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cousin_it comments on A problem with Timeless Decision Theory (TDT) - Less Wrong
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Why is cooperation more likely to qualify as "playing chicken" than defection here?
I was referring to the example Eliezer gives with your opponent being a DefectBot, in which case cooperating makes Omega's claim false, which may just mean that you'd make your branch of the thought experiment counterfactual, instead of convincing DefectBot to cooperate:
So? That doesn't hurt my utility in reality. I would cooperate because that wins if agent X is correlated with me, and doesn't lose otherwise.
Winning is about how alternatives you choose between compare. By cooperating against a same-action DefectBot, you are choosing nonexistence over a (D,D), which is not obviously a neutral choice.
I don't think this is how it works. Particular counterfactual instances of you can't influence whether they are counterfactual or exist in some stronger sense. They can only choose whether there are more real instances with identical experiences (and their choices can sometimes acausally influence what happens with real instances, which doesn't seem to be the case here since the real you will choose defect either way as predicted by Omega). Hypothetical instances don't lose anything by being in the branch that chooses the opposite of what the real you chooses unless they value being identical to the real you, which IMO would be silly.
What can influence things like that? Whatever property of a situation can mark it as counterfactual (more precisely, given by a contradictory specification, or not following from a preceding construction, assumed-real past state for example), that property could as well be a decision made by an agent present in that situation. There is nothing special about agents or their decisions.
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.