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Perplexed comments on Desirable Dispositions and Rational Actions - Less Wrong
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Because, in predicting my future decisions, he is performing Laplace demon computations based on Heisenberg demon measurements. And physics rules out such demons.
Anything which cannot consistently coexist with what is already known to exist
One possibility: Omega is running this universe as a simulation, and has already run a large number of earlier identical instances.
There may be many less obvious possibilities, even if you require Omega to be certain rather than just very sure.
Ok, that is possible, I suppose. Though it does conflict, in a sense, with the claim that he put the money in the box before I made the decision whether to one-box or two-box. Because, in some sense, I already made that decision in all(?) of those earlier identical simulations.
It is far from sure that the decisions made by human brains rely heavily on quantum effects and that the relevant data can't be obtained by some non-destructive scanning, without Heisenberg-demonic measurements. The Laplace-demon aspects is in fact a matter of precision. If Omega needed to simulate the brain precisely (unfortunately, the formulations of the paradox here on LW and in the subsequent discussions suggest this), then yes, Omega would have to be a demon. But the Newcomb's paradox needn't happen in its idealised version with 100% success of Omega's predictions to be valid and interesting. If Omega is right only 87% of the time, the paradox still holds, and I don't see any compelling reason why this should be impossible without postulating demonic abilities.