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Median Stable Matching for College Admission

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Abstract

We give a simple and concise proof that so-called generalized median stable matchings are well-defined stable matchings 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," UFAE and IAE Working Papers 632.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 16 Feb 2006.
  • Handle: RePEc:aub:autbar:632.04
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    References listed on IDEAS

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    1. Bettina Klaus & Flip Klijn, 2006. "Procedurally fair and stable matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 431-447, January.
    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, May.
    3. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    4. Jinpeng Ma, 1996. "On randomized matching mechanisms (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-381.
    5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    6. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    8. 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.
    9. 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.
    10. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-570, May.
    11. 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. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
    2. 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.
    3. 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.
    4. 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.
    5. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," UFAE and IAE Working Papers 706.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 27-33.
    7. Martin Van der linden, 2016. "Deferred acceptance is minimally manipulable," Vanderbilt University Department of Economics Working Papers 16-00019, Vanderbilt University Department of Economics.
    8. Horstschräer, Julia, 2012. "Decentralizing university admission: Evidence from a natural experiment," ZEW Discussion Papers 12-076, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    9. 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.
    10. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.

    More about this item

    Keywords

    Matching; College admissions problem; Stability; Fairness.;

    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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