Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

TL;DR

This paper analyzes the computational complexity of manipulation and control in various approval-based multiwinner voting rules, showing resistance in most cases and providing fixed-parameter tractability results and polynomial algorithms for special cases.

Contribution

It offers a comprehensive complexity analysis of manipulation and control problems across multiple approval-based multiwinner voting rules, highlighting resistance and tractability results.

Findings

Most voting rules resist manipulation and control.

Several fixed-parameter tractability results are established.

Polynomial-time algorithms are provided for specific cases.

Abstract

We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.