Wed, 28 Sep 2005 17:22:20 +0000 (GMT) Andy Latto <andy.latto@pobox.com> Since men and women will of course have the same mean number of partners, Everyone seems to accept this, even up to the "of course", but why? It's possible that I am missing something obvious, and I'm the one who is innumerate --- but isn't this (mean number of partners equal for both men and women) only true if you make some very specific assumptions? It seems to me that even under the assumption of perfectly accurate reporting, this need not be true. First of all, even if you are assuming only heterosexual pairings, the number of women in the pool may be larger than the number of men. Consider 20 women, 10 men, every man and woman pair up, then the mean number of partners for women is 10 and for men it is 20. Second of all, if you include homosexual pairings, then all bets are off, no? Consider a pool of 20 monogamous heterosexual women, 1 heterosexual man, and 19 homosexual men, where all the men are aggressively polygamous. For the purpose of a mathematical example, and not to cater to stereotypical prejudices, let's assume that the men want to, and willingly do, pair with every possible partner (the 20 women for the lone heterosexual man, and the other 18 homosexual men for the 19 homosexual men). The 20 monogamous women, each partner with the one heterosexual man (presumably unaware that he's not monogamous). The homosexual men each pair up with every possible homosexual partner. Then we'd have a mean of 1 partner for the women, but a mean of about 18.1 partners for the men. [Please note, I am *not* saying that there are no obvious inconsistencies in the report (which I haven't read), I am just saying that it is possible for men and women to have different mean number of partners because (a) there may be more women than men, and (b) not all "sexual partnerships" consist of one man and one woman. Similarly, to jump on an earlier example meant to highlight this seeming inconsistency, it is certainly possible that the mean number of pieces of email sent by each person is smaller than the mean number of pieces of email received by each person (multiple recipients). The ratio could be reversed, too, by the phenomena of mis-addressed email (if enough people were clumsy error-prone typists).]. Also: Date: Mon, 26 Sep 2005 03:55:11 -0700 From: David Gale <gale@math.berkeley.edu> For example, Tables 10 and 11 of the survey show that the median number of partners "in lifetime" for males over forty is 8 while that for females is 3.8. To immediately recognize the inconsistency imagine the same survey with but with the words sexual partners replaced by spouses. It's entirely possible that this data contains reporting error, of course, but I don't think that it is inconsistent; it seems entirely possible to me that these statistics are both correct. I am not arguing with your main point, but I am not sure how the *median* can be 3.8, frankly. Suppose there were 20 men and 20 women in a population. Suppose that 15 of the women have no sexual partners, and the other 5 women each have sex with all 20 men. In that situation, the median number of partners for the men is 5, and the median number of partners for the women is 0. the fact that the median for women is much smaller than it is for men suggests that the distribution of number-of-partners for women is more skewed than it is for men. This is confirmed by other studies I've seen that reported the full distribution, rather than just the mean or median. A few female prostitutes who have sex with a very large number of men, raising the female mean a lot with virtually no effect on the female median, is certainly part of the cause of such a skew. .... Is this an example of innumeracy in high places? I think that at least some of the innumeracy is here on the math-fun list, where no-one seems to have noticed that in expecting the median for men and women to be the same, you are attributing to the median a property that is held by the mean, but need not be held by the median. Andy Latto andy.latto@pobox.com