Hal, that’s why I specified human beings. Human beings often find themselves with common knowledge that they disagree about a question of fact. And indeed, genuine Bayesians would not find themselves in such a pickle to begin with, which is why I question that we can clean up the mess by imitating the surface features of Bayesians (mutual agreement) while departing from their causal mechanisms (instituting an explicit internal drive to agreement, which is not present in ideal Bayesians).
The reason my addition fixes the problem is that in your scenario, the disagreement only holds while the two observers do not have common knowledge of their own probability estimates—this can easily happen to Bayesians; all they need to do is observe a piece of evidence they haven’t had the opportunity to communicate. So they disagree at first, but only while they don’t have common knowledge.
Hal, that’s why I specified human beings. Human beings often find themselves with common knowledge that they disagree about a question of fact. And indeed, genuine Bayesians would not find themselves in such a pickle to begin with, which is why I question that we can clean up the mess by imitating the surface features of Bayesians (mutual agreement) while departing from their causal mechanisms (instituting an explicit internal drive to agreement, which is not present in ideal Bayesians).
The reason my addition fixes the problem is that in your scenario, the disagreement only holds while the two observers do not have common knowledge of their own probability estimates—this can easily happen to Bayesians; all they need to do is observe a piece of evidence they haven’t had the opportunity to communicate. So they disagree at first, but only while they don’t have common knowledge.