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common_law comments on Confound it! Correlation is (usually) not causation! But why not? - LessWrong
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Comments (34)
A critical mistake in the lead analysis is false assumption: where there is a causal relation between two variables, they will be correlated. This ignores that causes often cancel out. (Of course, not perfectly, but enough to make raw correlation a generally poor guide to causality.
I think you have a fundamentally mistaken epistemology, gwern: you don't see that correlations only support causality when they are predicted by a causal theory.
If two variables are d-separated given a third, there is no partial correlation between the two, and the converse holds for almost all probability distributions consistent with the causal model. This is a theorem (Pearl 1.2.4). It's true that not all causal effects are identifiable from statistical data, but there are general rules for determining which effects in a model are identifiable (e.g., front-door and back-door criteria).
Therefore I don't see how something like "causes often cancel out" could be true. Do you have any mathematical evidence?
I see nothing of this "fundamentally mistaken epistemology" that you claim to see in gwern's essay.
Causes do cancel out in some structures, and Nature does not select randomly (e.g. evolution might select for cancellation for homeostasis reasons). So the argument that most models are faithful is not always convincing.
This is a real issue, a causal version of a related issue in statistics where two types of statistical dependence cancel out such that there is a conditional independence in the data, but underlying phenomena are related.
I don't think gwern has a mistaken epistemology, however, because this issue exists. The issue just makes causal (and statistical) inference harder.
I agree completely.