Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to select multiple winners. These rules are proportional approval voting, reweighted approval voting, and satisfaction approval voting. Each rule is designed with the intention to compute a representative winning set. We show that computing the winner for proportional approval voting is NP-hard, closing an open problem (Kilgour, 2010). As none of the rules we examine are strategyproof, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NPhard for an agent or agents to compute how best to vote given a fixed set of approval ballots of the other agents. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; I.2.11 [Distributed Artificial Intelligence]: Multiagent Systems; J.4 [Com...

• Type: Journal
• Year: 2015
• Where: ATAL
• Authors: Haris Aziz, Serge Gaspers, Joachim Gudmundsson, Simon Mackenzie, Nicholas Mattei, Toby Walsh
• Keywords: ATAL 2015, Intelligent Agents