Agreeing to Disagree: Leveraging Consensus and Divergence in Bayesian Belief Aggregation

We present a new approach for combining the beliefs of many individuals using graphical models. Existing Bayesian belief aggregation methods break several theoretical assumptions for Bayesian reasoning. More practically, existing opinion pool functions that compute a single value to represent the belief of all contributors do not represent reality well, especially in cases where there are many diverse opinions. Divergence is a natural result of combining opinions from individuals with different beliefs, backgrounds and experiences. Instead of forming a single consensus value that will average out this diversity, we find clusters of agreement for each probability distribution and propagate the cluster means throughout the network during inference. We utilize a social network that tracks the agreement between individuals and the normalized graph cut algorithm to find emerging groups of consensus in the agreement network. We leverage the agreement that occurs across multiple belief estimates to help reduce the complexity that may arise as the means are propagated throughout a belief network. By monitoring agreement over time we may also expose the variety of backgrounds that will help explain divergence in belief. This paper discusses the approach, background and our motives for ongoing research.