I suppose not fighting the hypothesis here must include ignoring the possibility that there are things in the universe that can't be predicted by a mind localized in space and time. So An Omega can exist, it is possible to know everything about you including the position and momentum of every particle that makes up your body and your brain, and this gives enough information to predict all future values of position and momentum of every one of those particles.
I don't think it can exist in our universe either, but if it could exist in some universe and I could exist in that universe also, would I one box or two box? All I can really say is I hope I would one box, it is not entirely up to the me-now in this universe. Whether the hypotetical then-and-there-me would one box or not, I am confident that if he did one box he'd get the million in that universe, and if he didn't he wouldn't. Unless we assume we have already made hypotheses about whether what we thing we would do in other universes is by hypothesis correct once we state it, in which case we wouldn't want to fight that hypothesis either.
None of this seems to me to read on the question of how much effort should be devoted to making sure an AI in THIS universe would one box, which I thought was the original reason to bring up Necomb's problem here. To answer THAT question, you WOULD have to concern yourself with whether this is a universe in which an honest Omega could exist.
But for the pure problem where we don't get to give the sniff test to our hypotheses, you know what you must do.
First reading about Newcomb’s Problem my reaction was petty much "wow, interesting thought" and "of course I would one box, I want to win $ 1 million after all". But I had a lingering nagging feeling, that there is something wrong with the whole premise. Now, after thinking about it for a few weeks I think I have found the problem.
First of all I want to point out, that I would still one box after seeing Omega predicting 50 or 100 other people correctly, since 50 to 100 bits of evidence are enough to ovecome (nearly) any prior I have about how the universe works. Only I do not think this scenario is physically possible in our universe.
The mistake is nicely stated here:
This is only true in this sense if neither MWI is true nor there are any quantum probabilistic processes, i.e., our universe allows for a true Laplace's demon (a.k.a. Omega) to exist.
If MWI is true Joe can set it up so, that "after" Omega filled the boxes and left there "will" be Everett Branches, in which Joe "will" twobox and different Everett Branches in which Joe "will" onebox.
Intuitively I think Joe could even do this with his own brain by leaving it in "undecided" mode until Omega leaves and then using an algorithm which feels "random" to decide if he oneboxes or twoboxes. But of course I would not thrust my intuition here and I do not know enough about Joe's brain to decide if this really works. So Joe would use e.g. a single photon reflected/transmitted off/through a semitransparent mirror, ensuring, that he oneboxes respectively twoboxes in say 50% of the Everett Branches.
If MWI is not true but there are quantum probabilistic process, Omega simply cannot predict the future state of the universe. So the same procedure used above would ensure that Omega cannot predict Joes decision due to true randomness.
So I would be very very VERY surprised if I saw Omega pull this trick 100 times in a row and I could somehow rule out Stage Magic (which I could not).
I am not even sure if there is any serious interpretation of quantum mechanics that allows for the strict determinism Omega would need. Would love to hear about one in the comments!
Of course from an instrumental standpoint it is always rational to firmly precommit to onebox, since the extra $1000 are not worth taking the risk. Even the model uncertainity accounts for much more than 0.001.