Popular ranking

Authors:
Anke Van Zuylen;Frans Schalekamp;David P. Williamson
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Mathematics Department, College of William and Mary, USA;School of ORIE, Cornell University, Ithaca, NY, USA
Venue:
Discrete Applied Mathematics
Year:
2014

Citing 4
Cited 0

Rank aggregation methods for the Web

Proceedings of the 10th international conference on World Wide Web
Popular Matchings

SIAM Journal on Computing
The least-unpopularity-factor and least-unpopularity-margin criteria for matching problems with one-sided preferences

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Using complexity to protect elections

Communications of the ACM

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Abstract

In this paper we take a new approach to the very old problem of aggregating preferences of multiple agents. We define the notion of popular ranking: a ranking of a set of elements is popular if there exists no other permutation of the elements that a majority of the voters prefer. We show that such a permutation is unlikely to exist: we show that a necessary but not sufficient condition for the existence of a popular ranking is Condorcet's paradox not occurring. In addition, we show that if Condorcet's paradox does not occur, then we can efficiently compute a permutation, which may or may not be popular, but for which the voters will have to solve an NP-hard problem to compute a permutation that a majority of them prefer.