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What's the Matter with Tie-breaking? Improving Efficiency in School Choice

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Author Info
Aytek Erdil
Haluk Ergin
Abstract

Very little is known about the student-optimal stable mechanism when school priorities are weak. In current practice, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken with a lottery. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. We propose a simple procedure to compute a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. Abdulkadiroglu, Pathak, and Roth (2006) report that had our algorithm been applied to the preference data of the 2003-2004 New York City High School Match, 6,854 students (10.5% of the 63,795 matched students) would have been matched with schools higher on their preference lists without hurting the others. We run simulations to understand the qualitative effects of correlation in preferences and of locational preference on the size of the efficiency gain. We also investigate the strategic properties of the class of student-optimal stable mechanisms.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 349.

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Date of creation: 2007
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Handle: RePEc:oxf:wpaper:349

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Keywords: School Choice Student-Optimal Stable Mechanism Weak Priorities Stable Improvement Cycles

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References listed on IDEAS
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  1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 2006-04, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  4. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December. [Downloadable!] (restricted)
  6. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July. [Downloadable!] (restricted)
  7. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March. [Downloadable!] (restricted)
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