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, μ A and μ U . Which one of all possible stable assignments should be chosen in practice is answered in these terms: μ A is characterized as the unique choice mechanism that is either monotone, or strategy-proof, or efficient. Similar characterizations are given for μ U , though as a practical matter they are not persuasive.

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