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lackofcheese comments on Example decision theory problem: "Agent simulates predictor" - Less Wrong Discussion
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On an extremely similar note, as I've argued here, I'm pretty sure that AIXI two-boxes on Newcomb's problem.
Basically my argument is that AIXI can fairly trivially work out whether the box is full or empty, and hence it two-boxes due to causal assumptions implicit in the AIXI algorithm. Moreover, that line of reasoning is very easy for Omega to come across, and so Omega predicts two-boxing and the box ends up being empty, and then AIXI takes two boxes and ends up with $1000.