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(Il)legal assignments in school choice

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  • EHLERS, Lars
  • MORRILL, Thayer
Abstract
In public school choice, students with strict preferences are assigned to schools. Schools are endowed with priorities over students. Incorporating different constraints from applications, priorities are often modeled as choice functions over sets of students. It has been argued that the most desirable criterion for an assignment is fairness; there should not be a student having justified envy in the following way: he prefers some school to his assigned school and has higher priority than some student who got into that school. Justified envy could cause court cases. We propose the following fairness notion for a set of assignments: a set of assignments is legal if and only if any assignment outside the set has justified envy with some assignment in the set and no two assignments inside the set block each other via justified envy. We show that under very basic conditions on priorities, there always exists a unique legal set of assignments, and that this set has a structure common to the set of fair assignments: (i) it is a lattice and (ii) it satisfies the rural-hospitals theorem. This is the first contribution providing a "set-wise" solution for many-to-one matching problems where priorities are not necessarily responsive and schools are not active agents.

Suggested Citation

  • EHLERS, Lars & MORRILL, Thayer, 2017. "(Il)legal assignments in school choice," Cahiers de recherche 2017-02, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2017-02
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    File URL: http://hdl.handle.net/1866/18918
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    References listed on IDEAS

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    3. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    4. Chen, Yiqiu & Möller, Markus, 2024. "Regret-free truth-telling in school choice with consent," Theoretical Economics, Econometric Society, vol. 19(2), May.
    5. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.
    6. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    7. Dur, Umut & Hammond, Robert G. & Kesten, Onur, 2021. "Sequential school choice: Theory and evidence from the field and lab," Journal of Economic Theory, Elsevier, vol. 198(C).
    8. 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.
    9. Battal Doğan & M. Bumin Yenmez, 2020. "Consistent Pareto improvement over the student-optimal stable mechanism," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 125-137, April.
    10. Benoit Decerf & Guillaume Haeringer & Martin Van der Linden, 2024. "Incontestable Assignments," Papers 2401.03598, arXiv.org, revised Feb 2024.
    11. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    12. Imamura, Kenzo & Kawase, Yasushi, 2024. "Efficient matching under general constraints," Games and Economic Behavior, Elsevier, vol. 145(C), pages 197-207.
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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • I20 - Health, Education, and Welfare - - Education - - - General

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