the problem statement ... explicitly says you can't two-box if Omega decided you would one-box.
The decision is yours, Omega only foresees it.
These stop contradicting each other if you rephrase a little more precisely. It's not that you can't two-box if Omega decided you would one-box--you just don't, because in order for Omega to have decided that, you must have also decided that. Or rather, been going to decide that--and if I understand the post you linked correctly, its point is that the difference between "my decision" and "the predetermination of my decision" is not meaningful.
As far as I can tell--and I'm new to this topic, so please forgive me if this is a juvenile observation--the flaw in the problem is that it cannot be true both that the contents of the boxes are determined by your choice (via Omega's prediction), and that the contents have already been determined when you are making your choice. The argument for one-boxing assumes that, of those contradictory premises, the first one is true. The argument for two-boxing assumes that the second one is true.
The potential flaw in my description, in turn, is whether my simplification just now ("determined by your choice via Omega") is actually equivalent to the way it's put in the problem ("determined by Omega based on a prediction of you"). I think it is, for the reasons given above, but what do I know?
(I feel comfortable enough with this explanation that I'm quite confident I must be missing something.)
This post was inspired by taw urging us to mathematize Newcomb's problem and Eliezer telling me to post stuff I like instead of complaining.
To make Newcomb's problem more concrete we need a workable model of Omega. Let me count the ways:
1) Omega reads your decision from the future using a time loop. In this case the contents of the boxes are directly causally determined by your actions via the loop, and it's logical to one-box.
2) Omega simulates your decision algorithm. In this case the decision algorithm has indexical uncertainty on whether it's being run inside Omega or in the real world, and it's logical to one-box thus making Omega give the "real you" the million.
3) Omega "scans your brain and predicts your decision" without simulating you: calculates the FFT of your brainwaves or whatever. In this case you can intend to build an identical scanner, use it on yourself to determine what Omega predicted, and then do what you please. Hilarity ensues.
(NB: if Omega prohibits agents from using mechanical aids for self-introspection, this is in effect a restriction on how rational you're allowed to be. If so, all bets are off - this wasn't the deal.)
(Another NB: this case is distinct from 2 because it requires Omega, and thus your own scanner too, to terminate without simulating everything. A simulator Omega would go into infinite recursion if treated like this.)
4) Same as 3, but the universe only has room for one Omega, e.g. the God Almighty. Then ipso facto it cannot ever be modelled mathematically, and let's talk no more.
I guess this one is settled, folks. Any questions?