orthonormal comments on Rationality Quotes July 2011 - Less Wrong
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C.S. Lewis, "Bulverism"
(It's not exactly correct- evidence of bias is some evidence against a belief- but not always as strong of evidence as it's assumed to be.)
I've actually always found C.S. Lewis to be one of the single most fascinating and compelling Christian writers. Obviously I think he makes some very fundamental mistakes, but his approach to Christianity is about as rationalist as you can get. He really emphasizes that if you're going to believe in something, it better really be true not just "worth believing in" or "virtuous" or "helpful" -- he himself could have written Belief in Belief. Furthermore, he seems committed to a conception of "faith" that doesn't involve any conflict with rationality -- he thinks that the logical arguments for the existence of God do a lot of work, and he's fairly sophisticated scientifically (seems reasonably knowledgeable about evolution, quantum mechanics, etc.). I would actually highly recommend The Screwtape Letters to any rationalists who find religious arguments interesting (if not compelling).
One gets that impression if one reads Mere Christianity and the Screwtape Letters. But if one reads his works aimed at children one gets the impression that he wants children to believe despite evidence. See for example the scene in The Silver Chair where the protagonists are trapped underground and the Lady of the Green Kirtle tries to enchant them to think that Narnia, Aslan and the Sun are all things they made up as part of a game. They are almost taken in until they declare that they will believe in Aslan even if there's is no Aslan because the world they've imagined if it has been imagined is a better world than the one they live in.
He's proof that you can develop a quite rational account of human psychology, and then use it to shoot yourself in the foot.
(Thanks to ciphergoth for the pointer to this quote.)
Why should evidence of bias be some evidence against a belief? This would be like magic: using someone's failure of rationality to learn something about the world, which is absurd. (Example: Federer's wife is very confident that he will win, because she is biased in his favor. Does this give me any reason to bet against Federer? Obviously not.)
If you find out that someone believes A then that's evidence for A, so your beliefs change away from the priors. If you subsequently find that the person is likely biased then your beliefs return some way toward your priors. So finding out about the bias was in some sense evidence about A.
To be precise, knowing that someone is biased towards holding a belief decreases the amount you should update your own beliefs in response to theirs — because it decreases the likelihood ratio of the test.
(That is, having a bias towards a belief means people are more likely to believe it when it isn't true (more false positives), so a bias-influenced belief is less likely to be true and therefore weaker evidence. In Bayesian terms, bias increases P(B) without increasing P(B|A), so it decreases P(A|B).)
So CarmendeMacedo's right that you can't get evidence about the world from knowledge of a person's biases, but you should decrease your confidence if you discover a bias, because it means you had the wrong priors when you updated the first time.
On the contrary, in the absence of the time, resources, or inclination to completely retrace a person's reasoning, psychological factors (such as whether the result is desirable to the person in question) are indeed relevant to the probability that the person made a mistake since in general
P(made mistake | result is appealing) != P(made mistake | result not appealing)