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Allan Crossman: Only if they believe that their decision somehow causes the other to make the same decision.

No line of causality from one to the other is required.

If a computer finds that (2^3021377)-1 is prime, it can also conclude that an identical computer a light year away will do the same. This doesn't mean one computation caused the other.

The decisions of perfectly rational optimization processes are just as deterministic.

I apologize if this is covered by basic decision theory, but if we additionally assume:

  • the choice in our universe is made by a perfectly rational optimization process instead of a human

  • the paperclip maximizer is also a perfect rationalist, albeit with a very different utility function

  • each optimization process can verify the rationality of the other

then won't each side choose to cooperate, after correctly concluding that it will defect iff the other does?

Each side's choice necessarily reveals the other's; they're the outputs of equivalent computations.