This post is about an elementary fact of probability applied to University policy. The policy challenge is what many universities face, namely how to bring the racial and ethnic composition of the faculty in line with the pool of qualified candidates. One policy idea that gets voiced repeatedly is “When you conduct a faculty search, just make sure you invite the top few URM applicants  for an interview.” This sounds reasonable at first blush, but under current California law such a policy is illegal. Here is a way to understand why:
Suppose for the sake of argument that the targeted identity group are redheads. Policy proposal (A) is “Make sure you interview the top few redheads”. Because academic merit has nothing to do with hair color, the average redhead is just as good as the average blond, right? Yes, but not so for the top-ranked redhead. If redheads make up 5% of the applicant pool  then on a merit-ranked list of all applicants the top-ranked redhead will typically be at position #20.
Now consider this policy (B): “First rank all the applicants by merit. Then pull out the redheads and improve their rank by a factor of 20; for example a redhead ranked #60 on the list gets promoted to #3. Then invite people for interviews from the top of the list.”
Most people will look at policy (B) and say “that’s ridiculous, you can’t justify that”. But (A) and (B) are (on average) the same policy. The proof – as probability books love to say – is left to the reader.
 For non-US readers: URM = under-represented minority.
 I’m pulling that number out of thin air.