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School Choice Problems with Priority Adjustments

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  • Minoru Kitahara
  • Yasunori Okumura

Abstract

This paper studies school choice when each school has an original priority order and an adjusted priority order reflecting policies such as affirmative action. We introduce a weak notion of stability that permits justified envy under one priority order only when the opposite priority relation is supported by the other. We characterize weakly stable matchings as stable matchings under the intersection of the two priority profiles. Using the efficiency-adjusted deferred acceptance algorithm, we obtain a weakly stable matching that cannot be Pareto improved upon, within the set of weakly stable matchings, for any group containing all improved students by the adjustment. We also show that any Pareto improvement over this outcome necessarily creates justified envy under both priority profiles. Finally, our mechanism is responsive to stronger priority adjustments: the outcome under a stronger affirmative action policy is not Pareto dominated by that under a weaker policy for any group containing all students improved by the stronger adjustment.

Suggested Citation

  • Minoru Kitahara & Yasunori Okumura, 2026. "School Choice Problems with Priority Adjustments," Papers 2609.12558, arXiv.org.
    • Handle: RePEc:arx:papers:2609.12558
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    References listed on IDEAS

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    1. Qianfeng Tang & Yongchao Zhang, 2021. "Weak stability and Pareto efficiency in school choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 533-552, March.
    2. 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.
    3. Umut Dur & Yifan Xie, 2023. "Responsiveness to priority‐based affirmative action policy in school choice," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(2), pages 229-244, April.
    4. Orhan Aygün & Inácio Bó, 2021. "College Admission with Multidimensional Privileges: The Brazilian Affirmative Action Case," American Economic Journal: Microeconomics, American Economic Association, vol. 13(3), pages 1-28, August.
    5. Tayfun Sönmez & M. Bumin Yenmez, 2022. "Affirmative Action in India via Vertical, Horizontal, and Overlapping Reservations," Econometrica, Econometric Society, vol. 90(3), pages 1143-1176, May.
    6. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    7. Jiao, Zhenhua & Tian, Guoqiang, 2018. "Two further impossibility results on responsive affirmative action in school choice," Economics Letters, Elsevier, vol. 166(C), pages 60-62.
    8. Minoru Kitahara & Yasunori Okumura, 2026. "Stable Improvement Cycle Mechanism Versus Efficiency-adjusted Deferred Acceptance Mechanism beyond Weak Priority Orders," Papers 2609.12543, arXiv.org.
    9. Zhenhua Jiao & Ziyang Shen & Guoqiang Tian, 2022. "When is the deferred acceptance mechanism responsive to priority-based affirmative action?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 257-282, February.
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