This is amazing, Kevin! Really cool and weird results.
I don't quite understand them, actually, in your first case with imperfect memories. In case it helps to ask: Suppose the fair coin lands heads 100 of the 200 times. Then Blues think it landed heads 100–101 times, and Reds think it landed heads 99–100 times, right? Is that the only difference we need enough to make their average credences diverge as widely as is shown? Or is there some cumulative effect of the memory lapses I'm not factoring in, suggested by the notion in your post title of lapses "adding up"? Are the Reds and Blues differing not just about the total number of heads, but about the number of heads in subsets of the flips?
This is amazing, Kevin! Really cool and weird results.
I don't quite understand them, actually, in your first case with imperfect memories. In case it helps to ask: Suppose the fair coin lands heads 100 of the 200 times. Then Blues think it landed heads 100–101 times, and Reds think it landed heads 99–100 times, right? Is that the only difference we need enough to make their average credences diverge as widely as is shown? Or is there some cumulative effect of the memory lapses I'm not factoring in, suggested by the notion in your post title of lapses "adding up"? Are the Reds and Blues differing not just about the total number of heads, but about the number of heads in subsets of the flips?