Understanding the Impact of Proportionality in Approval-Based Multiwinner Elections

TL;DR

This paper investigates how proportionality axioms influence committee selection in approval-based multiwinner elections through computational analysis and experiments, revealing significant variability and introducing new importance measures.

Contribution

It provides the first comprehensive analysis of the practical impact of proportionality axioms and introduces novel measures for candidate importance beyond approval scores.

Findings

High variability in proportionality restrictiveness across instances

Unobserved high restrictiveness in some real-world elections

New measures for candidate importance that differ from approval scores

Abstract

Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the computational complexity of several natural problems related to the behavior of proportionality axioms, and (ii) conducting an extensive experimental study on both real-world and synthetic elections. Our findings reveal substantial variation in the restrictiveness of proportionality across instances, including previously unobserved high levels of restrictiveness in some real-world cases. We also introduce and evaluate new measures for quantifying a candidate's importance for achieving proportional outcomes, which differ clearly from assessing candidate strength by approval score.