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Solicitor General Elena Kagan, whom Barack Obama is expected to announce as his nomination to the Supreme Court later today, is not without her critics. Among other things, questions have been raised — in this case, by law professors Guy-Uriel Charles, Anupam Chandler, Luis Fuentes-Rowher, and Angela Onwuachi-Willig — over Kagan’s minority hiring record while she was Dean of Harvard Law School:

[Kagan] hired 32 tenured and tenure-track academic faculty members (non-clinical, non-practice). But when we sat down to review the actual record, we were frankly shocked. Not only were there shockingly few people of color, there were very few women. Where were the people of color? Where were the women? Of these 32 tenured and tenure-track academic hires, only one was a minority. Of these 32, only seven were women.

Although the critique by Charles, et. al. raises a number of interesting and perhaps uncomfortable questions, it is not beyond the realm of statistical analysis. How remarkable is it, for instance, that Kagan hired just one minority out of 32 faculty brought into tenure-track positions?

One place to start is the current composition of the faculty at the other Top 5 law programs (these are Stanford, Chicago, Columbia, and Yale). I went to the faculty directories for each school and identified (to the best of my ability) the women and racial minorities. It turns out that there are a lot of white men on the faculty at these programs:

Between the four schools, just 27 percent of the faculty are women and 12 percent are racial minorities. Harvard — counting Kagan’s hires as well as those made by others — tracks these numbers almost exactly.

Obviously, these are rather low numbers, and there are many good questions that one might raise about that. But, let’s put those aside for a moment and pose a strictly mathematical question. Suppose that, over the long-run, there was a 11.6 percent chance that each hire Kagan made was a minority. What are the odds that, over the short-run, just 1 of 32 hires would be?

They’re actually fairly high. Assuming that there was an 11.6 percent chance that each hire she made was a minority, and that each hire was made independently of the previous one (that is, Kagan wouldn’t be more inclined to offer her next job to a minority after giving the previous one to a white person, or vice versa), there is about a 10 percent chance (according to a binomial distribution) that she’d end up with either one or zero minorities after 32 hires.

Let me be very careful about this. I’m not endorsing the extreme whiteness of the faculty at elite law schools. It seems to me to be problematic. I’m just saying that it gives Kagan a very low bar to clear. If you had a basketball team — let’s call them the New Jersey Nets — that won only about 12 percent of its games, it would not be that remarkable if they had a stretch where they won just once out of 32 tries.

However, there are two important facts that cut against this conclusion, one of which makes Kagan’s record look better and the other of which makes it look worse.

On the one hand, many of these faculty have been around for years, and law school faculties are (quite gradually, evidently) becoming more diverse. That only 12 percent of the current faculty at these schools are minorities doesn’t mean that just 12 percent of new hires will be.

I don’t have statistics on the racial composition of recent hires at these schools. As of 2005, however, about 22 percent of those in the candidate pool at all law schools were minorities. If the benchmark were not 12 percent minority hires but 22 percent, Kagan’s track record would be more damning. There is only about a 1 in 280 chance that someone who was trying to hire a minority 22 percent of the time would only do so only 1 time out of 32 on account of chance alone, according to the binomial distribution.

On the other hand, Harvard (likewise Yale, Chicago, etc.) is the sort of place where you go to end your career, and not necessarily to begin it. I imagine that they hire relatively few people straight out of school, instead waiting for them to build a track record of legal scholarship somewhere else. If these elite schools are hiring older faculty, on average, that might explain why they lag behind their peers (as they in fact do) when it comes to minority hiring. Effectively, they may be drawing from (say) 1997′s hiring pool, when the percentage of minorities was lower. As about 30 percent of the students currently matriculating from Harvard Law are now minorities, these numbers will surely improve over time as the talented new graduates work their way through the system. But they’ll take longer to boomerang back to Harvard than they will to other places.

Also, the comparisons we’ve been making are not quite apples-to-applies. Charles, et. al. looked only at tenure-track faculty, whereas the statistics above pertain to all permanent faculty whether tenure track or not. According to a response circulated by the White House, three of the 12 clinical law professors that Kagan were minorities, which would bring her overall batting average up to 4-in-44, or about 9 percent. That would be a very normal number of minority hires if the target were 12 percent (the fraction of minorities currently on the faculty at Top 5 schools), though still somewhat lagging if it were 22 percent (the percentage of minorities in the hiring pool) instead.

In sum, this would be very weak evidence on which to convict Kagan of an active attempt to discriminate (and accusation which nobody has in fact made). At the same time, she certainly does not appear to have made an active effort to increase the share of minorities on Harvard’s faculty.

But in fact, there are two separate questions here: whether Kagan should have been concerned about minority hiring at Harvard Law, and whether she should have been concerned about the appearances thereof. They perhaps require two separate answers.

I think a lot of people in Kagan’s position — whether or not they held an affirmative goal of increasing the diversity of the faculty — would tend to become self-conscious about their low number of minority hires after some time. After they’d hired 12 or 13 white people in a row — some point at which the trend had become conspicuous — they’d bend over backward to hire a minority candidate or two, perhaps bypassing more qualified candidates in the process. Then, after having “checked the box”, they’d feel less pressure, and perhaps would be less likely than usual to hire a minority candidate for some period of time. In other words, I doubt that very many people, especially in academia, would truly make their hiring decisions independently of one another.

This evidently wasn’t a problem for Kagan — and unless you do want to accuse her of discrimination, it arguably speaks to certain kind of fair-mindedness. That is, she was treating every decision that came before her on a case-by-case basis, rather than behaving like the bad referee who calls a penalty on the next play to make up for a miscall on the previous one. To me, that potentially speaks to someone who has a strong ability to evaluate the evidence objectively and without regard to politics — qualities I’d generally find desirable in a candidate for the Supreme Court.

At same time, it might also speak to someone who is independent-minded, perhaps to an extent that many of us would regard as stubborn in other realms of life. If this were the only window we had into Kagan’s potential jurisprudence, it might suggest that she was more likely than usual to break from the liberal orthodoxy on some of the more idiosyncratic or implicitly political questions before the Supreme Court.

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