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jsalvatier comments on Smart people who are usually wrong - Less Wrong Discussion
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Remember that idea space is large, so maybe what you have found is people with a significantly different perspective/worldview on things. "Flipping a coin" is not a good analogy.
Consider the following case which I think would generate similar observations. LW members are of two different worldviews wv1 and wv2, and their opinions on some subset of topics is primarily determined by their worldview. Then whenever you write a post reflecting your worldview, the people with a different worldview will disagree consistently.
I suppose this is really a restatement of your last theory.
I have definitely found this to be the case at least when it comes to somewhat political issues, even among quite smart people.