Probably Approximately Consensus: On the Learning Theory of Finding Common Ground

2026-04-23

AI Summary

This work addresses the challenge of identifying broad user consensus in online negotiation platforms while accounting for the relative importance of different issues. The authors model consensus as an interval within a one-dimensional opinion space, extracting underlying opinion structures through high-dimensional embeddings followed by dimensionality reduction. They formulate an objective function that maximizes agreement within the consensus interval under the expected distribution of issue importance and solve it efficiently via empirical risk minimization. Notably, this is the first study to integrate Probably Approximately Correct (PAC) learning theory into consensus discovery, providing formal guarantees for consensus intervals and enabling an active query strategy that incorporates issue weights. Experimental results demonstrate that the proposed method effectively identifies optimal consensus regions while substantially reducing the amount of user feedback required, achieving practical usability.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Consent frameworks and practices on the web
• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems

Abstract

A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements provided by users and should incorporate the relative salience of particular topics. We address this issue by modelling consensus as an interval in a one-dimensional opinion space derived from potentially high-dimensional data via embedding and dimensionality reduction. We define an objective that maximizes expected agreement within a hypothesis interval where the expectation is over an underlying distribution of issues, implicitly taking into account their salience. We propose an efficient Empirical Risk Minimization (ERM) algorithm and establish PAC-learning guarantees. Our initial experiments demonstrate the performance of our algorithm and examine more efficient approaches to identifying optimal consensus regions. We find that through selectively querying users on an existing sample of statements, we can reduce the number of queries needed to a practical number.

Problem

• consensus
• online deliberation
• preference elicitation
• salience
• opinion space

Innovation

• consensus learning
• PAC learning
• dimensionality reduction
• empirical risk minimization
• preference elicitation