Deliberation via Matching

2025-11-02

AI Summary

This paper studies deliberative social choice, where voters refine their preferences through pairwise deliberation before collective decision-making. To address the performance bottleneck of tournament-based rules under the metric distortion framework, we propose a pairwise deliberation mechanism that constructs deliberation pairs via maximum matching and aggregates outcomes using a weighted uncovered set rule. We establish, for the first time, that this mechanism strictly reduces the distortion ratio of tournament rules from the prior lower bound of 3.11 (without deliberation) to the optimal value of 3—matching the theoretical limit for deterministic social choice rules. Technically, we model the problem via a bilinear relaxation of a nonlinear program and derive tight distortion bounds by leveraging supermodularity and convexity analyses. Our results demonstrate that pairwise deliberation endows tournament rules with expressive power equivalent to that of general deterministic rules, thereby introducing a novel paradigm for deliberative mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Machine Learning: Learning Preferences or Rankings

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study deliberative social choice, where voters refine their preferences through small-group discussions before collective aggregation. We introduce a simple and easily implementable deliberation-via-matching protocol: for each pair of candidates, we form an arbitrary maximum matching among voters who disagree on that pair, and each matched pair deliberates. The resulting preferences (individual and deliberative) are then appropriately weighted and aggregated using the weighted uncovered set tournament rule. We show that our protocol has a tight distortion bound of $3$ within the metric distortion framework. This breaks the previous lower bound of $3.11$ for tournament rules without deliberation and matches the lower bound for deterministic social choice rules without deliberation. Our result conceptually shows that tournament rules are just as powerful as general social choice rules, when the former are given the minimal added power of pairwise deliberations. We prove our bounds via a novel bilinear relaxation of the non-linear program capturing optimal distortion, whose vertices we can explicitly enumerate, leading to an analytic proof. Loosely speaking, our key technical insight is that the distortion objective, as a function of metric distances to any three alternatives, is both supermodular and convex. We believe this characterization provides a general analytical framework for studying the distortion of other deliberative protocols, and may be of independent interest.

Problem

• Studying deliberative social choice with voter discussions
• Introducing matching-based protocol for pairwise preference deliberation
• Analyzing distortion bounds for tournament rules with deliberation

Innovation

• Pairwise voter matching for preference deliberation
• Weighted uncovered set tournament rule aggregation
• Bilinear relaxation for distortion analysis