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Nebu comments on Counterfactual Mugging - Less Wrong
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Comments (257)
That's not the situation in question. The scenario laid out by Vladimir_Nesov does not allow for an equal probability of getting $10000 and paying $100. Omega has already flipped the coin, and it's already been decided that I'm on the "losing" side. Join that with the fact that me giving $100 now does not increase the chance of me getting $10000 in the future because there is no repetition.
Perhaps there's something fundamental I'm missing here, but the linearity of events seems pretty clear. If Omega really did calculate that I would give him the $100 then either he miscalculated, or this situation cannot actually occur.
-- EDIT --
There is a third possibility after reading Cameron's reply... If Omega is correct and honest, then I am indeed going to give up the money.
But it's a bit of a trick question, isn't it? I'm going to give up the money because Omega says I'm going to give up the money and everything Omega says is gospel truth. However, if Omega hadn't said that I would give up the money, then I wouldn't of given up the money. Which makes this a bit of an impossible situation.
Assuming the existence of Omega, his intelligence, and his honesty, this scenario is an impossibility.
I don't see this situation is impossible, but I think it's because I've interpreted it differently from you.
First of all, I'll assume that everyone agrees that given a 50/50 bet to win $10'000 versus losing $100, everyone would take the bet. That's a straightforward application of utilitarianism + probability theory = expected utility, right?
So Omega correctly predicts that you would have taken the bet if he had offered it to you (a real no brainer; I too can predict that you would have taken the bet had he offered it).
But he didn't offer it to you. He comes up now, telling you that he predicted that you would accept the bet, and then carried out the bet without asking you (since he already knew you would accept the bet), and it turns out you lost. Now he's asking you to give him $100. He's not predicting that you will give him that number, nor is he demanding or commanding you to give it. He's merely asking. So the question is, do you do it?
I don't think there's any inconsistency in this scenario regardless of whether you decide to give him the money or not, since Omega hasn't told you what his prediction would be (though if we accept that Omega is infallible, then his prediction is obviously exactly whatever you would actually do in that situation).