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Lotteries in student assignment: An equivalence result

Author

Listed:
  • Pathak, Parag A.

    () (Department of Economics, Massachusetts Institute of Technology)

  • Sethuraman, Jay

    () (Department of Industrial Engineering and Operations Research, Columbia University,)

Abstract

This paper formally examines two competing methods of conducting a lottery in assigning students to schools, motivated by the design of the centralized high school student assignment system in New York City. The main result of the paper is that a single and multiple lottery mechanism are equivalent for the problem of allocating students to schools in which students have strict preferences and the schools are indifferent. In proving this result, a new approach is introduced, that simplifies and unifies all the known equivalence results in the house allocation literature. Along the way, two new mechanisms---Partitioned Random Priority and Partitioned Random Endowment---are introduced for the house allocation problem. These mechanisms generalize widely studied mechanisms for the house allocation problem and may be appropriate for the many-to-one setting such as the school choice problem.

Suggested Citation

  • Pathak, Parag A. & Sethuraman, Jay, 2011. "Lotteries in student assignment: An equivalence result," Theoretical Economics, Econometric Society, vol. 6(1), January.
  • Handle: RePEc:the:publsh:816
    as

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    References listed on IDEAS

    as
    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
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    Citations

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    Cited by:

    1. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    2. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    3. repec:jmi:articl:jmi-v2i1a3 is not listed on IDEAS
    4. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    5. Aytek Erdil, 2013. "Strategy-Proof Stochastic Assignment," Cambridge Working Papers in Economics 1333, Faculty of Economics, University of Cambridge.
    6. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    7. 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.
    8. 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.
    9. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    10. Christian Basteck, 2016. "Fair solutions to the random assignment problem," Working Papers 2016001, Berlin Doctoral Program in Economics and Management Science (BDPEMS).
    11. Carroll, Gabriel, 2014. "A general equivalence theorem for allocation of indivisible objects," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 163-177.
    12. repec:wly:emetrp:v:85:y:2017:i::p:1373-1432 is not listed on IDEAS
    13. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    14. Atila Abdulkadiroğlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation," Econometrica, Econometric Society, vol. 85, pages 1373-1432, September.
    15. repec:eee:jetheo:v:170:y:2017:i:c:p:145-168 is not listed on IDEAS
    16. André Schmelzer, 2016. "Single versus Multiple Randomization in Matching Mechanisms," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2016_08, Max Planck Institute for Research on Collective Goods, revised Mar 2017.
    17. Sophie Bade, 2016. "Pareto-optimal matching allocation mechanisms for boundedly rational agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 501-510, October.
    18. repec:eee:gamebe:v:103:y:2017:i:c:p:94-115 is not listed on IDEAS
    19. 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.

    More about this item

    Keywords

    Matching; random assignment;

    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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