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pragmatist comments on Stuff That Makes Stuff Happen - Less Wrong
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In my example, I specified that the BB is in a reference class with all other brains, including the psychic cousin's. Given that they are both in the reference class, the fact that the BB and the cousin share the same cognitive history implies that the probabilities of their cognitive histories relative to this reference class are the same. The reference class is what fixes the probability distribution over possible outcomes if you're determining probabilities by relative frequencies, and if they are in the same reference class, they will have the same probability distribution.
I suspect Eliezer was thinking of a different probability distribution over brain states when he said the psychic's brain state is correlated with the deck of cards. The probabilities he is referring to are something like the relative frequencies of brain states (or brain state types) in a single observer's cognitive history (ETA: Or perhaps more accurately for a Bayesian, the probabilities you get when you conditionalize some reasonable prior on the sequence of instantiated brain states). Even using this distribution, the BB's brain state will be correlated with the top card.
Even if the BB and the psychic are in causally disconnected parts of your model, them having the same probability of being correlated with the card doesn't imply that the Causal Markov Condition is broken. In order to show that, you would need to specify all of the parent nodes to the BB in your model, calculate the probability of it being correlated with the card, and then see whether having knowledge of the psychic would change your probability for the BB. Since all physics currently is local in nature, I can't think of anything that would imply this is the case if the psychic is outside of the past light cone of the BB. Larger boundary conditions on the universe as a whole that may or may not make them correlate have no effect on whether the CMC holds.
I'm having trouble parsing this comment. You seem to be granting that the BB's state is correlated with the top card (I'm assuming this is what you mean by "having the same probability"), that there is no direct causal link between the BB and the psychic, and that there are no common causes, but saying that this still doesn't necessarily violate the CMC. Am I interpreting you right? If I'm not, could you tell me which one of those premises does not hold in my example?
If I am interpreting you correctly, then you are wrong. The CMC entails that if X and Y are correlated, X is not a cause of Y and Y is not a cause of X, then there are common causes of X and Y such that the variables are independent conditional on those common causes.