Newcomb's problem splits people 50/50 in two camps, but the interesting thing is that both sides think the answer is obvious, and both sides think the other side is being silly. When I created a video criticizing Veritasium's video This Paradox Splits Smart People 50/50 I received a ton of feedback particularly from the two-box camp and I simply could not convince anyone of why they were wrong.
That lead me to believe there must be some cognitive trap at play: someone must be not seeing something clearly. After a ton of debates, reading the literature, considering similar problems, discussing with LLMs, and just thinking deeply, I believe the core of the problem is recursive thinking.
Some people are fluent in recursivity, and for them certain kind of problems are obvious, but not everyone thinks the same way.
My essay touches Newcomb's problem, but the real focus is on why some people are predisposed to a certain choice, and I contend free will, determinism, and the sense of self, all affect Newcomb's problem and recursivity fluency predisposes certain views, in particular a proper understanding of embedded agency must predispose a particular (correct) choice.
I do not see how any of this is not obvious, but that's part of the problem, because that's likely due to my prior commitments not being the same as the ones of people who pick two-boxes. But I would like to hear if any two-boxer can point out any flaw in my reasoning.
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Notes -
These are not in tension. In some game theory scenarios adding randomness, if such a thing is actually possible, is useful to some agent. But Newcome's problem is not such a scenario. Adding any chance of walking away without the $1 million is not worth going for the extra $1k and to the best of my knowledge the best you could do by adding randomness would be to make your expected value $500,500. Whereas your expected value if you cooperate is $1m
As for the rest of the post, yeah just seems like you're demanding the hypothetical grant you libertarian free will and say something different than it says. It's very "But I did eat breakfast this morning" fighting of the hypothetical. If you want to demand that actually you can't be predicted, even hypothetically then you're just not willing to engage with the question.
I'm not demanding that I can't be predicted, I'm asking "what does that even mean?" and also "if that's true in the hypothetical, then what's the point? there's nothing left." The problem just axiomatically erases the game away with no details.
Consider another game. Suppose you are given an opportunity to play Tic Tac Toe against Umega. If you choose to play and you lose, you get 0 points. If you win or tie, you get 1000 points. But if you forfeit prior to playing the game you can get 100 points. Umega can't predict the future, but instead is extremely tricky. Somehow, it always wins at Tic Tac Toe. No matter what you originally intend to do or plan you make, things don't go the way you intended and it tricks you and lose anyway. What do you do?
The way to maximize your points here is to forfeit. Because if you try to play the game then, axiomatically, Umega tricks you and you lose. If you present a winning strategy for Tic Tac Toe that cannot be beaten and say you'll stick to that strategy no matter what Umega does then I retort that you attempt to do that, but then Umega tricks you and you lose anyway. It's a master of psychology and deceit beyond human comprehension. Okay, fine, you have no agency, you forfeit and get the 100 points because the game mathematically reduces to "forfeit: 100 points, don't forfeit: 0 points" with no other options.
Now suppose I go around presenting this to Chess Grandmasters or something (since Tic Tac Toe masters don't exist), and present it as some deep and extremely challenging variant of Tic Tac Toe and grand strategy. Chess Grandmasters stumped by this challenging variant of Tic Tac Toe!
It's not Tic Tac Toe! The optimal strategy of the game is completely and utterly independent to strategies for winning Tic Tac Toe. No matter how much or how little someone knows about Tic Tac Toe, it has nothing to do with the optimal strategy for this game (which is just forfeit) because it's not even engaging with the rules at all. You could substitute basically any strategy game there, I merely used Tic Tac Toe to point out the apparent contradiction of axiomatically declaring that you lose despite there being a known winning strategy.
This has the same fundamental problem as Newcomb's problem. If your agency is stripped from you then what even is the point of the thought experiment? "Suppose you have no free will, and will be punished for trying to act as if you have free will. What do you do?" I guess I forfeit and hope that next time I'm offered a thought experiment it allows me to make choices.
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