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cousin_it comments on Formulas of arithmetic that behave like decision agents - Less Wrong
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Thanks for taking the time to think about this! But it seems to me that Löb's theorem should not be required to prove proposition 3 for a properly defined A. I'm guessing that you inadvertently defined A asymmetrically, as described in "AI cooperation in practice", instead of the symmetric way described in "model of UDT with a halting oracle" where swapping C and D shouldn't affect anything except the chicken stage.
Ah, I see. The agent described in "A model of UDT with a halting oracle" is more symmetric, because it has a choice of three actions: "Cooperate", "Defect", and "Break down and cry" (if we count failing to act as an action).
I think I see a way to prove the proposition without using Löb's theorem, and I don't even need to change the definition of A. I'll post here whether it works out.
Thanks for the comment!
Did it work out?
I still intend to write up an answer to that question.
Great!
I finally did it, and I believe it works.