I tried to follow your proof in the paper. I think I understand the math, but maybe there is some notation that I have misunderstood.Firstly, what's up with not numbering all your equations? That is just rude to anyone trying to comment on you paper.Secondly, what happens between the fist and second equation in the proof of Theorem 1? I understand how you arrive at the fist equation of the proof of Theorem 1. But the next equation seems wrong to me.If start from the second equation of the proof of Theorem 1, and then you take out X from the sum on the left hand side (since X is a constant in that sum), and then divide by the remaining sum, so that you get only X on the left hand side. (Same as how you got the previous equation, only backwards.) Then you end up with:E[V|I(w*)] = E[V|(I and J)(w*)]and that does not look right?What is going on here? What am I misunderstanding?Expand full comment
 Barkley, yes, in a large space beliefs need not converge with evidence. But my result has nothing to do with whether beliefs converge with evidence; it should apply to the situations you describe as well.Expand full comment
 It has been well known since a famous paper by Diaconis and Freeman in the Annals of Statistics quite some time ago that if the game is infinite-dimensioned and the basis is not continuous, then there may be no Bayesian convergence at all. A cyclical outcome is quite likely, the players simply bounce back and forth between two (or more) given priors that never agree and are never correct (this of course assumes an "objective Bayesianism" in which there are "correct" probabilities that the posteriors are supposed to converge to).Expand full comment
 Hal, yes financial disagreement seems small compared to verbal disagreement. Different models only explains it if we don't realize we have different models, and that other people might have good models. Clearly our ancestors must have gained some evolutionary advantage from the tendencies that make us disagree; the challenge is to tease those out and decide which are still relevant today. On the rationality of priors, see the post Why Common PriorsExpand full comment