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Title

Local and global consistency properties for student placement

AuthorsKlaus, Bettina; Klijn, Flip
KeywordsConsistency
Converse consistency
Priority structure
Student placement
Issue DateJan-2013
PublisherElsevier
CitationJournal of Mathematical Economics 49(3): 222-229 (2013)
AbstractIn 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. A related but stronger necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property is unit acyclicity.We provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. First, 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. Second, 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. © 2013 Elsevier B.V.
Publisher version (URL)http://dx.doi.org/10.1016/j.jmateco.2013.03.002
URIhttp://hdl.handle.net/10261/125698
DOI10.1016/j.jmateco.2013.03.002
Identifiersdoi: 10.1016/j.jmateco.2013.03.002
issn: 0304-4068
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