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cousin_it comments on What's wrong with this picture? - Less Wrong Discussion
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I don't see the paradox. P(Alice saw this sequence) is low, and P(Alice presented this sequence) is low, but P(Alice saw this sequence | Alice presented this sequence) is high, so Bob has no reason to be incredulous.
Bob has always been like this.
I think, but am not certain, that you're missing the point, by examining Bob's incredulity rather than the problem as stated. Let's say your probability that the universe is being simulated is 2^x.
Alice flips a coin (x+1) times. You watch her flip the coins, and she carefully marks down the result of each flip.
No matter what sequence you watch, and she records - that sequence has less likelihood of having occurred naturally than that the universe is simulated, according to your priors. If it helps, imagine that a coin you know to be fair turns up Heads each time. (A sequence of all heads seems particularly unlikely - but every other sequence is equally unlikely.)
I agree that the probability of seeing that exact sequence is low. Not sure why that's a problem, though. For any particular random-looking sequence, Bob's prior P(see this sequence | universe is simulated) is pretty much equal to P(see this sequence | universe is not simulated), so it shouldn't make Bob update.