It’s often claimed (at least by politicians, journalists and their ilk) that affirmative action tends to “stigmatize” succcessful members of the favored group, in the sense that a Harvard professorship is less prestigious when it’s held by someone who might not have made it to Harvard without an affirmative action boost.
It’s approximately equally often claimed that this is effect is too small to worry about.
I’m not aware of anyone on either side of this argument having attempted to settle the question with arithmetic.
In their defense, the question can’t be settled by arithmetic, because it’s pretty hard to quantify the difference in “prestige” between a professorship that reveals you’re likely to be in the top one-one-hundredth of one percent of the population and a professorship that only reveals you’re likely to be in the top two-one-hundredths of one percent of the population. But we can at least give some answers contingent on different assumptions about this issue. (And contingent also, of course, on various modeling assumptions.)
To that end, here is a primitive first-pass model:
