# Proportionality Degree of Multiwinner Rules

arXiv: https://arxiv.org/abs/1810.08799 · HTML: https://mlsanity.com/paper/1810.08799/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2018.

## Built on by (most cited first, 7 of 7)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Proportional Representation in Metric Spaces and Low-Distortion Committee Selection](https://mlsanity.com/paper/2312.10369/) (2023)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [Large Language Models for Designing Participatory Budgeting Rules](https://mlsanity.com/paper/2602.09349/) (2026)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [Reverse Sequential Proportional Approval Voting Rule: Proportionality and Approximation Guarantees](https://mlsanity.com/paper/2609.35331/) (2026)

## Abstract (arXiv)

We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size k; the goal is to select a committee (a~subset) of k alternatives according to the preferences of the voters. We investigate a number of election rules and ask whether the committees that they return represent the voters proportionally. In contrast to the classic literature, we employ quantitative techniques that allow to measure the extent to which the considered rules are proportional. This allows us to arrange the rules in a clear hierarchy. For example, we find that Proportional Approval Voting (PAV) has better proportionality guarantees than its sequential counterpart, and that Phragm'en's Sequential Rule is worse than Sequential PAV. Yet, the loss of proportionality for the two sequential rules is moderate and in some contexts can be outweighed by their other appealing properties. Finally, we measure the tradeoff between proportionality and utilitarian efficiency for a broad subclass of committee election rules.