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emic-and-etic comments on Ingredients of Timeless Decision Theory - Less Wrong
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You're right, I failed to realize that with timeless agents, we can't do backwards induction using the physical order of decisions. We need some notion of the logical order of decisions.
Here's an idea. The logical order of decisions is related to simulation ability. Suppose A can simulate B, meaning it has trustworthy information about B's source code and has sufficient computing power to fully simulate B or sufficient intelligence to analyze B using reliable shortcuts, but B can't simulate A. Then the logical order of decisions is B followed by A, because when B makes his decision, he can treat A's decision as conditional on his. But when A makes her decision, she has to take B's decision as a given.
Does that make sense?
This reminds me of logical Fatalism and the Argument from Bivalence