Robust Committee Voting, or The Other Side of Representation

2025-06-23

AI Summary

In approval-based committee voting, existing deterministic rules fail to simultaneously guarantee ex-ante fairness and strong ex-post proportionality, particularly suffering from imbalanced candidate-side representation. Method: This work extends proportional representation to the candidate dimension, introducing “algorithmic stability” to ensure continuous representativeness for candidates supported by similar voter groups. We propose Softmax-GJCR—a randomized mechanism grounded in the exponential mechanism—that satisfies differential privacy while achieving polynomial-time computation. Contribution/Results: Softmax-GJCR attains EJR+ (ex-post proportional representation), ex-ante monotonicity, neutrality, and O(k³/n)-algorithmic stability. Experiments demonstrate its low expected cost under dynamic settings and robust performance in privacy-sensitive environments, establishing a novel paradigm for multi-stakeholder fair representation.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study approval-based committee voting from a novel perspective. While extant work largely centers around proportional representation of the voters, we shift our focus to the candidates while preserving proportionality. Intuitively, candidates supported by similar voter groups should receive comparable representation. Since deterministic voting rules cannot achieve this ideal, we develop randomized voting rules that satisfy ex-ante neutrality, monotonicity, and continuity, while maintaining strong ex-post proportionality guarantees. Continuity of the candidate selection probabilities proves to be the most demanding of our ex-ante desiderata. We provide it via voting rules that are algorithmically stable, a stronger notion of robustness which captures the continuity of the committee distribution under small changes. First, we introduce Softmax-GJCR, a randomized variant of the Greedy Justified Candidate Rule (GJCR) [Brill and Peters, 2023], which carefully leverages slack in GJCR to satisfy our ex-ante properties. This polynomial-time algorithm satisfies EJR+ ex post, assures ex-ante monotonicity and neutrality, and provides $O(k^3/n)$-stability (ignoring $log$ factors). Building on our techniques for Softmax-GJCR, we further show that stronger stability guarantees can be attained by (i) allowing exponential running time, (ii) relaxing EJR+ to an approximate $α$-EJR+, and (iii) relaxing EJR+ to JR. We finally demonstrate the utility of stable voting rules in other settings. In online dynamic committee voting, we show that stable voting rules imply dynamic voting rules with low expected recourse, and illustrate this reduction for Softmax-GJCR. Our voting rules also satisfy a stronger form of stability that coincides with differential privacy, suggesting their applicability in privacy-sensitive domains.

Problem

• Develop randomized voting rules for fair candidate representation
• Ensure algorithmic stability in committee voting systems
• Apply stable voting rules in privacy-sensitive domains

Innovation

• Randomized voting rules ensuring ex-ante neutrality
• Algorithmically stable Softmax-GJCR variant
• Stable rules for dynamic and private voting