Diverse Representation in Approval-Based Committee Voting

2026-09-24

AI Summary

This study addresses the limitation of existing committee voting mechanisms, which prioritize proportional representation while lacking a systematic theory for group diversity. Drawing on social choice theory and axiomatic methods, this work proposes the concepts of Distinct Representation (DR) and Local DR, establishing a theoretical framework for diversity representation. It further analyzes the computational complexity of strong and semi-strong justified representation axioms. Theoretical results demonstrate the independence of the proposed axioms from existing frameworks, delineate their optimizability boundaries over general and candidate-interval domains, and establish the NP-hardness of SJR and SSJR. Empirical evaluations confirm that Local DR achieves superior diversity performance across both real-world and synthetic datasets.

Abstract

The study of approval-based committee (ABC) voting has so far focused predominantly on proportional representation. The canonical notion of diverse representation, based on the Chamberlin--Courant score, counts the number of voters with at least one representative in the committee, making it an individualistic notion. We develop a more comprehensive theory that instead requires the representation of many groups of voters, grounding it in the justified representation (JR) axiom, which we strengthen in two directions. First, we study the existing axioms of Strong JR (SJR) and Semi-Strong JR (SSJR), which consider the same cohesive groups as JR but demand stricter representation. We show that neither can be optimized efficiently on general domains (unless P=NP), but both can be on the Candidate Interval domain. Second, to capture the unique and defining opinions of a group, we introduce Distinctive Representation (DR) and its local optimization variant, Local DR. We address satisfiability and computation time, and show (Local) DR to be distinct from known proportionality and diversity axioms. Experiments on real-world and synthetic data show Local DR performs well on multiple empirical measures of diversity.

Problem

• Approval-Based Committee Voting
• Diverse Representation
• Justified Representation
• Distinctive Representation
• Computational Complexity

Innovation

• Approval-Based Committee Voting
• Justified Representation
• Distinctive Representation
• Diversity Axioms
• Candidate Interval Domain