The New York Times reports on gender imbalance on American college campuses, where women often account for as many as 55% of enrolled students. This is apparently making the few remaining men being chased by eager crowds of women, and the men hook up and cheat a lot. As explained by W. Keith Campbell, a psychology professor at the University of Georgia, which is 57 percent female: “When men have the social power, they create a man’s ideal of relationships,” which the author of the article translates as “more partners, more sex.”

Another interesting quote: “(…) the university [of North Carolina] has a high female presence in part because it does not have an engineering school.”

Meanwhile, in China lately about 54% of newborns are boys, a result presumably of selective abortions, motivated by a societal preference for male children together with the one-child policy. According to a Forbes article, this might be one of the causes of China’s extremely high savings rate, because “Wealth helps to increase a man’s competitive edge in the marriage market.”

(I found the Forbes article via a post on the excellent blog of Patrick Chovanec, a Tsinghua professor of economics. His posts on the real estate market in China and on regional differences are fascinating. ~~Anyway, what is the mathematical mistake in his post linked above?~~)

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Why is the gender imbalance in China only 54% male? Moore’s Law would seem to imply that the one child policy result in a >90% imbalance. That would be funnier, too.

20/122 < 1/6 – but why didn't you ask this on mathoverflow?

I caught my own error … silly of me.

Ah good catch, it’s one in 6 not one in 5 young men who will not be able to find a partner, but this was already in the Forbes article. I meant a different (more interesting) mathematical mistake, which is original to the blog post.

There’s also health-care spending. U.S. citizens also pay for their health care along their lives and this is delaying an expense, hence saving. What is different about the Chinese? Perhaps the Chinese are over-saving, for catastrophes that usually don’t happen? Anyway I cannot convince myself there is a flaw here and I couldn’t see anything else. By now I am really intrigued – could you please post the error if nobody comes up with it in a couple of days?

I had found the error earlier today, but that whole sentence seems to have been edited out!

It said (now that sentence has been removed) that people who do not obey the one-child rule (because they are exempt or because they find other ways around it) will have children until they have a boy and then stop, and this practice increases the fraction of boys. But this is not true because any “stopping rule” will always produce on average an equal fraction of boys and girls.

57% of one gender isn’t very extreme as far as college gender imbalances go. I know at least one engineering school that is about 75% male. There are also a few schools that are 100% female by design.

Luca: gender of children are not drawn i.i.d. fair coin flips. For example stressed parents tend to have more daughters. Overall there tend to be a few more boys born then girls (correcting for boys getting killed prematurely in wars and accidents).

Parents having children until they have the first boy may have some small effect on the fraction of boys. If I had to guess I would say that a repeat-until-male policy may slightly _decrease_ the fraction of boys since parents with a lower probability of having a male child (for whatever subtle reasons) would on average have more children.

I agree that martingales are cool and that the deleted sentence was presumably very wrong, but replacing it with something that’s less wrong is only partial progress.

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Seconding Anon 2, I have been a woman in an engineering college where the ratio of women to men was 1:20 (over the entire campus). I think the students at NC State with a 57% gender imbalance will survive :-)

Why 20/122? According to the post 22 in 122 men won’t find a partner. And that is more than one in six.

I guess that stopping rule probably does increase the gender imbalance (if only slightly), since there’s a small finite limit to the number of children one can have in a lifetime.

That is, I’m not disputing that 1/2 + 1/4 + 1/8 + … = 1, but that some people who use the above stopping rule will have 4 girls and then simply stop having children, failing to ever have a boy. Since children are expensive and people are poor, they might even stop after fewer.

If every newborn is a boy with probability 50% and a girl with probability 50%, and all births are independent events, then it does not matter what “algorithm” the parents choose to decide when to stop, on average half of all births will be boys and half girls. For example if the parents stop once they have a boy or once they have four daughters, whichever comes first, then on average they will have 15/16 sons and 15/16 daughters.

Anon 2 is right that if different couples have a different probability of having a boy vs girl, then stopping at the first son will produce a slight excess of girls, although the effect is small.

For example, suppose that half of the couples are such that each of their children has probability 60% of being a boy, while another half of the couples has probability 40%, so that if each couple had exactly one child, for example, we would see 50% of boys and 50% of girls. If all couples have children until they have their first son, then the couples of the first type will have on average 5/3 children, 1 boy and 2/3 girls, while the couples of the second type will have on average 2.5 children, 1 boy and 1.5 girls, so that overall we have 13/6 girls for every 2 boys. In other words, if I am getting my 2nd grade arithmetic straight, 48% of newborns will be boys, which is a relatively small difference considering the huge variance that we assumed at the beginning.