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So8res 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.
I disagree. If the agent has a 95% probability of doing the same thing as me and a 5% chance of defecting, I still cooperate. (With 95% probability, most likely, because you gotta punish defectors.)
Indeed, consider the following game: You give me a program that must either output "give" or "keep". I roll a 20 sided die. On a 20, I play your program against a program that always keeps its token. Otherwise, I play your program against itself. I give you the money that (the first instance of) your program wins. Are you willing to pay me $110 to play? I'd be happy to pay you $110 for this opportunity.
I don't cooperate with myself because P(TheirChoice=Defect)=0, I cooperate with myself because I don't reason as if p is independent from my action.