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Perplexed comments on Defecting by Accident - A Flaw Common to Analytical People - Less Wrong
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I don't think "are generally" applies "no matter the the direction or even existence of causal relations".
If A causes E and B independently causes E, then there will be correlation between A and E and between B and E, but no reason to expect correlation between A and B.
You're right, and I really should have known better. This is one of the examples used in Judea Pearl's Casaulity, about how to assign plausible causation structures given only correlations.