In comments on an early post, It’s About Putting Shoes On Both Feet, Not On the Other Foot: Courtney Martin on the Myth of the Fairer Sex, Zilla proposed a great mathematical model for why it makes sense to make preferential microloans to women (and by extension to, well, extend differential preference to underserved demographics of any sort) despite there being no essential difference between sexes.

Leaving out the gender essentialism arguments (either side) and the culture arguments, I’d say that when you target the microloans to women, you get more bang for the buck, because there are more good investments as-yet unfunded, on the women’s side of the divide.

The men have historically had more access to those resources, so far more of their good investments have already been found and funded. The odds of getting good return by investing in a woman, are higher because the women have been historically under-invested.

Suppose you have 10 men and 10 women. 8 out of 10 men will do good things with investment money, and 2 will waste it. And say that women are exactly the same: 8 good, 2 bad. Randomly select 5 men to invest in, and ignore the women. Of the men invested in, 4 succeed with their investment, and remove themselves from the pool. The 1 who wasted the money still has his hands out in round two. So now the people seeking investments are:

Men: 4 good, 2 bad
Women: 8 good, 2 bad

If you again invest in five randomly chosen men, your returns are statistically unlikely to be as good, as they would be if you invested in five randomly chosen women.

The more rounds of investment are targeted to men alone, the more extreme the disparity becomes, and the better a bet on women looks. With successive rounds targeted to women, the effect will fade, but I think there’s a long way to go before that happens.

Zilla said it here.

It’s a nice, closely-reasoned explanation for what I was only able to say intuitively. It’s also generalizable to almost any situation where prejudice artificially distorts economic, social, or political access. It’s not that women are inherently better investments, it’s that thanks to discrimination the men who are better investments will tend to have already been invested in whereas the pool of women who would be good investments has not had access.

It also helps highlights why any argument that we’d be better off just putting women in charge instead of men… or keeping the status quo instead… will fail: to do so would only switch the pools of the under- vs. over-covered; it wouldn’t increase overall coverage. And finally, it demonstrates rather nicely why, in the long run as power equalizes, arguments of gender essentialism or exceptionalism would tend to evaporate. As would incentives for “preferential” treatment.

Further down in comments Zilla adds

Even if you believe men are inherently superior, this works as a mathematical argument that women are the better investment bet in any culture that has historically favored men.

That too! It works even if you think men have situational superiority due to, say, greater experience or the benefit of traditional narratives for dealing economically, or socially, or politically, or whatever. (For instance microloans for women tend to be a lot more boot-strappy — more conditions, more use of network effects for enforcement, more initial attached education and supervision, etc.)

I happen to think economists have a bit too much veto power when it comes to assessing social interactions. But they do. So it’s nice to see an economic/mathematics rather than political or moral argument for doing the right thing anyway.

Update: The case is obviously, obviously not just about microloans. See also Stubbornella’s post, Women in Technology, plus comments there on the topic of Google’s decision to sponsor female students to attend JSConf. (Via Geekfeminism.)