Causation, Probability and Objectivity

antigonus

Most people here seem to endorse the following two claims:

1. Probability is "in the mind," i.e., probability claims are true only in relation to some prior distribution and set of information to be conditionalized on;
2. Causality is to be cashed out in terms of probability distributions á la Judea Pearl or something.

However, these two claims feel in tension to me, since they appear to have the consequence that causality is also "in the mind" - whether something caused something else depends on various probability distributions, which in turn depends on how much we know about the situation. Worse, it has the consequence that ideal Bayesian reasoners can never be wrong about causal relations, since they always have perfect knowledge of their own probabilities.

Since I don't understand Pearl's model of causality very well, I may be missing something fundamental, so this is more of a question than an argument.

Most people here seem to endorse the following two claims:

Since I don't understand Pearl's model of causality very well, I may be missing something fundamental, so this is more of a question than an argument.

In the referenced paper, Pearl writes:

Unfortunately, aspirations for reducing causality to probability are both untenable and unwarranted.

Really? Has no one made any progress on this? I would think it would be a fairly straightforward application of comparing the entropy of f(y|x) versus f(x|y), and preferring the model with minimal entropy. I'd expect this to work because causal relations will in general be many to one, so that the causal model gives a tight effect, while the anticausal model would have a spread entropy covering the multiple causes for the effect. When a relation is one to one, then either model suffices for accurate predictions, and I don't need to care.

I'd doubt that a brain, or the mathematics to describe it, would need more than this. We call x a sufficient cause of y if f(y|x) satisfies some condition on it's entropy.

I agree with Pearl about the wonders of baking in our causal knowledge in terms of our choice of functions in a networked representation, but only see that as injecting our prior knowledge of the entropy of the the conditional distributions above.

I haven't followed the literature for years. Does anyone know where this issue stands?

"Really? Has no one made any progress on this?"

(Interventionist) causality is not about probability, it is about responses to hypothetical interventions. Probability is just there to model uncertainty, it is not at all needed (in fact Pearl's first definition of causal models is deterministic).

I think it is also a fair claim that "causality is in the mind," since there does not seem to be any causality in quantum mechanics.

0jsteinhardt14y

This or something similar is the starting point for most approaches to causality, but in general there are going to be many factors having a causal relationship with each variable in your model, and so there are plenty of opportunities for the inequality relating f(y|x) and f(x|y) to switch sign. I haven't done much stuff with causality, though, so take this with a grain of salt. Here is a recent paper in the subject, if you're interested. EDIT: I guess what I'm really trying to say is that x may only have a causal influence on y if a bunch of other factors are present, so it can be hard to tell what's going on just from your graphical model. I'm substantially less confident than 15 seconds ago that this comment makes sense, though.

0Richard_Kennaway14y

I'm only starting to get into this stuff, so I don't have an answer, only some more references. Here is chapter 11 of Pearl's Book, consisting of his 2009 responses to and discussions with readers, which begins with a strong defence of the necessity of separating causal and statistical concepts. Here is a later state of the Pearl/Rubin discussion on Gelman's blog, with links to earlier instalments.