Utilitarian Welfare and Representation Guarantees of Approval-Based Multiwinner Rules

TL;DR

This paper quantitatively analyzes approval-based multiwinner voting rules, evaluating their effectiveness in approximating representation and utilitarian objectives through theoretical and experimental methods.

Contribution

It introduces a framework to compare multiwinner rules based on approximation of representation and utilitarian goals, highlighting tradeoffs involved.

Findings

Multiwinner rules vary significantly in approximating representation and utilitarian objectives.

The study classifies rules based on their quantitative alignment with the two objectives.

Tradeoffs are fundamental when selecting multiwinner voting rules.

Abstract

To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms---we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin--Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we classify multiwinner rules in terms of their quantitative alignment with these two opposing objectives. Our results provide fundamental information about the nature of multiwinner rules and, in particular, about the necessary tradeoffs when choosing such a rule.