The "paradox" of Newcomb's Problem arises because Omega leaves the room. I'm going to steel-man the situation a little bit by stipulating that Omega doesn't put the million in the black box if it predicts that you will take longer than 1 minute to decide, or if it predicts that you will somehow randomize your decision using some process external to your brain.
Now, instinctively, some people want to say something to themselves like "Well, Omega has left the room. No matter whether I reach for one box or both of them, the amounts of money within them aren't going to change. So I might as well take both and get as much money as I can, given what has already occurred.", and then they take both boxes. The problem is, Omega predicted that they would go through that very chain of reasoning, and thus didn't fill the black box with a million dollars.
A better approach is to say to yourself, "Omega has probably correctly predicted what I'm going to do. So, I'll perform the action that, if Omega predicted it, will end up with me getting the most money." And then you end up with the million.
Now, some counter by saying "Wait a second...then for the two boxers, it's already too late for them to change their decision! So they're not irrational, just unlucky (to have the disposition to two-box)." And, from the outside, I might agree. But the person interacting with Omega can't make the same argument! Because then Omega would have predicted that the two-boxer would say that, and then proceed to use that as an excuse to take both boxes.
However, humans can't predict each other's behavior anywhere close to as well as a hypothetical brain-scanning superintelligence can. So we use precommitment instead. AIs who can read each other's code, though...again, they might be able to very accurately predict each other's decisions.
I don't see how quantum physics has anything to do with this problem. Quantum randomness events don't (with probability epsilon) reach such a high macro-scale as that of a human decision. I've never dropped a penny and seen quantum randomness carry it a meter (or even a centimeter) off to the right.
I don't see how quantum physics has anything to do with this problem. Quantum randomness events don't (with probability epsilon) reach such a high macro-scale as that of a human decision.
Yes they do reach macrocsopic level, or QM would not be an experimental science.
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.