Selecting the Most Conflicting Pair of Candidates

TL;DR

This paper introduces conflict-based voting rules for committee elections, aiming to identify the most conflicting candidates, and analyzes their properties through axioms, measures, and experiments.

Contribution

It proposes new conflictual voting rules that satisfy specific axioms, addressing a gap in existing multiwinner voting methods.

Findings

Existing rules do not meet the proposed axioms for conflict maximization.

Conflictual voting rules can effectively identify highly conflicting candidates.

Experimental results demonstrate the practical applicability of the proposed rules.

Abstract

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.