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jimrandomh comments on Open Thread: February 2010 - Less Wrong
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I seem to be entering a new stage in my 'study of Less Wrong beliefs' where I feel like I've identified and assimilated a large fraction of them, but am beginning to notice a collusion of contradictions. This isn't so surprising, since Less Wrong is the grouped beliefs of many different people, and it's each person's job to find their own self-consistent ribbon.
But just to check one of these -- Omega's accurate prediction of your choice in the Newcomb problem, which assumes determinism, is actually impossible, right?
You can get around the universe being non-deterministic because of quantum mechanical considerations using the many worlds hypothesis: all symmetric possible 'quark' choices are made, and the universe evolves all of these as branching realities. If your choice to one-box or two-box is dependent upon some random factors, then Omega can't predict what will happen because when he makes the prediction, he is up-branch of you. He doesn't know which branch you'll be in. Or, more accurately, he won't be able to make a prediction that is true for all the branches.
What Omega can do instead is simulate every branch and count the number of branches in which you two-box, to get a probability, and treat you as a two-boxer if this probability is greater than some threshold. This covers both the cases where you roll a die, and the cases where your decision depends on events in your brain that don't always go the same way. In fact, Omega doesn't even need to simulate every branch; a moderate sized sample would be good enough for the rules of Newcomb's problem to work as they're supposed to.
But the real reason for treating Omega as a perfect predictor is that one of the more natural ways of modeling an imperfect predictor is to decompose it into some probability of being a perfect predictor and some probability of its prediction being completely independent of your choice, the probabilities depending on how good a predictor you think it really is. In that context, denying the possibility that a perfect predictor could exist is decidedly unhelpful.