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Thomas comments on Rationality is Systematized Winning - Less Wrong
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That's brilliant! (I'm not sure what you mean by understand though.)
In other words, Omega does one of the two things: it either offers you $1000 + $1, or only $10. It offers you $1000 + $1 only if it predicts that you won't take the $1, otherwise it only gives you $10.
This is a variant of counterfactual mugging, except that there is no chance involved. Your past self prefers to precommit to not taking the $1, while your present self faced with that situation prefers to take the 1$.
You have to understand this twist, to be able to call yourself rational, by my book.
You understood the twist, as I see.
This reply is too mysterious to reveal whether you got the criterion right.