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On extensions of partial priorities in school choice

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  • Minoru Kitahara
  • Yasunori Okumura

Abstract

We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms to derive one of the extensions of a binary relation and characterize them by using the class. We show that if the binary relations are the partial orders, then for each stable matching for the profile of the binary relations, there is an extension for which it is also stable. Moreover, if there are multiple stable matchings for the profile of the binary relations that are ranked by Pareto dominance, there is an extension for which all of those matchings are stable. We provide several applications of these results.

Suggested Citation

  • Minoru Kitahara & Yasunori Okumura, 2023. "On extensions of partial priorities in school choice," Papers 2305.00641, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2305.00641
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    References listed on IDEAS

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    1. 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.
    2. Yasunori Okumura, 2023. "Consistent Linear Orders for Supermajority Rules," Papers 2304.09419, arXiv.org, revised Oct 2023.
    3. 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.
    4. Okumura, Yasunori, 2016. "A stable and Pareto efficient update of matching in school choice," Economics Letters, Elsevier, vol. 143(C), pages 111-113.
    5. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    6. Dur, Umut & Gitmez, A. Arda & Yılmaz, Özgür, 2019. "School choice under partial fairness," Theoretical Economics, Econometric Society, vol. 14(4), November.
    7. Tang, Qianfeng & Yu, Jingsheng, 2014. "A new perspective on Kesten's school choice with consent idea," Journal of Economic Theory, Elsevier, vol. 154(C), pages 543-561.
    8. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
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    Cited by:

    1. Emilio Guaman & Juan Pablo Torres-Martinez, 2023. "Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences," Working Papers wp547, University of Chile, Department of Economics.
    2. Minoru Kitahara & Yasunori Okumura, 2023. "School Choice with Multiple Priorities," Papers 2308.04780, arXiv.org, revised Oct 2024.

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