Robert Aumann’s Agreement Theorem shows that honest Bayesians cannot agree to disagree—if they have common knowledge of their probability estimates, they have the same probability estimate.
In addition to what James Annan said, they also both have to know (with very high confidence) that they are in fact honest bayesians. Both sides being honest isn’t enough if either suspects the other of lying.
Robert Aumann’s Agreement Theorem shows that honest Bayesians cannot agree to disagree—if they have common knowledge of their probability estimates, they have the same probability estimate.
In addition to what James Annan said, they also both have to know (with very high confidence) that they are in fact honest bayesians. Both sides being honest isn’t enough if either suspects the other of lying.