# Proportional Committee Elections with Positive and Negative Votes

arXiv: https://arxiv.org/abs/2503.01985 · HTML: https://mlsanity.com/paper/2503.01985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Collective Constitutional AI: Aligning a Language Model with Public Input](https://mlsanity.com/paper/2406.07814/) (2024)
- [Justified Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/1407.8269/) (2014)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [Proportional Justified Representation](https://mlsanity.com/paper/1611.09928/) (2016)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [Participatory Budgeting: Data, Tools, and Analysis](https://mlsanity.com/paper/2305.11035/) (2023)
- [Phragm'en's Voting Methods and Justified Representation](https://mlsanity.com/paper/2102.12305/) (2021)
- [Computational Aspects of Multi-Winner Approval Voting](https://mlsanity.com/paper/1407.3247/) (2014)
- [The (Computational) Social Choice Take on Indivisible Participatory Budgeting](https://mlsanity.com/paper/2303.00621/) (2023)
- [Proportionality Degree of Multiwinner Rules](https://mlsanity.com/paper/1810.08799/) (2018)
- [Phragm'en's and Thiele's election methods](https://mlsanity.com/paper/1611.08826/) (2016)
- [Approval-Based Voting with Mixed Goods](https://mlsanity.com/paper/2211.12647/) (2022)
- [Proportionality in Committee Selection with Negative Feelings](https://mlsanity.com/paper/2101.01435/) (2021)
- [A Lower Bound for Local Search Proportional Approval Voting](https://mlsanity.com/paper/2408.02300/) (2024)

## Built on by (most cited first, 1 of 1)

- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)

## Abstract (arXiv)

In the classic committee election setting each voter approves a subset of candidates and the goal is to select k winners based on these preferences. A central focus of recent research in the area has been to achieve proportional representation. In this work, we explore notions of proportionality in a more expressive setting that allows voters to vote against candidates---a common feature on online polling platforms and beyond. We propose two conceptually distinct interpretations of negative votes, resulting in different perspectives of proportionality. In the first, preventing the election of disapproved candidates is as important to voters as electing approved ones. In the second, approvals and disapprovals are treated separately, with each receiving its own fairness guarantees. For each approach, we introduce suitable axioms capturing proportionality and examine their satisfiability by appropriate variants of Phragm'en's rule, Proportional Approval Voting rule (PAV), and the Method of Equal Shares (MES).