Sometimes following the best available answer will lead you to an answer that is incorrect, but from your own perspective it is always the way to maximize your chance of being right.
To recap, what I originally said here was:
I don't think it is true that both parties necessarily wind up with more accurate estimates after updating and agreeing, or even an estimate closer to what they would have obtained by sharing all their data.
The scenario in the grandparent provides an example of an individual's estimate becoming worse after Aumann agreeing - and also an example of their estimate getting further away from what they would have believed if both parties had shared all their evidence.
I am unable to see where we have any disagreement....
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