Here is a remarkable variation on that puzzle. A tiny change makes it work out completely differently.
Same setup as before, two private dice rolls. This time the question is, what is the probability that the sum is either 7 or 8? Again they will simultaneously exchange probability estimates until their shared estimate is common knowledge.
I will leave it as a puzzle for now in case someone wants to work it out, but it appears to me that in this case, they will eventually agree on an accurate probability of 0 or 1. And they may go through several rounds of agreement where they nevertheless change their estimates - perhaps related to the phenomenon of "violent agreement" we often see.
Strange how this small change to the conditions gives such different results. But it's a good example of how agreement is inevitable.
To whom it may concern:
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.
(After the critical success of part II, and the strong box office sales of part III in spite of mixed reviews, will part IV finally see the June Open Thread jump the shark?)