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cousin_it comments on A Problem About Bargaining and Logical Uncertainty - Less Wrong
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It's dangerous to phrase it this way, since coordination (which is what really happens) allows using more knowledge than was available at the time of a possible precommitment, as I described here.
Not if the correct decision depends on an abstract fact that you can't access, but can reference. In that case, P should implement a strategy of acting depending on the value of that fact (computing and observing that value to feed to the strategy). That is, abstract facts that will only be accessible in the future play the same role as observations that will only be accessible in the future, and a strategy can be written conditionally on either.
The difference between abstract facts and observations however is that observations may tell you where you are, without telling you what exists and what doesn't (both counterfactuals exist and have equal value, you're in one of them), while abstract facts can tell you what exists and what doesn't (the other logical counterfactual doesn't exist and has zero value).
Good point, thanks. I think it kills my argument.
ETA: no, it doesn't.
As Tyrrell points out, it's not as simple. When you're considering the strategy of what to do if you're on the giving side of the counterfactual ("Should P pay up if asked?"), the fact that you're in that situation already implies all you wanted to know about the digit of pi, so the strategy is not to play conditionally on the digit of pi, but just to either pay up or not, one bit as you said. But the value of the decision on that branch of the strategy follows from the logical implications of being on that branch, which is something new for UDT!