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.