Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On absolutely and simply popular rankings   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 \emph{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 Zuylen et al. We also point out strong connections to the
famous open problem of finding a Kemeny consensus with 3 voters.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat