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lackofcheese comments on Causal decision theory is unsatisfactory - LessWrong
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Assume it's not a perfect clone, it can defect with probability p even if you cooperate. Then apply CDT. You get "defect" for any p>0. So it is reasonable to implicitly assume continuity and declare that CDT forces you to defect when p=0. However, if you apply CDT for the case p=0 directly, you get "cooperate" instead.
In other words, the conterfactual reasoning gets broken when the map CDT(p, PD) is not continuous at the point p=0.
It's not entirely clear what you're saying, but I'll try to take the simplest interpretation. I'm guessing that:
- If you're going to defect, your clone always defects.
- If you're going to cooperate, your clone cooperates with probability 1-p and defects with probability p
In that case, I don't see how it is that you get "defect" for p>0; the above formulation gives "cooperate" for 0<=p<0.5.