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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I mean, kinda no? That's where the Wolpert/Benford critique comes in. You can't formalize the problem in terms of game theory without adding additional assumptions. If your additional assumptions to formalize it are, "It's actually a clock, and there's no feasible action set with cardinality greater than one," then sure, you have a suitable formalization... but it's kinda not game theory. If you want to back away from that being your additional assumption, it's kinda still on you to state other formal additional assumptions that make it a well-posed game.
EDIT: Perhaps another way of describing it would be as follows. Suppose one is just analyzing a clock. We'll discretize time for now just to make it simple. Say that we observe from our analysis that in the transition from time t_1 to t_2, the clock will become one second slow compared to some 'objective' time (handwave any difficulties here). We could observe that this is, in some sense, suboptimal, sure.
Now, does it make sense to say something like, "What if we just call this suboptimal action y' and hypothesize an alternative action y that doesn't result in being one second slow?" Would it make sense to say that we have constructed a decision theory problem? Note that we're not specifying anything about any sort of real policy space or anything; it's not like we're saying, "Here is the policy space of possible mechanisms that a non-clock can choose from to design the clock."1 We just have a clock.
Suppose we say that there is some being, Omega, who will accurately predict that said clock will take action y' and become one second slow, and then put some quantity of money in front of the clock. Suppose we say, "Well, imagine the clock took hypothetical action y, which it can't do, then imagine that Omega would put a different quantity of money in front of the clock in that case." Does this become a game theory problem? If so, what am I supposed to solve for? What is the space of possible solutions?
1 - This is perhaps related to my comment about what Yud did to the prisoner's dilemma problem. He created some different policy space about source codes.
Think of a fully clockwork universe, down to the apparently random quantum phenomena. IFF you have the full picture, can see the entanglement at the big bang, can calculate out the impossibly complex gear movements, you can know what a 'random' quantum event is going to be. But from the limited perspective, inside a finite light cone, you cannot. The initial entanglement is invisible, some of the gears are hidden. This doesn't make it not clockwork, it just means you don't have access and so quantum randomness is the best you can do.
We have the same thing here - from our perspective, lacking whatever it is that gives Omega the accuracy, whatever lets it see the gears we can't, our choice looks free and the answer uncorrelated. It is correlated, which is why Omega can be as accurate as it is, but we can't see the same thing. So ordinarily, we use our game theory and our strict domination and it works out fine. But here, we have a cheat. The problem has given us information we otherwise wouldn't have access to - we now know there is, in fact, a correlation between our 'future' choice and the contents of the box now. We don't know how it works, we don't know why it works, but we have been given that information. We can cheat the problem by leveraging that information. That's why one boxing is rational. That's why ordinary game theory goes away. We have something stronger to use in our thinking.
I don't follow. Every part of you that is necessary to follow the clockwork has appropriate access to the mechanisms of the clock, at least to the extent that is necessary for it to be able to follow the clockwork. If there were some part of you that didn't have such access, then it wouldn't be able to follow the clockwork, and we would reach a contradiction.
Like, maybe try to explain how this works directly on the example of analyzing an actual clock, with determined suboptimal action y' and a hypothesized optimal action y. What doesn't have access to what?
You have access to the gears that drive you (up to your particle horizon anyway, you can't necessarily see the whole train of gears leading to you because your lightcone is finite and smaller than the universe as a whole), but that doesn't mean you have access to the gears that drive everything else. Deterministic clockwork does not imply information or light propagation need be any faster than the traditional limit.
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