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August 13, 2007

I Caught a Fish THIS Big

Every survey, study, and poll finds the same thing -- men have more sexual partners than women. Men are relatively promiscuous, women relatively chaste. Gender roles describe real behaviors.

Only one problem: It's a mathematical impossibility for one gender to have more sexual partners than the other.

(Via Hayes)

August 13, 2007 | Permalink


from the NYT article: “Some might be imaginary,” Dr. Graham said. “Maybe two are in the man’s mind and one really exists.”

amended text: “Some might be imaginary,” Dr. Graham said. “Maybe two are in the man’s hand and one really exists.”

Posted by: JimPortlandOR | Aug 13, 2007 11:22:28 AM

It's very difficult to imagine how the descrepency could honestly be so much as it is, but the descrepency is not mathematically impossible -- as the descrepency is in the median number of sexual partners ... not the mean, which would be impossible.

Anyway, this reminds me of all those reports of "we are all in debt ... on average people are spending more money than they are making". If, on average, people are spending more money than they are making, where is the money going?

Posted by: DAS | Aug 13, 2007 11:27:05 AM

It's a mathematical impossibility for one gender to have more sexual partners than the other.

Unless, of course, some of partners are of the same gender.

Posted by: Elm | Aug 13, 2007 11:30:12 AM

This has been kicking around on several blogs. Here's my take.

First, I assume the question has to do with heterosexual encounters. Because of course if "sexual partners" can be of either gender there's not necessarily a discrepancy.

Second, are we talking about mean number of partners, or median? Because for heterosexual encounters, by definition the mean number of sexual partners have to be the same for men and women. But the median doesn't have to be. If there are just a few women who have an extremely large number of partners, the means can be the same, but the medians can be different. I've worked up an example.

Let's say we have 5 men, A through E. Here are the number of female sexual partners each has had:

A. 1
B. 3
C. 6
D. 7
E. 8

And here are five women, F through J, with the number of male partners they have had:

F. 1
G. 2
H. 3
I. 7
J. 12

The mean number of partners for each group is the same, 5. But the median for the men is 6, while the median for the women is 3.

Third, this question came up in a class I took with Robert Michael, who was one of the investigators on the big University of Chicago sex survey. My recollection is that his explanation for the discrepancy is that men and women define sex differently. They did follow-up interviews with some of the subjects of the sex survey, and found that women tended to define sex as intercourse only, whereas men tend to include not only intercourse but other types of genital contact (oral sex and the like). Researchers these days are trying to be a lot more precise in how they define sex, in order to avoid this problem.

Of course, the other explanation is that either or both genders are flat-out lying, and probably there's some of that going on. As well as the fact that probably not too many prostitutes get interviewed in these surveys, because they're such a marginalized population. But of course if they were included that would probably even things up a bit.

I tend to go with my professor's explanation, though. I don't think most people consciously lie in these surveys, but it's human nature to present the most flattering possible view of one's self. And men of course want to see themselves alpha male studs, while women want to avoid being stigmatized as sluts and whores.

I wonder if there's less of a discrepancy among younger people. I'd like to think so, because I'd like to think the sexual double standard is dying and is less powerful among young people. But I don't know the data on this.

Posted by: Kathy G. | Aug 13, 2007 11:30:46 AM

If, on average, people are spending more money than they are making, where is the money going?

Well, if they're spending money on imported goods, the money is going abroad, right?

Posted by: Tyro | Aug 13, 2007 11:35:14 AM

Prostitutes. It's really that simple.

Posted by: Dan | Aug 13, 2007 11:36:36 AM

Well, not exactly. The mean number of hetero sexual partners certainly has to be the same for men and women. But the *median* numbers could accurately diverge a great deal, with a small group of promiscuous women as outliers.

People who want to have sex with a long succession of male partners, and who aren't especially picky, can easily do so. It stands to reason that the most promiscuous women would have more partners than the most promiscuous (straight) men--people trying to have sex with women will be turned down quite a bit more often.

It distresses me that neither Gina Kolata nor the people she interviewed seemed to realize that "mean" and "median" are two different but equally meaningful measures of a norm.

On preview: DAS got it.

Posted by: Mike B. | Aug 13, 2007 11:37:01 AM

IIRC, at least one of the studies asked "How many partners have you had since turning 18?"

If 18-19 year old boys frequently have sex with 16-17 year old girls, and the reverse doesn't hold, this could account for at least part of the discrepancy.

Posted by: Brock | Aug 13, 2007 11:42:52 AM

Yeah, I thought it was odd that the article didn't mention the whole mean/median thing more clearly. The mean number of partners for men and women should be equal, but not the medians.

Prostitutes have a large number of sexual partners, and are mostly women. Their existence would tend to push the mean of non-prostitute women down, but have little effect on the median.

Still you have to ask yourself, how many men sleep with prostitutes? If the men surveyed excluded sex they'd had with prostitutes, I don't imagine the median would fall by more than 1.

Differing definitions of sex sounds like a more plausible explanation. Overtime, if people are looking to skew their totals in one direction or the other, it may effect which encounters they remember as sex. Also, in the case of oral sex, I can certainly imagine only the recipient counting it/remembering it as sex. I'd also guess that men receive oral sex more often than women.

Posted by: EERac | Aug 13, 2007 11:55:26 AM

My understanding has always been that these are mean numbers, as median numbers tend to specifically be reported that way. But this would be worth finding out.

Posted by: Ezra | Aug 13, 2007 12:00:33 PM

I got all into trying to mathematically demonstrate that the survey results are possible, you just have to assume a small but very promiscuous number of women. Unfortunately, I think it still doesn't work for the mean. But yes, it would work for the median results. Either way, it's just a numbers game, though; I agree the most likely explanation is women underreporting and/or men overreporting, or counting partners outside the survey pool incorrectly (or counting homosexual encounters as heterosexual, who knows.)

You know, I almost wrote a comment to Yglesias' recent post about the high number of people who believe really loopy stuff, arguing that it might show something disturbing about people in general but then again it might show something disturbing about the inadequacies of polls. But this seems like an even better place for it. 90 percent of polls are based on one out of two assumptions: people give honest answers to personal questions asked by complete strangers, or people give thoughtful answers to esoteric questions that don't have much to do with daily life. Either of those is a pretty big assumption.

If, on average, people are spending more money than they are making, where is the money going?

Possibly out of the country, but more likely, most of it is going to non-people, such as, for example, corporations.

Posted by: Cyrus | Aug 13, 2007 12:02:23 PM

It is embarrassing that the NY Times would do a story that hinges on the definition of the word "median" without understanding what the word means.

It is deeply embarrassing that at least four supposed math professors, statisticians and the like were all confronted with this and apparently, none of THEM knew the definition of the word "median" either.

Consider a population of ten men and ten women. Six males have had sex with all ten women. Four males have had no sex. The median number of partners for the men is "ten". The median number of partners for the women is "six". Nobody styling themselves a statistician or math professor should not understand this. How is it that not one editor at the Times understood that this piece is total idiocy?

Posted by: Anon | Aug 13, 2007 12:03:16 PM

Hmmm. It seems I should have previewed. When I began writing my comment there were only two comments, but in the meantime Kathy G. actually did the math I started, albeit not in exactly the same way, and showed her work.

Also, I forgot to mention that it was funny to see that the researchers in the NYT article were unable to imagine that the problem might be caused by underreporting or overreporting. The article mentioned three or four researchers, none of whom were quoted as saying that, you know, the men just might be bragging and/or the women just might be making themselves look better. It could be selective quoting by the writer, of course, but if not, it's a data point supporting what I said above. Many polls are inherently flawed — and the poll designers don't even notice it.

Posted by: Cyrus | Aug 13, 2007 12:12:44 PM

Ezra: the survey, according to the Times article, is indeed discussing results about the median, not the mean. Which makes me feel dumb cuz I totally missed that on the first go-round. Which makes me really, really confused about the article which as it currently stands makes no real sense because they keep talking about the median and the average like the same thing and, yeah, someone at the Times should have caught that. Not to say that all the conclusions inspired by the article are necessarily bogus, but the article just literally doesn't make sense.

This reminds me of the time a friend of mine tried to convince me that he heard somewhere that the average IQ was dropping because people with lower IQs were having more children than people with higher IQs and I spent several minutes puzzling why this might be so, coming up with theories invoving the fact that people with restricted access to proper nutrition during pregnancy & early childhood, not to mention education in general, all of which affect IQ, also have less access to family planning, before remembering that the average IQ literally can't drop because the IQ is specifically calculated so that the average is 100.

Posted by: Isabel | Aug 13, 2007 12:24:26 PM

Also note that due to military service, a much higher percentage of adult men than women spent significant time in the prime sex years outside of the Untied States, having sex with non-Americans.

Posted by: arthur | Aug 13, 2007 12:26:51 PM

Its perfectly plausible that the difference is partly explained by the existence of a large majority of chaste women and a small minority of promiscuous women compared to more stable patterns of promiscuity among straight men. But, realistically, I think that explanation can only go so far. Most of the discrepancy has to be due to unreliable data. People lie shamelessly about sex when they wouldn't lie about anything else even when its confidential and seemingly in their interest to tell the truth (e.g., at the doctor's office).

Posted by: Joseph Hovsep | Aug 13, 2007 12:40:29 PM

And when they do lie, they probably tend to tell quantitatively big enough lies to have a real impact on statistics. If Suzy is so embarassed about having had sex with 20 guys that she feels compelled to lie, she's more likely to say she's only been with 5 than 15.

Posted by: Joseph Hovsep | Aug 13, 2007 12:46:14 PM

But, realistically, I think that explanation can only go so far. Most of the discrepancy has to be due to unreliable data.

It's realistic to abandon existing theory on the basis of math that's just been proven to be in error?

There is certainly a reporting bias that drives the numbers up for men and down for women. Why does that bias exist in the first place? Because, by and large, men aspire to higher numbers and try to achieve them, and women do not. At best the bias exaggerates an existing situation--it doesn't create it out of whole cloth.

Posted by: Mike B. | Aug 13, 2007 1:02:00 PM

Mike B., I agree there's some slopply statistical reporing here. I'm just saying that if the average man reports 12.7 sexual partners and the average women reports 6.5 partners, two forces are at work. And I'd put my money on reporting bias as accounting for more of the discrepency than a few really promiscuous women, prostitutes or overseas lovers.

Posted by: Joseph Hovsep | Aug 13, 2007 1:18:10 PM

Wait, Joseph...I think we're talking about several different discrepancies here. The fact that men and women report different numbers of sexual partners is clearly due to multiple factors, one of which is reporting bias. These numbers probably can't be captured with any great accuracy, though my sense is that there really has to be *some* gap between men and women if we're to make sense of our entire lifetimes' worth of anecdotal evidence.

But the point remains: the math is in error. It proves nothing that the mean number of hetero partners across the entire population has to be the same for both sexes, because the key figure is the median and that moves differently. The median for the men will be higher than the mean, and the median for the women will be lower. That gap is to be expected, probably has some validity outside of reporting bias, and is really not worth writing an entire article about.

Posted by: Mike B. | Aug 13, 2007 1:29:49 PM

I dragged out my copy of The Social Organization of Sexuality, the book based on the large University of Chicago sex study that was done in the 1990s. I found a couple of interesting things.

The authors go into the gender imbalance problem when it comes to reporting number of sexual partners and posit various possible explanations. In addition to the ones that have already been mentioned on this thread, they point out that there are 8 million more adult women than adult men in the U.S., so a (somewhat) smaller number of male partners for women and a larger number for men can be reconciled. In short, since men in this country have a higher mortality rate, some of the dudes who would have been included in the survey have died, but their female partners haven't. So this may be a small source of the discrepancy, if we assume the dead guys had fewer partners on average than the living guys.

Overall, though, they think the main reason for the discrepancy is that men overreport the number of partners and women underreport. But my professor, who's one of the authors of the book, seemed to think the main thing driving it was differing definitions of sex between the sexes. At least that's what I recall him saying.

The survey the book is based on was done as a written, self-administered questionnaire (SAQ). In the SAQ, respondents were asked how many sex partners they'd had. Sex, interestingly, was not defined. In follow-up face-to-face interviews, sex was defined as follows: "mutually voluntary activity with another person that involves genital contact and sexual excitement or arousal, that is, feeling really turned on, even if intercourse or orgasm did not occur."*

Wow. That definition kind of floors me. Besides the groovy 60s-speak about "feeling really turned on,", there's all that jazz about "sexual excitement or arousal." A man who has sexual activity of most types almost by definition has to feel aroused, but as we all know, women don't. I think it's a staggeringly sexist assumption to assume that having sex = "excitement or arousal." So much for the non-normative objectivity of social science.

And actually, in this particular survey, I would think the arousal part of the definition might be one important source of the gender disparity.

An even more important potential source of the imbalance is so blindingly obvious I'm surprised I didn't think of it before: the whole issue of consent. It's quite possible that men include non-consensual encounters in their total but women don't. This could be a problem in this particular survey, even though the follow-up question explicitly defines sex as a consensual activity. Because of course many sexual encounters occur which men believe are consensual but about which women might feel otherwise.

Btw, the neither the arousal question nor the consent question is mentioned by the authors as a potential source of the gender imbalance in the number of sex partners question.

Of course, the really big question about this and other sex surveys is the extent to which we should trust them. Sex is the most deeply personal issue there is and we know people lie about it all the time. This particular survey was very carefully done. It was based on a random sample and respondents were guaranteed anonymity and confidentiality. In the face-to-face interviews, many of the questions were coded in an elaborate way. For example, the respondent would be given a list of sexual activities and asked which activities they'd experienced. But they would respond in code, telling the interviewer "I've done X, Y, and Z." The interviewer, however, didn't have access to the key to the code, so (supposedly) they would have no idea of what specifically the respondent was referring to.

I should point out that this study has been criticized by some -- for example, the percentage of respondents who admitted to adultery is suspiciously low. Also, my professor said there was an unusually large number of people who were asked to respond to the survey but refused, which makes you worry that the people who agreed to participate were different in some important way from the nonrespondents, and thus are unrepresentative of the general population. Also, my prof, to his credit (an unprompted by me, even!), said that it was problematic that all the principal investigators were straight white dudes, and that it probably would have been a better survey if their team had been more diverse.

*Note: with the more explicit definition of sex in the follow-up survey, there was a smaller but still substantial gender imbalance in the number of sexual partners questions.

Posted by: Kathy G. | Aug 13, 2007 1:33:12 PM

These numbers probably can't be captured with any great accuracy, though my sense is that there really has to be *some* gap between men and women if we're to make sense of our entire lifetimes' worth of anecdotal evidence.

In my lifetime's worth of anecdotal evidence men and women do in fact have roughly equivalent numbers of sexual partners on average. Is this so unusual? Going by your name, you are a dude, so maybe your female friends are less inclined to tell you about their sexual escapades past or present (I don't mean that in a bad way, just that it's certainly possible that a lot of people feel more comfortable talking about their sexual histories with members of the same sex, though admittedly in my own group of friends this does not seem to be the case. We are quite young though and also a little strange).

Posted by: Isabel | Aug 13, 2007 1:38:53 PM

Mike B., I agree that there's a theoretical/anecdotal case to be made for the median for the men to be higher than the mean, and vice versa for women, and that a discrepency between the real (as opposed to reported) means does not necessarily prove anything. I don't think we really disagree there. And the math professor quoted in the article doesn't necessarily disagree either. He says "the conclusion that men have substantially more sex partners than women is not and cannot be true for purely logical reasons.” The difference between the mean/median can account for some of the difference, as can prostitution or travel outside the surveyed population, but not such a dramatic difference. I just think reporting bias likely skews the data so much that even good statistical analysis would be irrelevant.

Posted by: Joseph Hovsep | Aug 13, 2007 1:49:46 PM

Going by your name, you are a dude, so maybe your female friends are less inclined to tell you about their sexual escapades past or present...

Also a gay dude, so I do get a certain level of detail as a quid pro quo.

I doubt the actual numbers are so radically different for heterosexual men and women that a lot of ink needs to be spilled on the subject, because in the end the pool *is* the same, there are only so many really promiscuous people of either gender out there, and there are ultimately better things to do with one's time. All the same, I think the patterns of behavior gays and lesbians are telling: we don't really have any reason to exaggerate our numbers among our friends, and the differences are...well, let's leave it at "orders of magnitude." It would be remarkable if those patterns didn't show up at all among heterosexuals.

Posted by: Mike B. | Aug 13, 2007 2:00:05 PM

And Joseph, I think we do essentially agree. Hard to keep track sometimes when the subject is statistical analysis. :-)

Posted by: Mike B. | Aug 13, 2007 2:11:41 PM

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