13 August 2007

The high-school prom theorem

The Myth, The Math, The Sex, in yesterday's New York Times. Gina Kolata talks about the fact that studies consistently report that on average, men have had more sexual partners than women. The article refers to, among other things, the study I wrote about in July. David Gale offers a proof of what he calls the "High School Prom" theorem -- which is that the total number of sexual partners of men and women should be the same, and therefore the population means should be the same. Apparently the sex researchers are aware of this, but cannot find a better way to collect the data.

Last time I wrote about this I claimed that the most likely thing was that women were either not having sex at all or having lots and lots of sex (the "madonna-whore complex"), and that that would create the observed difference in the medians. (The study reported medians, not means.) I acknowledged that self-reporting might create problems, but I phrased it in terms of people "forgetting" who they'd had sex with. In retrospect this is probably not the best way to phrase it; people lie about who they've had sex with.

I forgot to take that into account, because I wouldn't lie about such things. (Especially not in an anonymous survey!) But I tend to be more honest than other people, both because I have ethical objections to dishonesty and because I am not very good at keeping alternate versions of the world which correspond with my lies in my head. In short, I think it's wrong and I'm bad at it.

I suspect that mathematicians in general don't like lying, because it goes against everything that our profession stands for. (Also, there are persistent rumors that mathematicians are more likely than the average person to be autistic, and autistic people in general aren't good at lying because it requires having a "theory of other minds" -- that is, being able to understand what people are thinking, apart from what is actually true about the world.) But I imagine that being a mathematician is compatible with being good at lying, or at least with coming up with believable lies -- we do it all the time in proofs by contradiction. Collecting data on how likely people are to lie, though, is probably even harder than collecting data on people's sexual habits.

David Gale also says that "It is about time for mathematicians to set the record straight". To what extent is it the duty of mathematicians to point out when other people claim to be doing things which are mathematically impossible?


dan said...

I think that pointing out statistical flaws is a basic part of the work of mathematicians, so I suppose by extension, noting that in a bipartite graph, the total of the degrees of one part equals the total of the degrees of the other part, is presumably something we should do, too...

Michael Cassidy said...

"I suspect that mathematicians in general don't like lying, because it goes against everything that our profession stands for."

Hummmm, are CS undergrads and grads related to mathematicians? In the '60's at Cornell no one I knew cheated; the feeling was there was more dignity if flunking then cheating. Plus, in the '60's many of us took nothing too serious except the civil right movement and later the anti-war movement.

Later at Columbia, I was shocked that everyone was cheating. A friend who was very very bright cheated. Believe me she didn't need to cheat; without cheating she would have gotten an A and with cheating she got an A.

Plus, sex bends and twists us