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Minimal consistent enlargements of the immediate acceptance rule and the top trading cycles rule in school choice

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  • Paula Jaramillo

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Abstract

We consider school choice problems. We are interested in solutions that satisfy consistency. Consider a problem and a recommendation made by the solution for the problem. Suppose some students are removed with their positions in schools. Consider the “reduced” problem consisting of the remaining students and the remaining positions. Consistency states that in the reduced problem, the solution should assign each remaining student to the same school as initially. Neither the immediate acceptance rule (also known as the Boston mechanism) nor the top trading cycles rule is consistent. We show that the efficient solution is the smallest consistent solution containing the immediate acceptance rule. It is also the smallest consistent solution containing the top trading cycles rule.

Suggested Citation

  • Paula Jaramillo, 2014. "Minimal consistent enlargements of the immediate acceptance rule and the top trading cycles rule in school choice," DOCUMENTOS CEDE 012343, UNIVERSIDAD DE LOS ANDES-CEDE.
  • Handle: RePEc:col:000089:012343
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    1. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    2. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    3. Parag A. Pathak, 2011. "The Mechanism Design Approach to Student Assignment," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 513-536, September.
    4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    5. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
    6. Burak Can & Bettina Klaus, 2013. "Consistency and population sensitivity properties in marriage and roommate markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 835-862, October.
    7. 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.
    8. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
    9. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 13-31, April.
    10. Chen, Yan & Onur, Kesten, 2013. "From Boston to Chinese parallel to deferred acceptance: Theory and experiments on a family of school choice mechanisms," Discussion Papers, Research Unit: Market Behavior SP II 2013-205, Social Science Research Center Berlin (WZB).
    11. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics.
    12. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    13. Sönmez, Tayfun & Ünver, M. Utku, 2010. "House allocation with existing tenants: A characterization," Games and Economic Behavior, Elsevier, vol. 69(2), pages 425-445, July.
    14. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    15. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    16. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 113-126, January.
    17. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    18. Thomson, William, 1994. "Consistent extensions," Mathematical Social Sciences, Elsevier, vol. 28(1), pages 35-49, August.
    19. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    20. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
    21. Kumano, Taro, 2013. "Strategy-proofness and stability of the Boston mechanism: An almost impossibility result," Journal of Public Economics, Elsevier, vol. 105(C), pages 23-29.
    22. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
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    Keywords

    school choice; consistency; Boston mechanism; top trading cycles; minimal consistent enlargement;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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