The New York Times reports:
In study after study and in country after country, men report more, often many more, sexual partners than women.
One survey, recently reported by the federal government, concluded that men had a median of seven female sex partners. Women had a median of four male sex partners. Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5.
But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women. Those survey results cannot be correct.
Well, heterosexual men generally can't have more partners on average than heterosexual women, where "average" means "sum up the partner counts and divide by the number of people." I say generally because there are possible boundary cases (e.g., if you asked all live men and women in the U.S. how many opposite-sex sexual partners they've had, and they answered completely accurately, the numbers wouldn't match because some of their partners are now dead, or are now outside the country, or because the partners are prostitutes and the study doesn't ask prostitutes or ask them enough), but it's generally so. As the article points out, "invoking women who are outside the survey population cannot begin to explain a difference of 75 percent in the number of partners, as occurred in the study saying men had seven partners and women four." (Perhaps prostitution might explain the difference, but the numbers that I've seen suggests that it doesn't suffice.)
But the medians may well be very different. Just as a sample, imagine a population with men A, B, C, D, E, and women P, Q, R, S, T, in which the sex partners map out this way:
| A | B | C | D | E | |
| P | Y | ||||
| Q | Y | ||||
| R | Y | ||||
| S | Y | Y | Y | Y | Y |
| T | Y | Y | Y | Y | Y |
The median number of sex partners for the women is 1 (since the women's partner counts are 1, 1, 1, 5, 5); the median number of sex partners for the men is 3 (since the men's partner counts are 2, 2, 3, 3, 3). The arithmetic means for both are 2.6, since there are 13 male-female pairings; but the medians differ substantially.
Now this having been said, the bottom line is likely still correct; as I understand it, there is substantial reason to believe that men overreport their sexual partner counts and women underreport them. And it may well be that the 6.5 and 12.7 numbers are arithmetic means (the article doesn't say), which would be substantial evidence for this theory. But the "men had a median of seven female sex partners" / "[w]omen had a median of four male sex partners" data is extremely weak evidence, if evidence at all; and it surely can't be confounded with the "average" in the sense of arithmetic mean, which the article does.
Thanks to reader John Crawford for the pointer.
Just in case your day wasn't ruined by this fact of our sexually liberated world, http://www.hotchickswithdouchebags.com will be the salt for your wounds. Yes, it hurts. The pain, the horror.
Actually, if the median for men is higher (which is what the first survey cited reports), then it would mean a relatively small portion of the women were getting a relatively large percentage of the nookie, not vice versa.
Anyway, I'll continue to run these calculations while you go get some play....
After all, there are self-identified heterosexuals who have at one point or another had same-sex partners, and there are plenty of self-identified non-heterosexuals who've had heterosexual opposite-sex partners at one point or another (self-identified bisexuals are perhaps worth mentioning explicitly, although they aren't the only relevant group).
If self-identified heterosexual men were inclined to count their former same-sex partners for the total without counting them against their own heterosexuality, or if there were a large group of self-identified non-heterosexual women who were willing to sleep with self-identified heterosexual men, that could push the arithmetic means apart, even if we ignore death, migration, sampling error, and other effects.
However, a commenter on another site pointed out that there is evidence that men and women define sex differently and that this, in addition to deliberate under-/over-reporting, may partially explain the discrepency.
"The median number of missed days is [x]. However, many employees take more days than that."
Yeah, I'm thinking that probably EXACTLY HALF take more than that. But it was from an HR person, so I didn't try to instruct her.
It's even worse than that, The MSM is always saying things like "The average stock portfolio is down 10%, but some people are doing much worse than that."
I think I can remember their shock that 20% of the population is in the bottom quintile economically, but maybe I'm making it up.
Professor Bernstein might say that my anecdotal data cannot be extrapolated to the population at large, just as my success in using homeopathic remedies must merely be an illusion. And he may be right. But I wonder if anyone has believed it to be otherwise -- and the mathematical impossibility tends to support this, er, theory.
For men/women 16.7/25.0 claimed 0-1 partners, 33.8/44.4 2-6 partners, 20.7/21.2 7-14 partners, 28.9/9.4 15+ partners, and a crude median of 6.8/3.7. The first thing to note is that they use a fractional median, and the second is that the distributions are significantly different.
Since the NYTimes didn't actually sight the British research, it is a bit harder to find out what was going on there.
-cite, not sight
-the figures 16.7/25.0 ... figures are in percent, which I neglected to mention
It's been my experience that people who claim cures by mens of mystical practices (religion, chiropractic, homeopathy, qi gong etc.) overestimate their illnesses.
If women indeed had a median of 6.5 and a mean of, say, 9, and men had a median of 12.7 with the same median, that would mean
1) that there is a large percentage of women who are having an incredible amount of sex with a large amount of partners, and/or a (extreme) relative paucity of women having 1 or 0 partners.
*and*
2) that, at the same time, there is a relatively *small* amount of men who are having large amounts of partners, and/or an (extreme) relative plethora of men having only 1 or 0 partners.
Unless these two statements seem reasonable (and on first glance, while either one by themselves seem reasoanbly possible, both statements being true seems highly unlikely), then even if the mean is undiscoverable by the survey, the difference in median is very strong evidence of the survey's flaw.
The claim that the two means must be the same assumes equal numbers of men and women.
Bill Poser: this, I think, is what Eugene was getting at with "possible boundary cases."
I agree - the magnitude of the disparity in this case is not likely to be accounted for by the difference in male and female populations. I was just making a mathematical point.
I.e., in a 10 person world, if you have a data pool of 1, 2, 3, 4, 5, 5, 10, 20, 30, 50), you end up with a median of 5 and a mean of 13. On the other hand, if you have a data pool of 1, 2, 3, 4, 5, 5, 5, 5, 5, 5 then you have a median of 5 and a mean of 4.
(1) The survey didn't specify the partners had to be human.
(2) Alchoholic amnesia.
I wonder how Amanda Grayson would answer...
That being said, I think that the median/mean distinction isn't the big problem here; the problem is that people lie about their sex lives, and men and women do it in different ways.
It would be interesting to see if age is a factor (could be wrong, but boys often have sex before girls do).
(Can anyone supply the exact quote? I'd like to keep it and cherish it. He almost caused me to have an accident when I heard it on my car radio.)
Of course, everyone assumes that the male and female populations are essentially equal (although this requires inductive reasoning, and is not a "proof" at all). However, there could be significantly different numbers of *heterosexual* men than *heterosexual* women, or vice versa.