# Consistent Approval-Based Multi-Winner Rules

arXiv: https://arxiv.org/abs/1704.02453 · HTML: https://mlsanity.com/paper/1704.02453/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2017.

## Built on by (most cited first, 6 of 6)

- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences](https://mlsanity.com/paper/2604.05953/) (2026)
- [The Complexity of Learning Approval-Based Multiwinner Voting Rules](https://mlsanity.com/paper/2110.00254/) (2021)
- [Indivisible Participatory Budgeting under Weak Rankings](https://mlsanity.com/paper/2207.07981/) (2022)
- [A Linear Theory of Multi-Winner Voting](https://mlsanity.com/paper/2503.03082/) (2025)
- [Algorithms for Structured Elections under Thiele Voting Rules](https://mlsanity.com/paper/2607.28575/) (2026)

## Abstract (arXiv)

This paper is an axiomatic study of consistent approval-based multi-winner rules, i.e., voting rules that select a fixed-size group of candidates based on approval ballots. We introduce the class of counting rules and provide an axiomatic characterization of this class based on the consistency axiom. Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin--Courant rule. Our results demonstrate the variety of multi-winner rules and illustrate three different, orthogonal principles that multi-winner voting rules may represent: individual excellence, diversity, and proportionality.