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Normal_Anomaly comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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The definition of omega as something that can predict your actions leads it to have some weird powers. You could pick a box based on the outcome of a quantum event with a 50% chance, then omega would have to vanish in a puff of physical implausibility.
I suspect Omega would know you were going to do that, and would be able to put the box in a superposition dependent on the same quantum event, so that in the branches where you 1-box, box B contains $1million, and where you 2-box it's empty.
Exactly what I was thinking.