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Local and Global Consistency Properties for Student Placement

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  • Bettina Klaus

  • Flip Klijn

Abstract

In the context of resource allocation on the basis of priorities, Ergin (2002) identifies a necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a consistency principle. Ergin (2002) formulates consistency as a local property based on a fixed population of agents and fixed resources -- we refer to this condition as local consistency and to his condition on the priority structure as local acyclicity. We identify a related but stronger necessary and sufficient condition (unit acyclicity) on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property. Next, we provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. We identify a necessary and sufficient condition (local shift-freeness) on the priority structure such that the student-optimal stable mechanism satisfies local converse consistency. Interestingly, local acyclicity implies local shift-freeness and hence the student-optimal stable mechanism more frequently satisfies local converse consistency than local consistency. Finally, in order for the student-optimal stable mechanism to be globally conversely consistent, one again has to impose unit acyclicity on the priority structure. Hence, unit acyclicity is a necessary and sufficient condition on the priority structure for the student-optimal stable mechanism to satisfy global consistency or global converse consistency.

Suggested Citation

  • Bettina Klaus & Flip Klijn, 2011. "Local and Global Consistency Properties for Student Placement," UFAE and IAE Working Papers 866.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:866.11
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    Cited by:

    1. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    2. Rodrigo Velez, 2014. "Consistent strategy-proof assignment by hierarchical exchange," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 125-156, May.
    3. Takashi Akahoshi, 2014. "A necessary and sufficient condition for stable matching rules to be strategy-proof," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 683-702, October.
    4. Abizada, Azar & Bó, Inácio, 2021. "Hiring from a pool of workers," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 576-591.
    5. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    6. Afacan, Mustafa Oğuz & Dur, Umut Mert, 2017. "Incompatibility between stability and consistency," Economics Letters, Elsevier, vol. 150(C), pages 135-137.
    7. 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.
    8. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    9. Nanyang Bu, 2014. "Characterizations of the sequential priority rules in the assignment of object types," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 635-645, October.
    10. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.

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    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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