(1) Why would Joe intend to use the random process in his decision? I'd assume that he wants million dollars much more than to prove Omega's fallibility (and that only with 50% chance).
(2) Even if Joe for whatever reason prefers proving Omega's fallibility, you can stipulate that Omega gives the quest only to people without semitransparent mirrors at hand.
(3) How is this
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.
compatible with this
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).
(emphasis mine)?
Note about terminology: on LW, dissolving a question usually refers to explaining that the question is confused (there is no answer to it as it is stated) together with pointing out the reasons why such a question seems sensible at the first sight. What you are doing is not dissolving the problem, it's rather fighting the hypo.
ad 1: As I pointed out in my post twice, in this case he percommits to oneboxing and and that's it, since assuming atomic resolution scanning and practically infinite processing power he cannot hide his intention to cheat if he wants to twobox.
ad 2: You can, I did not, I suspect - as pointed out - that he could do that with his own brain too, but of course if so Omega woud know and still exclude him.
ad 3:
...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
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.