The Proportional Veto Principle for Approval Ballots

TL;DR

This paper introduces the flexible-voter representation (FVR) principle for approval ballots, proposing a scoring rule that guarantees FVR optimality across all thresholds and extending the concept to multi-winner elections.

Contribution

It adapts the proportional veto principle to approval voting and identifies a scoring rule that is FVR-optimal universally, also extending the framework to multi-winner settings.

Findings

Approval voting and scoring rules have limited FVR guarantees at certain thresholds.

A specific scoring rule achieves universal FVR optimality.

Results extend to multi-winner voting scenarios.

Abstract

The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for approval ballots, which we call flexible-voter representation (FVR). We show that while the approval voting rule and other natural scoring rules provide the optimal FVR guarantee only for some flexibility threshold, there exists a scoring rule that is FVR-optimal for all thresholds simultaneously. We also extend our results to multi-winner voting.