# Selecting the Most Conflicting Pair of Candidates

arXiv: https://arxiv.org/abs/2405.05870 · HTML: https://mlsanity.com/paper/2405.05870/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 7 of 7)

- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [Proportional Rankings](https://mlsanity.com/paper/1612.01434/) (2016)
- [What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain](https://mlsanity.com/paper/1901.09217/) (2019)
- [Diversity, Agreement, and Polarization in Elections](https://mlsanity.com/paper/2305.09780/) (2023)
- [Axiomatic Characterization of Committee Scoring Rules](https://mlsanity.com/paper/1604.01529/) (2016)
- [Measuring and Controlling Divisiveness in Rank Aggregation](https://mlsanity.com/paper/2306.08511/) (2023)

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

- [Independence of Approximate Clones](https://mlsanity.com/paper/2601.20779/) (2026)

## Abstract (arXiv)

We study committee elections from a perspective of finding the most conflicting candidates, that is, candidates that imply the largest amount of conflict, as per voter preferences. By proposing basic axioms to capture this objective, we show that none of the prominent multiwinner voting rules meet them. Consequently, we design committee voting rules compliant with our desiderata, introducing conflictual voting rules. A subsequent deepened analysis sheds more light on how they operate. Our investigation identifies various aspects of conflict, for which we come up with relevant axioms and quantitative measures, which may be of independent interest. We support our theoretical study with experiments on both real-life and synthetic data.