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robzahra comments on Excuse me, would you like to take a survey? - Less Wrong
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No, you can't ask yourself what you'll do. It's like a calculator that seeks the answers to the question of "what is 2+2?" in a form "what will I answer to the question "what is 2+2"?", in which case the answer 57 will be perfectly reasonable.
If you are cooperating with your copy, you only know that the copy will do the same action, which is a restriction on your joint state space. Given this restriction, the expected utility calculation for your actions will return a result different from what other restrictions may force. In this case, you are left only with 2 options: (C,C) and (D,D), of which (C,C) is better.
you're right. speaking more precisely, by "ask yourself what you would do", I mean "engage in the act of reflecting, wherein you realize the symmetry between you and your opponent which reduces the decision problem to (C,C) and (D,D), so that you choose (C,C)", as you've outlined above. Note though that even when the reduction is not complete (for example, b/c you're fighting a similar but inexact clone), there can still be added incentive to cooperate...