# Completing Priceable Committees: Utilitarian and Representation Guarantees for Proportional Multiwinner Voting

arXiv: https://arxiv.org/abs/2312.08187 · HTML: https://mlsanity.com/paper/2312.08187/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2023.

## Built on by (most cited first, 5 of 5)

- [Temporal Elections: Welfare, Strategyproofness, and Proportionality](https://mlsanity.com/paper/2408.13637/) (2024)
- [Not in My Backyard! Temporal Voting Over Public Chores](https://mlsanity.com/paper/2508.08810/) (2025)
- [The Price of Proportional Representation in Temporal Voting](https://mlsanity.com/paper/2605.11157/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [Fairness in the Multi-Secretary Problem](https://mlsanity.com/paper/2511.23097/) (2025)

## Abstract (arXiv)

When selecting committees based on preferences of voters, a variety of different criteria can be considered. Two natural objectives are maximizing the utilitarian welfare (the sum of voters' utilities) and coverage (the number of represented voters) of the selected committee. Previous work has studied the impact on utilitarian welfare and coverage when requiring the committee to satisfy minimal requirements such as justified representation or weak proportionality. In this paper, we consider the impact of imposing much more demanding proportionality axioms. We identify a class of voting rules that achieve strong guarantees on utilitarian welfare and coverage when combined with appropriate completions. This class is defined via a weakening of priceability and contains prominent rules such as the Method of Equal Shares. We show that committees selected by these rules (i) can be completed to achieve optimal coverage and (ii) can be completed to achieve an asymptotically optimal approximation to the utilitarian welfare if they additionally satisfy EJR+. Answering an open question of Elkind et al. (2022), we use the Greedy Justified Candidate Rule to obtain the best possible utilitarian guarantee subject to proportionality. We also consider completion methods suggested in the participatory budgeting literature and other objectives besides welfare and coverage.