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cousin_it comments on Solve Psy-Kosh's non-anthropic problem - Less Wrong Discussion
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I'm not sure if this is relevant either, but I'm also not sure that such an assumption is needed. Note that failing to coordinate is the worst possible outcome - worse than successfully coordinating on any answer. Imagine that you inhabit case 2: you see a good argument for "yea", but no equally good argument for "nay", and there's no possible benefit to saying "nay" unless everyone else sees something that you're not seeing. Framed like this, choosing "yea" sounds reasonable, no?
There's no particular way I see to coordinate on a "yea" answer. You don't have any ability to coordinate with others while you're answering questions, and "nay" appears to be the better bet before the problem starts.
It's not uncommon to assume that everyone in a problem like this thinks in the same way you do, but I think making that assumption in this case would reduce it to an entirely different and less interesting problem -- mainly because it renders the zero in the payoff matrix irrelevant if you choose a deterministic solution.