Stronger group representation methods in approval voting systems
Diverse Representation in Approval-Based Committee Voting
Computer Science and Game Theory
Summary
Choosing a committee that fairly represents voters often focuses on proportional representation. The authors redefine what diverse representation means by making sure many groups of voters, not just individuals, have their views represented. They introduce new fairness criteria that demand stricter group representation and analyze their computational challenges. Their new methods work well in certain special cases and perform strongly in tests on real and simulated voting data.
What this means in practice
- •For election system designers: Design approval voting methods that ensure many voter groups get distinct representation in committees, improving perceived fairness.
- •For online community managers: Use new voting rules to select committees that better represent diverse online user groups in moderation or advisory roles.
Authors
Julian Chingoma, Davide Grossi, Feline Lindeboom, Jan Maly
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.