Abstract
We consider the problem of choosing the best matching of people to positions based on preferences expressed by the people, for which many different optimality criteria have been proposed. A matching is popular if no other matching beats it in a majority vote of the people. The popularity criterion has a manipulation-resistance property, but unfortunately, some sets of preferences admit no popular matching. In this paper, we introduce the least-unpopularity-factor and least-unpopularity-margin criteria, two generalizations of popularity that preserve the manipulation-resistance property but give an optimal matching for every set of preferences. Under each of these generalizations, we show that the “badness” of a given matching can be calculated efficiently but it is NP-hard to find an optimal matching.
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McCutchen, R.M. (2008). The Least-Unpopularity-Factor and Least-Unpopularity-Margin Criteria for Matching Problems with One-Sided Preferences. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_51
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DOI: https://doi.org/10.1007/978-3-540-78773-0_51
Publisher Name: Springer, Berlin, Heidelberg
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