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Group differences are distressing because the more of a difference there is, the more grounds there are for discriminating on the basis of race or sex, and it is incredibly frustrating to find oneself continually judged not for one's own manifested abilities, but for the average abilities manifested by other people who who share one's race or sex.

Yes, if there is an average group difference, then race or sex alone would count as Bayesian evidence of a particular level of ability. A perfect Bayesian, looking at all the evidence, would be justified in statistically discriminating. But there aren't any perfect Bayesians; that's why this blog exists. One needn't contend that all groups have identical average capacities in order to be worried about discrimination. The problem is not discrimination itself, considered abstractly in some toy domain; the problem with discrimination is that in the real world, people are going to do it wrong, and do it wrong in all sorts of harmful and oppressive ways.

In "An Intuitive Explanation of Bayesian Reasoning," Eliezer writes that people don't pay enough attention to priors, but I wonder if the opposite isn't the case when the task is evaluating people whose race and sex are known.