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.

翻译：Van Zuylen等人[35]在投票情境中引入了流行排序的概念，其中每位选民对所有候选人提交严格排序。候选人的一个流行排序$\pi$在以下意义上至少与任何其他排序$\sigma$同样好：若比较$\pi$与$\sigma$，至少半数选民始终弱偏好于$\pi$。选民对排序的偏好基于肯德尔距离计算。更传统的流行性定义——如应用于计算社会选择中成熟课题的流行匹配——更为严格，因为它要求在$\pi$与$\sigma$之间非无差异的选民中至少半数偏好$\pi$。本文在两种设定下推导了结构与算法结果，并改进了[35]中的结论。我们还指出了这些结果与寻找三名选民肯梅尼共识这一著名开放问题之间的关联。