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Vladimir_Nesov comments on Counterfactual Mugging - Less Wrong
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I'm actually not quite satisfied with it. Probability is in the mind, which makes it difficult to know what I mean by "perfect knowledge". Perfect knowledge would mean I also knew in advance that the coin would come up tails.
I know giving up the $100 is right, I'm just having a hard time figuring out what worlds the agent is summing over, and by what rules.
ETA: I think "if there was a true fact which my past self could have learned, which would have caused him to precommit etc." should do the trick. Gonna have to sleep on that.
ETA2: "What would you do in situation X?" and "What would you like to pre-commit to doing, should you ever encounter situation X?" should, to a rational agent, be one and the same question.
MBlume:
This phrasing sounds about right. Whatever decision-making algorithm you have drawing your decision D when it's in situation X, should also come to the same conditional decision before the situation X appeared, "if(X) then D". If you actually don't give away $100 in situation X, you should also plan to not give away $100 in case of X, before (or irrespective of whether) X happens. Whichever decision is the right one, there should be no inconsistency of this form. This grows harder if you must preserve the whole preference order.