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Jack comments on What do professional philosophers believe, and why? - Less Wrong Discussion
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Omega's not dumb. As soon as Omega knows you're trying to "come up with a method to defeat him", Omega knows your conclusion - coming to it by some clever line of reasoning isn't going to change anything. The trick can't be defeated by some future insight because there's nothing mysterious about it.
Free-will-based causal decision theory: The simultaneous belief that two-boxing is the massively obvious, overdetermined answer output by a simple decision theory that everyone should adopt for reasons which seem super clear to you, and that Omega isn't allowed to predict how many boxes you're going to take by looking at you.
I am not saying anything weird, merely that the statements of the Newcomb's problem I heard do not specify how Omega wins the game, merely that it wins a high percentage (all?) of the previous attempts. The same can be said for the punching game, played by a human (who, while quite smart about the volition of punching, is still defeatable).
There are algorithms that Omega could follow that are not defeatable (people like to discuss simulating players, and some others are possible too). Others might be defeatable. The correct decision theory in the punching game would learn how to defeat the punching game and walk away with $$$. The right decision theory in the Newcomb's problem ought to first try to figure out if Omega is using a defeatable algorithm, and only one box if it is not, or if it is not possible to figure this out.