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WHAT IF SUMMERS HAD SAID:

"The distribution of natural endowments for math abilities for men show the same mean but greater variance than math abilities for women. Therefore, men will be disproportionately represented at the tails of the distribution relative to women. In other words, there are likely to be more men in society than women with unusually poor and below-average math skills."

Some evolutionary theorists have predicted exactly this sort of effect--that because of the nature of mating strategies (e.g., high status men mate much more than average or low-status men, whereas average-status men only mate marginally more than low-status), men may gain adaptive benefit from having greater variance in their genetic abilities, whereas woman benefit from less variance because of the much smaller marginal benefit from extraordinarily high abilities. In evolutionary terms, pretty much any woman would have an opportunity to mate with some man, but not every man will necessarily have the opportunity to mate with a woman, and high-status men mate with many women (prior to the social evolution of monogamy).

I haven't followed the empirical evidence on this closely, and from what I know, the jury is still out on whether this is scientifically accurate. But if it is true, and it is certainly plausible, one prediction of the theory would be that men would be overrepresented both at the very top of competitive professions ("stars" in academia, medicine, chefs, violinists, etc.) as well as being overrepresented in the dregs of society in terms of being intellectually below-average and prone to dropping out of school, prison, substance abuse, violence, and other correlates to that state. By contrast, under the hypothesis, woman will tend to be more consistently average or above-average than men in these same occupations. And it is obviously meaningless and silly to suggest that it is somehow "better" to be overrepresented at the extreme tails and underreprested around the averages than the opposite. I don't know whether it is true that men are overrepresented in the dregs of society, but casual empricism suggests to me that it is a plausible description of the world.

The hypothetical statement, it turns out, is therefore functionally identical to the bastardized interpretation of Summers's statement. But somehow I suspect it would be less outrageous if he had said it in such a manner to denigrate the propensity of men to be losers in the genetic lottery.

Update:

A reader points me to the federal Bureau of Prisons, which, for what it is worth, reports that 93.2% of inmates in the federal prison system are male.