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FAWS comments on A problem with Timeless Decision Theory (TDT) - Less Wrong
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Why do you think something can influence it? Whether you choose to cooperate or defect, you can always ask both "what would happen if I cooperated?" and "what would happen if I defected?". In as far as being counterfactual makes sense the alternative to being the answer to "what would happen if I cooperated?" is being the answer to "what would happen if I defected?", even if you know that the real you defects.
Compare Omega telling you that your answer will be the the same as the Nth digit of Pi. That doesn't you allow to choose the Nth digit of Pi.