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Eliezer_Yudkowsky comments on Counterfactual Mugging - Less Wrong
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The counterfactual anti-mugging: One day No-mega appears. No-mega is completely trustworthy etc. No-mega describes the counterfactual mugging to you, and predicts what you would have done in that situation not having met No-mega, if Omega had asked you for $100.
If you would have given Omega the $100, No-mega gives you nothing. If you would not have given Omega $100, No-mega gives you $10000. No-mega doesn't ask you any questions or offer you any choices. Do you get the money? Would an ideal rationalist get the money?
Okay, next scenario: you have a magic box with a number p inscribed on it. When you open it, either No-mega comes out (probability p) and performs a counterfactual anti-mugging, or Omega comes out (probability 1-p), flips a fair coin and proceeds to either ask for $100, give you $10000, or give you nothing, as in the counterfactual mugging.
Before you open the box, you have a chance to precommit. What do you do?
I would have no actionable suspicion that I should give Omega the $100 unless I knew about No-mega. So I get the $10000 only if No-mega asks the question "What would Eliezer do knowing about No-mega?" and not if No-mega asks the question "What would Eliezer do not knowing about No-mega?"