TY - GEN
T1 - Tight approximation for proportional approval voting
AU - Dudycz, Szymon
AU - Manurangsi, Pasin
AU - Marcinkowski, Jan
AU - Sornat, Krzysztof
N1 - Funding Information:
This research is partially supported by the National Science Centre, Poland (grant numbers 2015/18/E/ST6/00456, 2018/28/T/ST6/00366, 2018/29/B/ST6/02633) and the Israel Science Foundation (grant number 630/19). Part of this work was done while Pasin was visiting University of Wroclaw. Krzysztof Sornat is partially supported by the Foundation for Polish Science (FNP) within the START programme. We would like to thank Mateusz Lewandowski for initial discussion and the anonymous reviewers for their helpful comments.
Publisher Copyright:
© 2020 Inst. Sci. inf., Univ. Defence in Belgrade. All rights reserved.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).
AB - In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).
UR - http://www.scopus.com/inward/record.url?scp=85097337948&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85097337948
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 276
EP - 282
BT - Proceedings of the 29th International Joint Conference on Artificial Intelligence, IJCAI 2020
A2 - Bessiere, Christian
PB - International Joint Conferences on Artificial Intelligence
T2 - 29th International Joint Conference on Artificial Intelligence, IJCAI 2020
Y2 - 1 January 2021
ER -