Converging Predictions with Shared Information

We describe a concept from a paper by Blackwell and Dubins concerning the merging of opinions or probability predictions between two individuals, Alex and Ben, as they observe increasing amounts of shared information. The central idea is that if their predictive models are updateable based on new evidence and they agree on what events are absolutely impossible, their predictions for future events will become increasingly similar over time, eventually converging. While their short-term predictions converge based on shared evidence, their underlying long-term beliefs about the general nature of the world may remain distinct. This merging of opinions highlights how sufficient shared data can overcome initial differences in probabilistic beliefs for specific future outcomes.