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

TL;DR

This paper models consensus in online deliberation as an interval in a reduced opinion space, proposing an ERM algorithm with PAC guarantees to efficiently identify broadly agreeable ideas.

Contribution

It introduces a novel approach to consensus elicitation using embedding, dimensionality reduction, and PAC-learning guarantees, with practical querying strategies.

Findings

The ERM algorithm effectively finds consensus intervals.

Selective querying reduces the number of user queries needed.

Initial experiments demonstrate promising performance of the proposed method.

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.