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swestrup comments on Counterfactual Mugging - Less Wrong
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It's not capricious in the sense you give: you are capable of predicting some of its actions: because it's assumed Omega is perfectly trustworthy, you can predict with certainty what it will do if it tells you what it will do.
So, if it says it'll give you 10k$ in some condition (say, if you one-box its challenge), you can predict that it'll give it the money if that condition arises.
If it were capricious in the sense of complete inability of being predicted, it might amputate three of your toes and give you a flower garland.
Note that the problem supposes you do have certainty that Omega is trustworthy; I see no way of reaching that epistemological state, but then again I see no way Omega could be omnipotent, either.
On an somewhat unrelated note, why would Omega ask you for 100$ if it had simulated you wouldn't give it the money? Also, why would it do the same if it had simulated you would give it the money? What possible use would an omnipotent agent have for 100$?
If we assume I'm rational, then I'm not going to assume anything about Omega. I'll base my decisions on the given evidence. So far, that appears to be described as being no more and no less than what Omega cares to tell us.
Fine, then interchange "assume omega is honest" with, say, "i've played a billiion rounds of one-box two-box with him" ...It should be close enough.
I realize this is fighting the problem, but: If I remember playing a billion rounds of the game with Omega, that is pretty strong evidence that I’m a (slightly altered) simulation. An average human takes about a ten million breaths each year...
OK, so assume that I’m a transhuman and can actually do something a billion times. But if Omega can simulate me perfectly, why would it actually waste the time to ask you a question, once it simulated you answering it? Let alone do that a billion times... This also seems like evidence that I’m actually simulated. (I notice that in most statements of the problem, the wording is such that it is implied but not clearly stated that the non-simulated version of you is ever involved.)