Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the complexity of Winner Verification and Candidate Winner for
  Multiwinner Voting Rules   The Chamberlin-Courant and Monroe rules are fundamental and well-studied
rules in the literature of multi-winner elections. The problem of determining
if there exists a committee of size k that has a Chamberlin-Courant
(respectively, Monroe) score of at most r is known to be NP-complete. We
consider the following natural problems in this setting: a) given a committee S
of size k as input, is it an optimal k-sized committee, and b) given a
candidate c and a committee size k, does there exist an optimal k-sized
committee that contains c?
  In this work, we resolve the complexity of both problems for the
Chamberlin-Courant and Monroe voting rules in the settings of rankings as well
as approval ballots. We show that verifying if a given committee is optimal is
coNP-complete whilst the latter problem is complete for $\Theta_{2}^{P}$. We
also demonstrate efficient algorithms for the second problem when the input
consists of single-peaked rankings. Our contribution fills an essential gap in
the literature for these important multi-winner rules.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol