Tight approximation for proportional approval voting

Szymon Dudycz, Pasin Manurangsi, Jan Marcinkowski, Krzysztof Sornat

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

4 Scopus citations

Abstract

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
Pages276-282
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
Volume2021-January
ISSN (Print)1045-0823

Conference

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

ASJC Scopus subject areas

  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'Tight approximation for proportional approval voting'. Together they form a unique fingerprint.

Cite this