The Least-Unpopularity-Factor and Least-Unpopularity-Margin Criteria for Matching Problems with One-Sided Preferences
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.
Keywordsmatching one-sided preferences algorithms NP-hardness popular matching voting
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