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 -
That's not how time works. Sequential games in game theory are formally defined such that at each time step, players can make decisions that depend on events that have happened in the past, but not in the future (or present if there are turns with simultaneous moves from different players). A complete strategy profile for each player is defined a series of decisions and contingencies that cover every possible game state so it's always possible to know what they would do at any point. At time 1 I do X, with no conditions because nothing else would happen. At time 2 the other person does Y if I x or Z if I Y. At Time 3 I do A if they Y and B if they Z. I can't say "at time 1 I do X if they Y" because they haven't Y yet. Which means that whoever goes last IS special, because they get the last decision that nobody can respond to. That's how time works in real life, that is how sequential games that happen over time are defined in standard game theory.
If Y does or does not happen at time 2, then you can only condition on Y after time 2. If you claim to be conditioning on Y and it's time 1 then that's a contradiction. You are either lying, or have invented a brand new version of Game Theory and decision-making theory, which requires literal books to establish, not a couple of sentences at the beginning of a problem.
Two boxers think they are special because you told them they were. When you say "Omega can predict you" you are saying "you are not special." When you say "Omega leaves and then you make your decision afterwards" you are saying "you are special." One boxers believed your first sentence more, two boxers believed the second more. Either way you are lying because they can't both happen simultaneously. If Omega can respond to your decision then it goes after you. You have mathematically described the scenario "you pick one box or two, and then if you picked one box Omega puts more money in the big box", and then appended the statement "Omega goes before you." I am reminded of Yudkowsky's Parable of the Dagger. You can say whatever words you want to say, even if they're self-contradictory. They're just words. But then they no longer map to anything real or meaningful.
No it is not.
You didn't bother reading my essay, did you?
All this is explained very clearly in it.
Wrong.
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