Robustness of Approval-Based Multiwinner Voting Rules

TL;DR

This paper examines the stability of approval-based multiwinner voting rules against small vote changes, analyzing how easily election outcomes can be altered and the computational complexity of such modifications.

Contribution

It introduces a detailed study of the robustness of multiwinner voting rules, including complexity results and probabilistic analysis of outcome stability under vote perturbations.

Findings

Determines the difficulty of changing election outcomes with minimal vote modifications.

Provides complexity classifications for robustness-related decision problems.

Analyzes the probability of outcome changes under random vote perturbations.

Abstract

We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the computational complexity of deciding how many such operations are necessary to change the set of winning committees. We also consider the counting variants of our problems, which can be interpreted as computing the probability that the result of an election changes after a given number of random perturbations of the given election.