The Proportional Veto Principle for Approval Ballots

2025-05-02

AI Summary

This paper addresses the adaptation of the Proportional Veto Principle (PVP) to approval voting, aiming to prevent candidates vetoed by large voter blocs from being elected while ensuring flexible veto power for cohesive voter groups. We introduce the Flexible Voter Representation (FVR) principle, formally characterizing the role of veto coalitions of varying sizes in proportional representation, and pioneer the integration of PVP into the approval voting framework. We design a novel scoring rule that is globally optimal with respect to FVR—achieving theoretical optimality across all flexibility thresholds, unlike classical rules (e.g., Approval Voting), which satisfy optimality only for restricted thresholds. Through axiomatic modeling, worst-case analysis, and extension to multi-winner settings, we demonstrate that our rule naturally generalizes to committee elections, significantly enhancing veto fairness and proportional robustness.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Consent frameworks and practices on the web
• Security and Privacy: Large-scale security measurements

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.

Problem

• Extends proportional veto principle to approval ballots
• Introduces flexible-voter representation (FVR) for voting rules
• Identifies FVR-optimal scoring rule for all thresholds

Innovation

• Introduces flexible-voter representation for approval ballots
• Identifies FVR-optimal scoring rule for all thresholds
• Extends results to multi-winner voting scenarios