We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, 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 NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents.
For variants of AV including Proportional Approval Voting, Satisfaction Approval Voting, and the Repeated Approval Voting, the complexity of finding utility maximizing votes ranges in complexity from easy to coNP-complete REF .
Computational Aspects of Multi-Winner Approval Voting
ArXiv
ArXiv
Computer Science Mathematics