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Vladimir_Nesov comments on Counterfactual Mugging - Less Wrong
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Do they know before being confronted by Omega, or only once confronted?
If they did not know in advance that it's more likely for Omega to appear and conduct the counterfactual mugging than it is for anti-Omega to appear and reward those who wouldn't cooperate on the counterfactual mugging, then I can't see that there's any point in time where the agent should expect greater utility by committing to cooperate on the counterfactual mugging. If they do know in advance, then it's better to precommit.
It's an assumption of the thought experiment that the player justifiably learns about the situation after the coin is tossed, that they are dealing with Omega and not "anti-Omega" and somehow learn that to be the case.
In that case, it doesn't seem like there's any point in time where a decision to cooperate should have a positive expected utility.