This approach relies on the unspoken "positivity" assumption that the pool of applicants is large enough that there exist individuals in the biased-against cate

This approach relies on the unspoken "positivity" assumption that the pool of applicants is large enough that there exist individuals in the biased-against category that were not selected, and moreover that these denied applicants are "exchangeable" with the successful ones. For example, assume that we find that founders who won a MacArthur "genius" grant outperformed the others. Further assume that there are only a limited number of such founders, and that all available were selected. Certainly one wouldn't want to conclude in this case that there is a bias against MacArthur fellows. That seems obvious, but it gets trickier once you have lots of factors involved. What if the group you find to outperform consists of female founders with a PhD, substantial industry experience, and red hair[1]. Can you conclude that the process is biased against females? Males with PhD's? Anyone with red hair? Generally no, unless you are willing to assume that all of your factors are causal. Worse, you can't even assume that it's biased against people with all of the measured factors unless you also assume that all unmeasured factors are randomly distributed. If it turns out that "a positive mental attitude" is an unmeasured but defining characteristic of success, if the interviewers rejected applicants who had less of this but you failed to include this in your category, you would be wrong to conclude that there is an unfair bias. [1] http://www.nature.com/nature/journal/v453/n7194/full/453562a.html http://www.nature.com/nature/journal/v453/n7194/full/453562a...