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A Theory of School-Choice Lotteries

Author

Listed:
  • Onur Kesten

    () (Carnegie Mellon University)

  • M. Utku Ünver

    (Boston College)

Abstract

A new centralized mechanism was introduced in New York City and Boston to assign students to public schools in district school-choice programs. This mechanism was advocated for its superior fairness property, besides others, over the mechanisms it replaced. In this paper, we introduce a new framework for investigating school-choice matching problems and two ex-ante notions of fairness in lottery design, strong ex-ante stability and ex-ante stability. This frame- work generalizes known one-to-many two-sided and one-sided matching models. We first show that the new NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, the fractional deferred-acceptance mechanism, which is ordinally Pareto dominant within the class of strongly ex-ante stable mechanisms, and the fractional deferred- acceptance and trading mechanism, which satisfies equal treatment of equals and constrained ordinal Pareto efficiency within the class of ex-ante stable mechanisms.

Suggested Citation

  • Onur Kesten & M. Utku Ünver, 2010. "A Theory of School-Choice Lotteries," Boston College Working Papers in Economics 737, Boston College Department of Economics, revised 29 Jun 2012.
  • Handle: RePEc:boc:bocoec:737
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-016-0562-6 is not listed on IDEAS
    3. 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.
    4. Schlegel, J. C., 2017. "Welfare theorems for random assignments with priorities," Working Papers 17/05, Department of Economics, City University London.
    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. Antonio Miralles, "undated". "Pseudomarkets with Priorities in Large Random Assignment Economies," Working Papers 537, Barcelona Graduate School of Economics.
    7. Duddy, Conal, 2017. "The structure of priority in the school choice problem," MPRA Paper 81057, University Library of Munich, Germany.
    8. Schlegel, J. C., 2017. "A Note on Ex-Ante Stable Lotteries," Working Papers 17/06, Department of Economics, City University London.
    9. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Jan Christoph Schlegel, 2016. "Ex-Ante Stable Lotteries," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 16.23, Université de Lausanne, Faculté des HEC, DEEP.
    16. Hafalir, Isa Emin & Yenmez, M. Bumin & Yildirim, Muhammed Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    17. repec:eee:ecolet:v:164:y:2018:i:c:p:90-93 is not listed on IDEAS
    18. 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.
    19. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.

    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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