Quantifying Racial Discrimination
How would we quantify the amount of racial discrimination going on? Let’s take admission to colleges as an example. Suppose that we are in 1950, and a black student with a test score of 900 is rejected, while 80 white students with test scores of less than 900 are admitted. We could measure discrimination in terms of number of people in two ways. We could say that 1 person was discriminated against, or that 80 were discriminated in favor of. (We could look at the size of the test score discrepancy too, but let’s put that aside for now.)
The proper measure is the lesser of the two numbers. The reason is that the actual effect of the discrimination was that one black student was rejected who would have been accepted in the absence of discrimination, and one white student was accepted who would have been rejected. For the other 79 white students, the discrimination actually did not help them– they would have gotten in without it.
Similarly, if affirmative action nowadays got 5 black students accepted with test scores of 900 and 170 white students with better scores rejected, the quantity of discrimination is only 5, in terms of number of students.
Taking the larger of the two numbers does have a meaning, though. It gives some indication of the size of the discrimination gap in test scores and thus, perhaps, the degree of injustice per person. Thus, in the first example, the one discriminated-against was, very roughly speaking, closer to the ability of the worst person admitted than in the second example.
Deciding what measure to use would be important in trying to quantify the degree of discrimination in 1950 compared to 2000.