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 -
It behooves you to use more sunscreen because it's summer, not because you're eating ice cream. If you spend your summer holiday at the beach then you should use sunscreen, even if you eat little ice cream because the ice cream stand at the beach has been closed. Meanwhile, if it's january and you eat ice cream for comfort while huddling indoors after a bad breakup, there's no point in using sunscreen.
If you don't understand the causalities, or if you have no other information, ice cream is a proxy that lets you do better than random. But if you do understand it's actually about summer, ice cream is just a distraction.
If you present a variant of Newcomb as "Omega is giving you a choice between two options, "two-boxing" and "one-boxing". People who picked "two-boxing" on average gain $1000, "one-boxing" pickers gain on average $1,000,000", then, sure, obviously B is the optimal choice. But if you add information about what the choices are, and the causal mechanisms behind the payout, then it becomes reasonable to analyze that, and the disagreement about actual Newcomb is pretty much about causality.
You know that because I gave you the background of how I constructed my synthetic problem, but in the real world all you have is the correlation.
But to assume otherwise would be an inverse error fallacy. My question was in the form of
a⇒b, I didn't ask anything if¬a.Which is all that matters.
Consider another study that finds a correlation between a) "the number of nesting storks in European countries" and b) "human birth rates". Are you just going to discount that correlation just because the causal network is not immediately available?
That is literally what the original formulation of Newcomb's problem tells you is going to happen.
You are once again committing an inverse error fallacy.
The fact that you do not immediately see a direct causal link between the choice and the prediction doesn't mean that there isn't a causal network between the two. But more importantly: it doesn't negate the very real and undeniable correlation.
No, I know it because it's not hard to figure out the actual causation. But where I know it from doesn't matter, it still means I can do better in practice.
That you asked about a doesn't mean analyzing ¬a can't give useful further insight. This has nothing to do with inverse error fallacy.
Anyway, the point stands: Understanding the causality allows for a more successful strategy than just knowing a correlation.
For what purpose? For most purposes I could think of, I am indeed going to discount the correlation, because it's unlikely there's a direct causal effect between a and b. If I'm concerned about birth rates, I'm not going to conclude helping storks nest will matter just from that correlation.
The description of the problem tells me the causal rules that govern the problem. Statistical outcomes might be derived from that, but there's no further benefit to that if you already understand the causality.
What? How so?
In Newcomb's problem, the causal links are stated, and we know what direction they do not go in, and we can reason with that. Correlation, meanwhile, tells us little if we already know the causation.
I'm not even sure how Newcomb is supposed to be analogous to the ice cream example. In your post you claim it is, but you never lay it out.
You know A (ice cream) is correlated with B (sun screen is effective against skin cancer), and B implies action X. You observe A, therefore you should do X. Assuming you have indeed no other information, this is correct, and it works because A is a proxy for C (summer) that causes B. But what's A in Newcomb's problem, or the correlation version thereof? It can't be the same as your decision X, because if you touch A, it loses its value as a proxy for C. If you're worried about skin cancer, eating more ice cream won't help, because it doesn't actually affect sun screen efficacy. It's just correlated with it.
No it doesn't. The answer is the same regardless.
Then you are an irrational person. It's that simple.
a⇒b,¬a∴¬ba) find causation, b) choose X.If you find causation, then you choose X; you didn't find causation, you don't choose X. That's an obvious inverse error fallacy.
It's precisely the other way around. In the real world causation is merely a hypothesis, it's a tentative story you tell yourself. And the only reason you worked out a potential causation is because of the correlation.
Correlation is the only real information.
There is a high correlation between the choice and the prediction. Ignoring that correlation is irrational.
I gave two examples where my strategy of analyzing the causation yields better results than yours. Only in one restricted example they come out the same.
It's definitely not as simple as just claiming your interlocutor is irrational without doing any work to establish that.
That doesn't sound like what I've been saying. I haven't actually made a claim on what you should choose, only that you should reason from causation if available. What you actually do depends on the details.
And generally, "A implies B, Not A implies Not B" isn't an inverse error fallacy. Only concluding the latter from the former is.
You haven't done any work to establish that. You just claimed they're analogous and have the same conclusion. But I pointed out they're not actually analogous, so just repeating your claim isn't gonna cut it.
No you did not. You assumed the better results given that you were right. This is circular reasoning.
It is a mathematical fact that if
ais correlated withbandbleads to better outcomes, usingaas information tends to lead to better outcomes.I use
aand I get better outcomes, you don't useaand you get worse outcomes. I'm being rational. You are being irrational.Saying "it's not that simple" is just false.
No, you are not only saying that, you are also saying that if causation is not available, correlation should be ignored.
No, it's common knowledge that putting on sunscreen at the beach in summer is more useful than putting on sunscreen at home in winter. Or do you disagree?
In any case, if I know the causal effects, I can just derive the outcome.
You should replace "b leads to better outcomes" with "b affects the optimal strategy" for this to be meaningful. And "using a as information" does all the work here. Because in Newcomb there's no information A, and in the stork example you haven't specified what what the problem is and therefore what it would mean to "use A as information". "Using A as information" is not necessarily the same as "making your decision dependent on A in a specific way".
Assuming we fix your formulation to something reasonable: Better outcomes than random, on average, not necessarily better than a different strategy that takes advantage of a causal understanding of the problem.
You haven't done any work to establish I get worse outcomes. You haven't even stated the problem.
No, I'm not. What needs to be available is knowledge about causation. If I know A doesn't causally affect B, there's no point in picking A to influence B. That's knowledge about causation that affects the optimal strategy.
That is irrelevant.
No wrote it "leads to better outcomes" because it does lead to better outcomes.
The correlation is the information.
It is demonstrably better than all the other strategies.
I don't need to. It's a mathematical fact.
Otherwise you are going to ignore the causation. Which is precisely what I said.
It's what invalidates your argument, because it means you don't need to rely on correlation.
The point is that that doesn't allow for the conclusion you want, and you need to fix your statement in order to be actually correct.
The correlation between what? Your statement defined a correlation between some A which is observable and can be used as information and some B which is relevant. What is A?
Mathematics is not a field where you just get to make claims without supporting them. In fact it's among the fields the least like that. To establish a claim as mathematical fact, you need mathematical proof. Actually, scratch that, first you need to define the claim, which you haven't done yet.
I'm not sure what your argument is supposed to be here.
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