  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.
