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A Theory of School-Choice Lotteries

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  • 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.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 737.

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Date of creation: 01 May 2010
Date of revision: 29 Jun 2012
Handle: RePEc:boc:bocoec:737

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Related research

Keywords: Matching; School Choice; Deferred Acceptance; Stability; Ordinal Efficiency; Market Design;

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References

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  1. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-52, September.
  2. Athanassoglou, Stergios & Sethuraman, Jay, 2010. "House allocation with fractional endowments," MPRA Paper 24351, University Library of Munich, Germany.
  3. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, 01.
  4. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
  5. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
  6. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
  7. Haluk Ergin & Tayfun Sönmez, 2005. "Games of School Choice under the Boston Mechanism," Boston College Working Papers in Economics 619, Boston College Department of Economics.
  8. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics.
  9. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
  10. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2008. "Constrained School Choice: An Experimental Study," UFAE and IAE Working Papers 757.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
  12. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
  13. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
  14. Abdulkadiroglu, Atila & Pathak, Parag Abishek & Roth, Alvin E., 2009. "Strategy-Proofness Versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," Scholarly Articles 11077572, Harvard University Department of Economics.
  15. Yan Chen & Tayfun Sönmez, 2004. "School Choice: An Experimental Study," Boston College Working Papers in Economics 622, Boston College Department of Economics.
  16. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  17. Guillaume Haeringer & Flip Klijn, 2006. "Constrained School Choice," UFAE and IAE Working Papers 671.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 02 Dec 2008.
  18. 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.
  19. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 2006-04, Universite de Montreal, Departement de sciences economiques.
  20. Pais, Joana & Pintér, Ágnes, 2008. "School choice and information: An experimental study on matching mechanisms," Games and Economic Behavior, Elsevier, vol. 64(1), pages 303-328, September.
  21. Pathak, Parag A. & Sethuraman, Jay, 2011. "Lotteries in student assignment: An equivalence result," Theoretical Economics, Econometric Society, vol. 6(1), January.
  22. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
  23. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
  24. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
  25. 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 1954-78, December.
  26. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, MIT Press, vol. 125(3), pages 1297-1348, August.
  27. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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Citations

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Cited by:
  1. Antonio Miralles, 2011. "Pseudomarkets with Priorities in Large Random Assignment Economies," Working Papers 537, Barcelona Graduate School of Economics.
  2. 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.
  3. 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.
  4. 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 1954-78, December.
  5. 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.

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