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felipec  unbelief  14d ago (felipec.substack.com)   960 thread views

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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No it doesn't. The answer is the same regardless.

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.

Then you are an irrational person. It's that simple.

It's definitely not as simple as just claiming your interlocutor is irrational without doing any work to establish that.

a⇒b,¬a∴¬b a) find causation, b) choose X.

If you find causation, then you choose X; you didn't find causation, you don't choose X.

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.

It's precisely the other way around. In the real world causation is merely a hypothesis, it's a tentative story you tell yourself.

  1. It's not the real world, it's a thought experiment, and we do know the causation from the construction.
  2. Even in the real world it's still possible to understand something about causation. We do in fact understand the causal relation between weather, ice cream and skin cancer.

There is a high correlation between the choice and the prediction. Ignoring that correlation is irrational.

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.

I gave two examples where my strategy of analyzing the causation yields better results than yours.

No you did not. You assumed the better results given that you were right. This is circular reasoning.

It's definitely not as simple as just claiming your interlocutor is irrational without doing any work to establish that.

It is a mathematical fact that if a is correlated with b and b leads to better outcomes, using a as information tends to lead to better outcomes.

I use a and I get better outcomes, you don't use a and you get worse outcomes. I'm being rational. You are being irrational.

Saying "it's not that simple" is just false.

I haven't actually made a claim on what you should choose, only that you should reason from causation if available.

No, you are not only saying that, you are also saying that if causation is not available, correlation should be ignored.

You assumed the better results given that you were right.

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.

It is a mathematical fact that if a is correlated with b and b leads to better outcomes, using a as information tends to lead to better outcomes.

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.

I use a and I get better outcomes, you don't use a and you get worse outcomes.

You haven't done any work to establish I get worse outcomes. You haven't even stated the problem.

No, you are not only saying that, you are also saying that if causation is not available, correlation should be ignored.

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.

In any case, if I know the causal effects, I can just derive the outcome.

That is irrelevant.

You should replace "b leads to better outcomes" with "b affects the optimal strategy" for this to be meaningful.

No wrote it "leads to better outcomes" because it does lead to better outcomes.

Because in Newcomb there's no information A

The correlation is the information.

Better outcomes than random, on average, not necessarily better than a different strategy that takes advantage of a causal understanding of the problem.

It is demonstrably better than all the other strategies.

You haven't done any work to establish I get worse outcomes.

I don't need to. It's a mathematical fact.

What needs to be available is knowledge about causation.

Otherwise you are going to ignore the causation. Which is precisely what I said.

That is irrelevant.

It's what invalidates your argument, because it means you don't need to rely on correlation.

No wrote it "leads to better outcomes" because it does lead to better outcomes.

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 is the information.

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?

I don't need to. It's a mathematical fact.

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.

Otherwise you are going to ignore the causation.

I'm not sure what your argument is supposed to be here.

It's what invalidates your argument, because it means you don't need to rely on correlation.

No it doesn't. That's an inverse error fallacy. a ⇒ b. ¬a ∴ ¬b I didn't say correlation was necessary, I said correlation was sufficient. If you have correlation, you can conclude b, that doesn't mean if you don't have correlation you cannot conclude b.

The point is that that doesn't allow for the conclusion you want,

I does allow the conclusion I stated.

The correlation between what?

Choice and prediction.

Mathematics is not a field where you just get to make claims without supporting them.

Yes it does. If x is more likely than y, that means a rational agent should expect x more than y. That's what mathematics tells you.

I didn't say correlation was necessary, I said correlation was sufficient.

Building your strategy on causal understanding is better than building it on correlation. Correlation is for when you don't know the causation, when you do have the causation, it's not needed and you should instead reason on causation.

I does allow the conclusion I stated.

No, the conclusion you stated is incorrect.

Choice and prediction.

But your choice isn't information you can use to affect your choice. Correlation is not the same as causation, so it's only useful for observation.

Your ice cream example, as artificial as it is, works, because you can observe how much ice cream you ate and use that as a proxy for the time of year. But as soon as you're deciding how much ice cream to eat, it's no longer useful because that's not the way the causation runs. You can't make sun screen more effective by eating more icecream. And that's why taking the causation into account allows for superior results.

If x is more likely than y, that means a rational agent should expect x more than y.

That's true, but neither stated rigorously (which you'd need for actual mathematical argument) nor very interesting, and it's not the claim that needed defending. Or at least it's not clear how what you said follows from this. Also, you still haven't clarified the stork example.

Building your strategy on causal understanding is better than building it on correlation.

If causation is available, which in this case it's not. Even then I would argue that all the causation you think you know are nothing more than hypotheses directly reliant on observed correlation.

No, the conclusion you stated is incorrect.

It is demonstrably the case that one-boxing leads the better outcomes. It can be demonstrated mathematically and empirically.

I can write a computer simulation and compare the outcomes of one-boxers with the outcomes of two-boxers. The outcomes of one-boxers are always superior.

You "argument" against that is ipse dixit. "Nuh uh, it does not". That's not serious.

But your choice isn't information you can use to affect your choice.

Another ipse dixit. Yes it is.

Did you even read my essay? It starts with an example that shows the correct choice depends on your choice. I already proved you wrong.

Your ice cream example, as artificial as it is, works, because you can observe how much ice cream you ate and use that as a proxy for the time of year.

No, it works because all anyone needs is correlation, which is evidence of causation.

That's true, but neither stated rigorously (which you'd need for actual mathematical argument) nor very interesting, and it's not the claim that needed defending.

Probability theory is stated rigorously. I don't need to prove what has already been proven.

If causation is available, which in this case it's not.

Causation absolutely is available in Newcomb, because the statement of the though experiment describes the causation. In Ice Cream, because we know how ice cream and sun screen work.

It is demonstrably the case that one-boxing leads the better outcomes. It can be demonstrated mathematically and empirically.

  1. That was not the claim I was calling out
  2. It correlates with better outcomes. Whether this is the same as it being the right decision is disagreed upon.
  3. It can also be demonstrated mathematically that two-boxing is "better", by showing that it is the dominant strategy. That's why it's a paradox.
  4. It's a thought experiment. There is no empirical data available. And even if there were, I've repeatedly explained to you how correlation doesn't allow for such conclusion.

I can write a computer simulation and compare the outcomes of one-boxers with the outcomes of two-boxers.

No, you can't, because you have no satisfying way to operationalize Omega's prediction without breaking the causal structure of the thought experiment.

Did you even read my essay? It starts with an example that shows the correct choice depends on your choice.

  1. I've read it. And you asserted it wasn't a paradox, and your "proof" was that a different example isn't a paradox. That's not a valid argument.
  2. Your example is about the probability distribution of the outcomes. This does not counter my argument "your choice isn't information you can use to affect your choice".

Probability theory is stated rigorously.

Your claims aren't. Hence, they aren't probability theory, and you can't appeal to "probability theory" without doing the work to establish that your questioned claims follow from probability theory. For which you'd need to state them rigorously.

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