Student admissions and faculty recruitment

The student admissions and faculty recruitment problems are modeled and analyzed in terms of graphs. Stable assignments, potentially exponential in number, form a distributive lattice whose sup and inf are the applicant-optimal and university-optimal stable assignments, mu(A) and mu(U). Which one of all possible stable assignments should be chosen in practice is answered in these terms: mu(A) is characterized as the unique choice mechanism that is either "monotone," or "strategy-proof," or "efficient." Similar characterizations are given for mu(U), though as a practical matter they are not persuasive. (C) 2004 Elsevier B.V. All rights reserved.