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lmm comments on The sin of updating when you can change whether you exist - Less Wrong
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The naive answer to that situation still sounds correct to me. (At least, if one is to be consistent with the notion that one-boxing is the correct answer in the original Newcomb paradox).
To see the difference between these two scenarios, ask the following question: "what policy should I precommit to before the whole story unravels?" In Newcomb, you should clearly precommit to one-boxing: it causes Omega to put lots of money in the first box. Here, precommitting to push the button is BAD: it doesn't influence FOOM vs. DOOM, only influences in which scenario Omega hands you the button + whether you get tortured.