On Weakly and Strongly Popular Rankings

Kraiczy, S., Cseh, A. and Manlove, D. (2021) On Weakly and Strongly Popular Rankings. In: 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2021), London, UK (Virtual), 3-7 May 2021, pp. 1563-1565. ISBN 9781450383073 (doi: 10.5555/3463952.3464160)

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Van Zuylen et al. introduced the notion of a popular ranking in a voting context, where each voter submits a strictly-ordered list of all candidates. A popular ranking pi of the candidates is at least as good as any other ranking sigma in the following sense: if we compare pi to sigma, at least half of all voters will always weakly prefer pi. Whether a voter prefers one ranking to another is calculated based on the Kendall distance. A more traditional definition of popularity---as applied to popular matchings, a well-established topic in computational social choice---is stricter, because it requires at least half of the voters who are not indifferent between pi and sigma to prefer pi. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results by van Zylen et al. We also point out connections to the famous open problem of finding a Kemeny consensus with 3 voters.

Item Type:Conference Proceedings
Glasgow Author(s) Enlighten ID:Kraiczy, Ms Sonja and Manlove, Professor David
Authors: Kraiczy, S., Cseh, A., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
Copyright Holders:Copyright © 2021 International Foundation for Autonomous Agents and Multiagent Systems
First Published:First published in Proceedings of 20th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS '21)
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300808IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science