cousin_it comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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If 4/5 of the players conspire to answer 100, they win over the rest of the players who answer 0, so it's not always a good idea to abide by the above argument. See also this strategy.
Edit: I fixed the reply; this is the original mistaken/confused argument on which cousin_it replied below (although the conclusion remains the same):
Given that a sole player answering 100 wins when all others answer 0, it's not a failure of reason to not abide by the above argument.
Wrong. If we have two players, one says 100, other says 0, average is 50, 2/3 of average is 33, player 2 wins. Add more players saying 0 and it gets even worse.
You are right; fixed.