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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," Working Papers 538, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:538
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Afacan, Mustafa Oğuz & Dur, Umut Mert, 2017. "Incompatibility between stability and consistency," Economics Letters, Elsevier, vol. 150(C), pages 135-137.
    8. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.

    More about this item

    Keywords

    acyclicity; consistency; converse consistency; Student placement;

    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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