol. 97(C), pages 64-69.
    2. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, vol. 12(2), pages 1-15, April.
    3. Shuji Kijima & Toshio Nemoto, 2012. "On Randomized Approximation for Finding a Level Ideal of a Poset and the Generalized Median Stable Matchings," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 356-371, May.
    4. Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 27-33.
    5. Martin Van der Linden, 2019. "Deferred acceptance is minimally manipulable," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 609-645, June.
    6. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," Working Papers 315, Barcelona School of Economics.
    7. Greg Leo & Jian Lou & Martin Van der Linden & Yevgeniy Vorobeychik & Myrna Wooders, 2021. "Matching soulmates," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 822-857, October.
    8. Christian Haas, 2021. "Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1115-1148, April.
    9. Horstschräer, Julia, 2012. "Decentralizing university admission: Evidence from a natural experiment," ZEW Discussion Papers 12-076, ZEW - Leibniz Centre for European Economic Research.
    10. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
    11. Mukherjee, Saptarshi & Muto, Nozomu & Sen, Arunava, 2024. "Implementation in undominated strategies with applications to auction design, public good provision and matching," Journal of Economic Theory, Elsevier, vol. 216(C).
    12. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
    13. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
    14. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
    15. Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, vol. 146(2), pages 619-637, March.
    16. Peng, Zixuan & Shan, Wenxuan & Zhu, Xiaoning & Yu, Bin, 2022. "Many-to-one stable matching for taxi-sharing service with selfish players," Transportation Research Part A: Policy and Practice, Elsevier, vol. 160(C), pages 255-279.
    17. Yang Liu & Zhi-Ping Fan & Yan-Ping Jiang, 2018. "Satisfied surgeon–patient matching: a model-based method," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(6), pages 2871-2891, November.
    18. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
    19. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2021. "Quantile Stable Mechanisms," Games, MDPI, vol. 12(2), pages 1-9, May.
    20. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.

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    More about this item

    Keywords

    Matching; College admissions problem; stability; fairness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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