Thanks, Dan, Rich, Jim for taking an interest in my crusade on behalf of common sense. The Prom Theorem (or "Le theorem du bal de fin d'anne'e scolaire" in the Le Mond story) was about something that should be obvious to everyone but apparently isn't,. (You could think of the prom theorem as a special case of Fubini's theorem on changing the order of integration. There's a set X of boys and Y of girls and a function D on XxY where D(x,y) =1 if x danced with y and zero otherwise etc.. This makes the result seem a little less trivial). But now I found an application that wasn't so obvious, at least to me. Here it is. In the Center for Disease Control report mentioned in the Kolata story, one of the "Selected Highlights" reads, "Men were more likely to have two or more sexual partners in the past year (17%) than women (10%)." The survey asks subjects whether they have had (a) zero, (b) one, (c) more-than-one sex partner during the past year. Notice this is a much simpler question then asking people to estimate the number of their sex partners and, more important, there is much less chance that a respondent would misremember or falsify his/her response especially since the survey was at great pains to let the subjects respond in complete privacy . Ok, define a person's P-index to be the number of his/her partners during the past year. P stands for either Popularity in the high school case or Promiscuity in the other case. Finally let us call a person ACTIVE if he/she belongs to group (c) above. I don't want to prolong the suspense. The result is that using the CDC data one proves that the P-index of the active women is on average between 50 and 70 percent higher than that of the active men. Isn't this a bit of a surprise? I should think social scientists would find this interesting. Here's the data The percentage of men who had 0, 1, 2-or-more partners are 15, 68, 17 (rounded off to the nearest integer). The percentage of women who had 0, 1, 2-or-more partners are 18, 72, 10 I will assume the total population P of men is the same as that for women which is very nearly true during the sexually active years, Let m* stand for the average number of partners of an active man. Let w* stand for the average number of partners of an active woman. Then the total number of partners of ALL of the men is (.17m+.68)P, namely it is the sum of the number of partners of the active men plus the number of (partners of) monogamous men. Similarly, the total number of partners of all of the women is (.10w+.72)P But by the Prom-Fubini Theorem these two numbers must be equal. so (17m*+68)=(10w*+72) so (*) w*=(17m*-4)/10. and my assertion follows. If I've made a mistake in either modeling or computation, always a real possibility, I hope some of you will point it out to me. David PS. If your immediate reaction was, it's because of sex with sex workers, you belong to a large group. I'm currently trying to check this out quantitatively but data is hard to obtain. So far I find that paid sex can account for some but definitely not all of the difference between the male and female P-indeces. . At 07:36 AM 8/27/2007, you wrote:

Thanks for posting the link to that article, Dan!

If you step back a bit, it's kind of interesting that there's an article about this at all. None of this Prom Theorem stuff is really news to social scientists (aside from the way it's packaged); it's laypeople and science journalists who need to be reminded of things like this.

I suspect a review article on gender differences and "danciness" in the social science literature would mention all the points that we've mentioned in this forum, and more. (I mean, most of us doing the posting are amateurs when it comes to social science --- unless we're convinced that our Ph.D.'s in math make us competent in ALL disciplines, in which case we're not social science amateurs --- we're social science cranks. :-) )

So why does the Prom Theorem show up as news? Maybe there's an Emperor's New Clothes appeal to the story ("Mathematician Refutes Social Scientists!") --- although (a) competent social scientists have always understood the Prom Principle (and the ways it both is and is not relevant to the sorts of questions social scientists ask about gender difference), and (b) David counts as a social scientist at this point given all the work he's done in economics, regardless of what it says on his Ph.D. diploma or what department his office is in.

I guess it's good when newspapers offer remedial math in the guise of news. Maybe we could push this further, and have an article in which a physicist-statistician announces that causation is different from correlation. This is something that 99.9999% of educated people (myself included) should be reminded of on a frequent basis.

Incidentally, when we talk about whether men are "dancier" than women, we usually don't mean that men actualy DO more "dancing" than women; what we usually mean is that if men had their way, there'd be a lot more men-dancing-women than there'd be if women had THEIR way. And there's evidence for this if we look at the amount of dancing done by same-sex dance-couples. So there's a lot to be said in favor of the popular belief that men have trouble keeping their feet in their shoes (as it were).

Jim Propp

P.S. I haven't read the New York Times article; only the one that Dan gave the link to. So it's possible that Kolata's Times article is different and that some of what I wrote above doesn't apply to it.

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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley