Explanation Systems for Approval-Based Multiwinner Voting

2026-04-27

AI Summary

This study addresses the problem of quantifying the representativeness of committees in multi-winner approval voting and elucidating individual voters’ influence, the sources of candidate support, and the reasons for candidate elimination. To this end, it introduces a novel interpretability framework grounded in priceability, formulating an axiomatic pricing system that satisfies structural consistency, faithful attribution of influence, and alignment with proportionality principles. The authors design a polynomial-time rule that efficiently generates fine-grained explanations on both synthetic and real-world datasets. Experimental results demonstrate that the proposed method exhibits high correlation with established proportionality metrics and effectively identifies and reconstructs existing inequalities in voter influence.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Security and Privacy: Data transparency and provenance

Abstract

In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work has focused on the study of binary proportionality axioms that certify whether a given committee is proportionally representative or not. We take a more fine-grained perspective and initiate the study of explanation systems that quantify how a committee represents the electorate, i.e., how much influence each voter exerts, how this influence is allocated across selected candidates, how each candidate is backed by the voters, and why certain candidates were not chosen. Building on the notion of priceability, we propose price systems as a framework for such explanations. A price system assigns each voter an individual budget, which they can spend on selected candidates they approve, and each candidate needs to be purchased at a unit price. Since many price systems can exist for a given outcome, selecting among them requires care. We initiate an axiomatic study of price systems and propose several axioms capturing structural coherence, faithful attribution of influence, and alignment with proportionality. On the algorithmic side, we introduce a polynomial-time computable rule in which voters continuously gain and exercise influence and show that it satisfies all jointly satisfiable axioms. Experiments on synthetic and real-world instances indicate that our explanations correlate with established proportionality notions and can recover unequal influence when it is present.

Problem

• approval-based multiwinner voting
• explanation systems
• proportional representation
• priceability
• voter influence

Innovation

• explanation systems
• priceability
• multiwinner voting
• proportional representation
• axiomatic analysis