On weakly and strongly popular rankings

Kraiczy, S., Cseh, Á. and Manlove, D. (2023) On weakly and strongly popular rankings. Discrete Applied Mathematics, 340, pp. 134-152. (doi: 10.1016/j.dam.2023.06.041)

Abstract

Van Zuylen et al. (2014) introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking of all candidates. A popular ranking π of the candidates is at least as good as any other ranking σ in the following sense: if we compare π to σ, at least half of all voters will always weakly prefer π. 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 π and σ to prefer π. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results in Van Zuylen et al. (2014). We also point out connections to the famous open problem of finding a Kemeny consensus with three voters

• Item Type: Articles
• Additional Information: Sonja Kraiczy was supported by Undergraduate Research Bursary 19-20-66 from the London Mathematical Society, by the School of Computing Science, University of Glasgow, by EPSRC studentship EP/T517811/1 and by Merton College, Oxford. Ágnes Cseh was supported by OTKA grant K128611 and the János Bolyai Research Fellowship. David Manlove was supported by grant EP/P028306/1 from the Engineering and Physical Sciences Research Council.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David and Kraiczy, Ms Sonja
• Authors: Kraiczy, S., Cseh, Á., and Manlove, D.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Discrete Applied Mathematics
• Publisher: Elsevier
• ISSN: 0166-218X
• ISSN (Online): 1872-6771
• Published Online: 22 July 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Discrete Applied Mathematics 340:134-152
• Publisher Policy: Reproduced under a Creative Commons license

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300808		IP-MATCH: Integer Programming for Large and Complex Matching Problems	David Manlove	Engineering and Physical Sciences Research Council (EPSRC)	EP/P028306/1	Computing Science