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This paper formalizes the problem of identifying broadly agreeable ideas in online deliberation platforms as finding an interval in a one-dimensional opinion space that maximizes expected agreement over a distribution of issues. They propose an Empirical Risk Minimization (ERM) algorithm to learn this consensus interval and provide Probably Approximately Correct (PAC) learning guarantees. Experiments demonstrate the algorithm's performance and show that selective querying of users can significantly reduce the number of queries needed to identify optimal consensus regions.
Forget polling every user on every idea – this algorithm learns to find common ground by strategically asking for feedback on a few key statements.
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.
