Tight approximation for proportional approval voting

Szymon Dudycz, Pasin Manurangsi, Jan Marcinkowski, Krzysztof Sornat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


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)).

Original languageEnglish
Title of host publicationProceedings of the 29th International Joint Conference on Artificial Intelligence, IJCAI 2020
EditorsChristian Bessiere
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages7
ISBN (Electronic)9780999241165
StatePublished - 1 Jan 2020
Event29th International Joint Conference on Artificial Intelligence, IJCAI 2020 - Yokohama, Japan
Duration: 1 Jan 2021 → …

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Conference29th International Joint Conference on Artificial Intelligence, IJCAI 2020
Period1/01/21 → …

ASJC Scopus subject areas

  • Artificial Intelligence


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