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AllanCrossman comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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I believe the "correct" answer a is now given by the equation:
a = 2/3 * (100 + ((n-1) * a)) / n
where n is the total number of players, including cousin-it.
Except this doesn't take into account people who didn't see or ignored cousin-it 's post. But if cousin-it's guess was stated at the outset, I think the "correct" answer would be as above.
Edit: Richard Kennaway points out that this simplifies to a = 200 / (n+2)