Local and Global Consistency Properties for Student Placement

Bettina Klaus (bettina.klaus@unil.ch) and Flip Klijn

No 538, Working Papers from Barcelona School of Economics

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.

Keywords: consistency; Student placement; acyclicity; converse consistency (search for similar items in EconPapers)
JEL-codes: C78 D63 (search for similar items in EconPapers)
Date: 2015-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Local and global consistency properties for student placement (2013)
Working Paper: Local and Global Consistency Properties for Student Placement (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:bge:wpaper:538

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