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Extensions of partial priorities and stability in school choice

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  • Kitahara, Minoru
  • Okumura, Yasunori

Abstract

We consider a school choice matching model where priorities for schools are represented by binary relations that may not be linear orders. Even in that case, it is necessary to construct linear orders from the original priority relations to execute several mechanisms. We focus on the (linear order) extensions of the priority relations, because a matching that is stable for an extension profile is also stable for the profile of priority relations. We show that if the priority relations are partial orders, then for each stable matching for the original profile of priority relations, an extension profile for which it is also stable exists. Furthermore, if there are multiple stable matchings that are ranked by Pareto dominance, then there is an extension for which all these matchings are stable. We apply the result to a version of efficiency adjusted deferred acceptance mechanisms.

Suggested Citation

  • Kitahara, Minoru & Okumura, Yasunori, 2024. "Extensions of partial priorities and stability in school choice," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 1-4.
    • Handle: RePEc:eee:matsoc:v:131:y:2024:i:c:p:1-4
    DOI: 10.1016/j.mathsocsci.2024.06.002
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    References listed on IDEAS

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    1. Claudia Cerrone & Yoan Hermstrüwer & Onur Kesten, 2024. "School Choice with Consent: an Experiment," The Economic Journal, Royal Economic Society, vol. 134(661), pages 1760-1805.
    2. 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.
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    6. 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.
    7. Minoru Kitahara & Yasunori Okumura, 2023. "On extensions of partial priorities in school choice," Papers 2305.00641, arXiv.org, revised Oct 2023.
    8. Okumura, Yasunori, 2016. "A stable and Pareto efficient update of matching in school choice," Economics Letters, Elsevier, vol. 143(C), pages 111-113.
    9. 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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