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buybuydandavis comments on On the Importance of Systematic Biases in Science - Less Wrong Discussion
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Comments (14)
Maybe it's just that it's late, but what he's saying in this quote isn't making sense to me.
To demonstrate the validity of the italicized comment, he should give an example where the data values are causally independent, but not logically independent. But the example he gives, of shared conversations and folklore, strike me as not causally independent at all, so while it supports the basic point about systematic error, it doesn't support this particular comment.
What's more, that's not even the problem. Let's say you ask the Chinese people to estimate the height of the king of Samoa. Here they've never talked of him, and know nothing about him other than that he's human. You still can't magic the information out of repeated estimation.
I was confused about that too. I think he must mean conditionally causally independent, but then he has to say conditional on what.
Maybe he means that each interview of a citizen is causally independent, since interviewing one of them won't causally affect the answer of another.
You could analyze the interview as adding a perturbation to people's "pre" responses, and per jsalvatier's comment, say that those perturbations are conditionally independent, as conditioned by the pre responses.
But it's the independence of the response that matters, and it's not independent of the stories and folklore.
Maybe my confusion can be clarified by showing a case where you have logical dependence but causal independence. I'm not seeing it. Jaynes uses inferential reasoning using backward in time urn draws as his go to example for causal independence but logical dependence. But that still seems a case where there is shared causal dependence on the number and kinds of balls in the urn originally.