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Khoth comments on Chocolate Ice Cream After All? - Less Wrong
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But in that case, when Omega tells me that if I choose carrots I'll have a heart attack, then almost certainly I'm not in a freak world, and actually Omega is wrong.
Assuming i), I would rather say that when Omega tells me that if I choose carrots I'll have a heart attack, then almost certainly I'm not in a freak world, but in a "normal" world where there is a causal mechanism (as common sense would call it). But the point stands that there is no necessity for a causal mechanism so that c) can be true and the game can be coherent. (Again, this point only stands as long as one's definition of causal mechanism excludes the freak case.)
Seems like there are two possible cases. Either: a) There is a causal mechanism b) None of the reasoning you might sensibly make actually works.
Since the reasoning only works in the causal mechanism case, the existence of the freak world case doesn't actually make any difference, so we're back to the case where we have a causal mechanism and where RichardKennaway has explained everything far better than I have.