see comments on Can anyone explain to me why CDT two-boxes? - Less Wrong Discussion
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CDT calculates it this way: At the point of decision, either the million-dollar box has a million or it doesn't, and your decision now can't change that. Therefore, if you two-box, you always come out ahead by $1,000 over one-boxing.
So what you're saying is that CDT refuses the whole setup and then proceeds to solve a completely different problem, correct?
Well, Nozick's formulation in 1969, which popularized the problem in philosophy, went ahead and specified that "what you actually decide to do is not part of the explanation of why he made the prediction he made".
Which means smuggling in a theory of unidirectional causality into the very setup itself, which explains how it winds up called "Newcomb's Paradox" instead of Newcomb's Problem.
No.
No, it's just not aware that it could be running inside Omega's head.
Another way of putting it is that CDT doesn't model entities as modeling it.