On weakly and strongly popular rankings

Sonja Kraiczy; Agnes Cseh; David Manlove

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arXiv · 2102.01361

On weakly and strongly popular rankings

Sonja Kraiczy·Agnes Cseh·David Manlove

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Abstract

Van Zuylen et al. [35] introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking 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 in [35]. We also point out connections to the famous open problem of finding a Kemeny consensus with three voters.

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Sonja Kraiczy, Agnes Cseh, David Manlove. 2021-02-02. On weakly and strongly popular rankings. https://arxiv.org/abs/2102.01361

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