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A theory of school choice lotteries

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  • Kesten, Onur

    () (Tepper School of Business, Carnegie Mellon University)

  • Ünver, M. Utku

    () (Department of Economics, Boston College)

Abstract

A new mechanism was introduced in New York City and Boston to assign students to public schools. This mechanism was advocated for its superior fairness property, besides others. We introduce a new framework for school-choice problems and two notions of fairness in lottery design based on ex-ante stability. This framework unifies known many-to-one and one-sided matching models. We show that the NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, one that is ordinally Pareto-dominant within the class of strongly ex-ante stable mechanisms and one that satisfies ex-ante stability, equal treatment, and constrained ordinal-Pareto-efficiency.

Suggested Citation

  • Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
  • Handle: RePEc:the:publsh:1558
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    Citations

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    Cited by:

    1. Wonki Jo Cho & Battal Doğan, 2017. "Stability and the immediate acceptance rule when school priorities are weak," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 991-1014, November.
    2. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    3. Clayton Featherstone & Muriel Niederle, 2008. "Ex Ante Efficiency in School Choice Mechanisms: An Experimental Investigation," NBER Working Papers 14618, National Bureau of Economic Research, Inc.
    4. Jan Christoph Schlegel, 2016. "Ex-Ante Stable Lotteries," Cahiers de Recherches Economiques du Département d'économie 16.23, Université de Lausanne, Faculté des HEC, Département d’économie.
    5. Doğan, Battal & Yıldız, Kemal, 2016. "Efficiency and stability of probabilistic assignments in marriage problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 47-58.
    6. Duddy, Conal, 2017. "The structure of priority in the school choice problem," MPRA Paper 81057, University Library of Munich, Germany.
    7. Vergote, W., 2015. "One-to-One Matching Problems with Location Restrictions," CORE Discussion Papers 2015054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    9. Fuhito Kojima & M. Utku Ünver, 2010. "The 'Boston' School-Choice Mechanism," Boston College Working Papers in Economics 729, Boston College Department of Economics, revised 08 Oct 2010.
    10. Tommy ANDERSSON & Ágnes CSEH & Lars EHLERS & Albin ERLANSON, 2018. "Organizing Time Banks : Lessons from Matching Markets," Cahiers de recherche 11-2018, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Antonio Miralles, "undated". "Pseudomarkets with Priorities in Large Random Assignment Economies," Working Papers 537, Barcelona Graduate School of Economics.
    12. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org.
    13. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    14. 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.
    15. Schlegel, J. C. & Mamageishvili, A., 2017. "Welfare theorems for random assignments with priorities," Working Papers 17/05, Department of Economics, City University London.
    16. repec:eee:gamebe:v:110:y:2018:i:c:p:71-89 is not listed on IDEAS
    17. Wouter Vergote, 2019. "Revisiting stability in one-to-one matching problems," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 59-75, May.
    18. Haris Aziz & Bettina Klaus, 2017. "Random Matching under Priorities: Stability and No Envy Concepts," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 17.09, Université de Lausanne, Faculté des HEC, DEEP.
    19. Haris Aziz & Bettina Klaus, 2019. "Random matching under priorities: stability and no envy concepts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 213-259, August.
    20. Hafalir, Isa Emin & Yenmez, M. Bumin & Yildirim, Muhammed Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    21. Schlegel, Jan Christoph, 2018. "A note on ex-ante stable lotteries," Economics Letters, Elsevier, vol. 164(C), pages 90-93.
    22. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Ünver, M. Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    23. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    24. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    25. repec:eee:gamebe:v:117:y:2019:i:c:p:120-143 is not listed on IDEAS

    More about this item

    Keywords

    Matching; school choice; deferred acceptance; stability; ordinal efficiency; market design;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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