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Eugine_Nier comments on Don't Get Offended - LessWrong
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Ironically this is a case where p(a|b) is in fact a good proxy for p(b|a) and and the kind of filtering you're objecting to is in fact the correct thing to do from a Bayesian perspective.
See also: Offended by conditional probability
“The best mathematicians are disproportionately white and asian, therefore if I hire a white or asian I'll get an above-average mathematician” is Bayesianly correct if the race is the only thing you know about the candidates; but it isn't (a randomly-chosen white or Asian person is very unlikely to be a decent mathematician), and the other information you have about the candidates most likely mostly screens off the information that race gives you about maths skills.
Read the comment I linked to and possibly subsequent discussion if you're interested in these things.
Hmm, so E(the Math SAT score that X deserves|the Math SAT score that X got is 800, and X is male) is just 4 points more than E(the Math SAT score that X deserves|the Math SAT score that X got is 800, and X is female). That doesn't sound like terribly much to me, and I'd guess there are plenty of people who, due to corrupted mindware and stuff, would treat a male who got 800 better than a female who got 800 by a much greater extent than justified by that 4-point difference in the Bayesian posterior expected values. (Cf the person who told whowhowho that Obama must be dumber than Bush -- surely we know much more about them than their races?)
I'm not sure if this is correct, but I sometimes wonder given how they're surrounded by spin-doctors and other image manipulators how much we really know about prominent politicians, especially when the politician in question is new so you can't look at his record.