The recent Supreme Court decision on *Ricci vs. DeStefano* has sparked a lot of talk about affirmative action and “reverse discrimination.” I tend to agree with suggestions that affirmative action should be based on things other than race, such as income level, educational opportunities available where one grew up, and whether ones parents went to college.

However, I have been bothered by all the emphasis on “reverse discrimination.” My hunch has been that this doesn’t do justice to the magnitude of the discrimination that some minorities face. So, I tried to put some numbers on discrimination. The place I knew I could start was affirmative action in college admissions.

I attempted to make a crude estimate of how race-based admissions might decrease the chances that a member of a well-represented majority would be accepted to an elite university. To do this, I needed to compare the relative admission rates of those who are members of under-represented minorities, compared to those for the general population. Say that a fraction *f* of students are admitted to a school. That means that of *M* students that apply, *N=fM* are admitted. Now say that I know the fraction of those students that are under-represented minorities, *g*. To estimate the effect of racial preferences, I will assume that under-represented minority students were admitted at some factor *x* times the rate of non-minority students. I happen to have been able to find estimates for these numbers relatively easy, which is why I took this approach.

I then wanted to estimate the fraction of non-minorities admitted as a function of *x*, the effect of racial preferences. The number of non-minorities admitted is *n=(1-g)N*. The number of non-minority applicants is *m = (1-g/x)M*. The admissions rate for non-minorities is then *f’ = n/m = (1-g)/(1-g/x)N/M = (1-g)/(1-g/x) f*. By changing *x*, I can tell how the fraction of admitted non-minorities would be affected by affirmative action.

So, I found some admissions numbers for Harvard in the Boston Globe. In 2009, Harvard admitted *f*=7% of applicants. Other Ivy League schools admitted about 10%, so this seems like a good number to work with. Of the students accepted to Harvard, *g*=22% were from under-represented minorities. This seems to hold true generally at the Ivy League and University of California Schools, so I think this is also a good number to work with.

I was not able to find numbers for *x* for Harvard, but I needed to make some assumptions to construct any sort of argument. So, I tried to find numbers from other elite schools. From an article in UCLA’s student newspaper, it would appear that minorities are admitted at a rate up to *x*=2 times higher than the rates of other students (for MIT). This is roughly supported by the factor-of-two decline in under-represented minorities attending UCLA and UC Berkeley after California ended race-based admissions.

So, if I assume that under-represented minorities are equally qualified as other students, but are given favorable treatment, so that *x*=2, I get *f’* = (1-0.22)/(1-0.22/2) 7% = 6%. So, in this scenario, there is roughly a 1% chance that a non-minority would be negatively impacted by affirmative action.

If I wanted to take a worst-case scenario and assume that minorities are not in fact equally qualified, then I need to do a different calculation. I must emphasize that this is not at all what I believe — this is simply to get a mathematical bound. Let’s pretend that an elite school suddenly decides to admit no minorities. The number of non-minorities admitted could then go up to *n=N*, and the effective applicant pool would shrink by the fraction that are minorities, so that *m = (1-g/x)M*. Therefore, *f” = 1/(1-g)f *= 1/(1-0.22/2) 7% = 8%. So, by changing the rates of admissions for minority students, I could conceivably change the rate of admission for non-minority students to an elite school like Harvard by as little as 1%, and at most 2%.

Fractionally, this is a significant change in the chance that an individual in the majority would get admitted. However, because the absolute chances of getting into Harvard are small, the actual chance that any individual non-minority would be affected by affirmative action is slight — a couple percent at most.

To put this in perspective, I looked into other forms of racial discrimination. A pair of economists did an experiment in 2004, in which they tried to judge the effects of discrimination by sending resumes to employers in the Chicago and Boston areas. The resumes were made to be identical, although half had stereotypically “white” names (such as Emily Walsh), and the other half had stereotypically African-American names (such as Lakisha Washington). The resumes with white names got callbacks in 10% of the cases, while those with African-American names got callbacks in only 6% of cases. So, the effect is about twice as large as the worst-case scenario for “reverse discrimination” under affirmative action.

What about looking at the most dramatic racial disparity in American life — prison populations? In 2008, a black man was 6.6 times more likely to be in prison than a white man, and a hispanic man was 2.4 times more likely to be in prison than a white man. Some of this has to do with the violence of the inner cities. However, a big part of the problem is the fact that, despite the fact that drug use rates are very similar for all racial groups, black men are sentenced for drug offenses at 13 times the rate of white men.

I have to mistrust the motives of anyone who decries “reverse discrimination,” but won’t spend equal breath bemoaning the remnants of racial discrimination in the work force. And if one wants to address those issues, it should be in small breaths taken between shouting about the big issue: that unequal law enforcement policies undermine black and hispanic communities, and deprive their children of opportunity.

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