Local and global consistency properties for student placement

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. 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.