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entirelyuseless comments on Counterfactual Mugging Alternative - Less Wrong
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You are on path 3, but the button is not disabled. The purpose of spending the $100 is to decrease the number of possible worlds where the prophet would come up and talk to you in the first place. You wouldn't end up destroying your timeline by making it inconsistent; ideally, this timeline was just never created because if it had been you would've spent the $100.
Out of curiosity, would you pay Omega in the counterfactual mugging? If you'd pay in CF but not here, that makes me worry that this formulation isn't similar.
I would pay Omega in the counterfactual mugging, but I would not pay here.
The reason is that in the counterfactual mugging case, I would want to be the sort of person who pays when they get offered a deal like that.
Here, I would not want to be the sort of person who pays to fight an infallible prophecy.
However, I would want to be the sort of person who pays to fight a non-infallible prophecy, so I would be happy to precommit to pay in non-infallible prophecy situations.
The kind of person who pays to fight an infallible prophecy is the same kind of person to whom infallible prophecies are given 50% less often. In this case.