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Making just school assignments

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  • Morrill, Thayer

Abstract

It is impossible for a mechanism to be strategyproof, Pareto efficient, and eliminate justified envy. However, little is known to what extent a strategyproof and efficient mechanism can limit justified envy. We define an assignment to be unjust if a student i is not assigned to a school a that she prefers to her own assignment, i has higher priority at a than some student j who is assigned to a, and none of the students ranked higher at a than i are dependent on j. We prove that Top Trading Cycles is the unique mechanism that is strategyproof, efficient, and just. This demonstrates that a strictly stronger notion of fairness than justness is either unachievable by a strategyproof and efficient mechanism or it is only achievable by TTC. We extend this characterization to the general case when schools may have arbitrary capacities by introducing the concept of reducibility.

Suggested Citation

  • Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
    • Handle: RePEc:eee:gamebe:v:92:y:2015:i:c:p:18-27
    DOI: 10.1016/j.geb.2015.05.004
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    References listed on IDEAS

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    Cited by:

    1. Atila Abdulkadiroglu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2017. "Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp," NBER Working Papers 23265, National Bureau of Economic Research, Inc.
    2. Patrick Harless & William Phan, 2020. "On endowments and indivisibility: partial ownership in the Shapley–Scarf model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 411-435, September.
    3. Battal Doğan & Lars Ehlers, 2022. "Robust Minimal Instability of the Top Trading Cycles Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 556-582, November.
    4. Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    5. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    6. Yajing Chen, 2016. "New axioms for immediate acceptance," Review of Economic Design, Springer;Society for Economic Design, vol. 20(4), pages 329-337, December.
    7. Dur, Umut & Morrill, Thayer, 2018. "Competitive equilibria in school assignment," Games and Economic Behavior, Elsevier, vol. 108(C), pages 269-274.
    8. Altuntaş, Açelya & Phan, William, 2022. "Trading probabilities along cycles," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    9. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    10. Siwei Chen & Yajing Chen & Chia‐Ling Hsu, 2023. "New axioms for top trading cycles," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1064-1077, October.
    11. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    12. Yajing Chen, 2017. "New axioms for deferred acceptance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 393-408, February.

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    More about this item

    Keywords

    Top trading cycles; School choice; Assignment;
    All these keywords.

    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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