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Recursive thinking, Newcomb's problem, and free will

felipec.substack.com

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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If omega can be wrong then the entirety of the problem hinges on when/how/why it can be wrong.

No it doesn't. The entirety of intelligent agency relies partial knowledge, and you want to simplify Newcomb's problem to a problem of simply not having enough knowledge: "if only we knew how the system works then we could cheat the system".

The original formulation of the problem tells you explicitly that you have no reason to believe you will be any different, that is: you will not cheat the system.

It tells you explicitly your choice will be predicted almost certainly.

flip a very slightly weighted coin

The problem states that if you do that, Omega will put nothing in the mystery box.

Literally none of this is explained in the premise.

Yes it is.

It's not that I can't see a way for this to happen, it's that I can imagine a dozen hypothetical ways it could try to do this, and half of them let me two box anyway while half of them don't.

And these hypothetical ways violate what is very explicitly stated in the problem.