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Monday, August 13, 2007

Ask Math

posted by on August 13 at 13:34 PM

Historically, sex surveys have “confirmed” cultural stereotypes: Men will screw anything that walks, women choose their partners carefully. According to surveys of heterosexual men and women, the average man has had seven sex partners, while the average woman has had four. Women: close-legged. Men: Sluts.

Statistically, however, that’s impossible. Even accounting for female partners who may not be included in the survey (prostitutes, women overseas, etc.), there is simply no way that men can have nearly twice as many sex partners as women. The New York Times’s Gina Kolata proves it.

“By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B.

Theorem: G=B

Proof: Both G and B are equal to C, the number of couples who danced together at the prom.

The number of female and male heterosexual partners in the US must be roughly equal. And yet, in survey after survey, men consistently report having had many more partners than women. Why the discrepancy?

Possibility No. 1: Men may overreport, wanting to appear more “manly.”

Ronald Graham, a professor of mathematics and computer science at the University of California, San Diego, agreed with Dr. Gale. After all, on average, men would have to have three more partners than women, raising the question of where all those extra partners might be.

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

Women, meanwhile, may underreport, not wanting to look like “sluts.” The result: Statistically impossible conclusions that only reinforce the stereotype of men as promiscuous and women as chaste, compounding the problem in subsequent surveys.

If asked, a man, believing that he should have a lot of partners, may feel compelled to exaggerate, and a woman, believing that she should have few partners, may minimize her past.

“In this way,” Dr. Gale said, “the false conclusions people draw from these surveys may have a sort of self-fulfilling prophecy.”

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7 and 4? I'm 19 and I'm at 6. The guy I'm with now has been a number of women that goes into the double digits. Where do they get these numbers? Is there some criteria I'm missing here?

Posted by stiletto | August 13, 2007 1:40 PM

i think they're using the bill clinton definition of sex...

good thing they didn't include the gays in the survey...we'd completely eff up those numbers...

Posted by michael strangeways | August 13, 2007 1:41 PM

I believe this research was started a number of years ago with "The Rule of Threes", in the highly scientific research study titled "American Pie 2".

Posted by UNPAID BLOGGER | August 13, 2007 1:50 PM

Years ago I learned to always add 2 to a woman's number and subtract 4 from a man's. Or, don't freakin' worry about it at long as you're both healthy and ready to rock, why ask? Unless I suppose you attach nasty stereotypes to sex like the people in these surverys - The Puritans strike yet again.

Posted by Corliss | August 13, 2007 1:54 PM


Posted by wisepunk | August 13, 2007 1:57 PM

#4 wins. The survey seems to be fishing to make a point, and unintentionally made a different one.

Posted by Dougsf | August 13, 2007 2:02 PM

I always attributed the difference to a small number of highly sexual women who answer the survey with multiple choice answer, d., greater than x times, and a few prostitutes who up the numbers for a great deal of men.

Posted by David | August 13, 2007 2:02 PM

I support the hypothesis that female sex workers are being "missed" in these surveys. Just a few sex workers (who, by chance or choice, have a high probability of not being included in these population surveys) would really bump up the average number of partners reported by women.

Posted by mary-kate | August 13, 2007 2:04 PM

also, if they threw out the statistical outliers in a given survey, say, they average without this data point would be 4, but that data point is 107, so we throw it out... even if high-count persons were being surveyed, there is absolutely no guarantee that they were included in the reported average. and, statistically speaking, they would have been rightly excluded to give a representative "average."

Posted by clausti | August 13, 2007 2:15 PM

Surveys also discount the possibility that some of the people who participate could be lying.

They are horribly unreliable, and yet used as scientific evidence by sociologists. Yeah.

Posted by Gomez | August 13, 2007 2:16 PM

Nos. 7 and 8: Read the story. They take that into account. There's still no way that prostitutes could make up that huge a discrepancy.

Posted by ECB | August 13, 2007 2:17 PM

THEY DIDN"T 'PROVE' ANYTHING! They are wrong, wrong wrong, and obviously so.

Consider the prom. Suppose there are three girls who danced with every guy there. All other girls danced with 2 guys. All guys danced with two girls, plus the three who danced with everyone.

The article discusses the median # of partners data. "“Drug Use and Sexual Behaviors Reported by Adults: United States, 1999-2002,” which found that men had a median of seven partners and women four."

Ok - let's look a the median data for our prom above. The median number of partners for girls is the number such that half danced with more, half danced with less. Assuming there are more than 6 girls in attendance, the median is 2 partners for girls. For boys, the median is self-evidently 5.

For the "proof" to hold true, one would have to assume that the shape of the distribution curves for the two sexes is the same. In layman's terms, the proof overlooks the fact that all guys are tramps, but only some women are, while other women are prudes.

Doctor Gale is emeritus. He should know better.

p.s. note what clauti said also - even if a survey uses mean averages, it is very common to throw out outliers, which would have the exact same effect in my hypothetical prom.

Posted by A | August 13, 2007 2:18 PM

#11 - they didn't "take that into account" They dismissed it out of hand with neither a sociological nor statistical justification for doing so.

Posted by A | August 13, 2007 2:21 PM

Math is hard for girls.

Posted by pox | August 13, 2007 2:27 PM

@13, well the post at the top says "average", not "median". and it wouldn't be five for every boy, as the three girls who slept with everyone would each have 2 removed from the total. not only that, on a large scale -- to have the type of impact suggested, a very few amount of women would have to sleep with a very large number of men.

it would be interesting if the same survey was done, however, and asked the men NOT to included sex workers. of course, if their theory is correct that men may feel compelled to exaggerate, then they might not adjust their numbers accordingly.

Posted by infrequent | August 13, 2007 2:28 PM

it seems like the best way to figure out if sex work can account for the disparity is to find an estimate of the number of women who are engaged in sex work (i think i read about 1% of the population), figure out what their average number of lifetime partners is, and then do the math again. If something like 99% of women have an average of four partners, and 1% of women have an average of around 300 partners, then the actual mean number of partners for women would be right around 7. So it's not impossible, but it assumes that 1% of women who are prostitutes have a fairly high number of lifetime sexual partners.

Posted by tster | August 13, 2007 2:33 PM

What if the extra partners are in fact male impersonators? That would explain everything!

Posted by Seth | August 13, 2007 2:34 PM

Well, if there were a surprisingly large number of M-M-F threeways we didn't know about ...

But seriously, yes, it's obvious that this is underreporting by women and overreporting by men. (@12 misses the point that this is the _mean_ partner count we're talking about.) However, note that the _variance_ of male and female partner counts could be significantly different - if e.g. a small number of women could be banging all the guys, while most women have much fewer partners.

Posted by tsm | August 13, 2007 2:35 PM

ECB, some sexual behavior researchers did try to "take that into account" and found that, indeed, the missing sex workers might explain the differences in the average numbers of partners reported by men and women.

Posted by mary-kate | August 13, 2007 2:39 PM

Do these numbers include guys who can't get any? Most studies like that only include "sexually active" people.

In the prom theory, say you have 4 boys and 4 girls. 2 of the boys dance with 3 girls each, while the other 2 boys stay on the wall, contemplating suicide. If they tell the truth, the two "active" boys will say they danced with 3 girls, while the girls will report they danced with only 1.5 boys on average.

Besides virgin guys don't answer sex surveys because it just makes them feel worse.

Posted by FredE | August 13, 2007 2:47 PM

Actually, thinking about it more, I do think this could be a plausible result.

The reason is in the margin of error. I assume sex partner counts will follow a Zipf or "heavy-tailed" distribution, which basically means there will be a lot of respondents with low values ("Virgins") and a small number with high ones ("Whores"). However, if the set of Whores is particularly small relative to the number of Virgins, you may need a much larger sample of women to get the right proportions - it's easy to incorrectly sample a very small minority group within the larger group like that, and in this case it could seriously affect the result. If they had the same number of respondents for both genders, but the actual variances for male and female were significantly different, this could be a problem.

Posted by tsm | August 13, 2007 3:01 PM

@18 TSM - You may be talking about the *mean* number of partners, but in the NYTimes article, the only time they are specific about which brand of average they are using is when they say "median." That's why I quoted directly.

Posted by A | August 13, 2007 3:04 PM

@22 - huh, good point. Maybe the other survey was referring to means. I'd assume (or at least hope) the profs she consulted would've caught that error, if she didn't.

Posted by tsm | August 13, 2007 3:08 PM

No way. In my high school, just about every girl had one or two partners, but there were a hard core of about fifteen girls (out of 500) that slept around like a gay man on meth with a free pass to Club Z and a ten inch dick.

And is this just heterosexual men and women? Cause gay men could seriously throw off the numbers without affecting the womens' numbers. Especially me. Cause I've been a huge whore.

Posted by Gitai | August 13, 2007 3:42 PM

slate sorts out the math:

Posted by mark | August 13, 2007 3:48 PM

Some math:
Lets say a woman is sexually active for 50 years.
365 days x 50 years = 18,250 days.

Now, what if a woman has sex with a new man on average, once per day, sometimes having sex with two men, sometimes not having sex. That would be 18,250 partners. In a town of 10000 men and 10000 women, this individual has raised the average number of partners for men by 1.8 without changing the mean for women, unless she is included in the survey.

Posted by David | August 13, 2007 3:58 PM

There is a difference between an OPEN and CLOSED population with regards statistical gathering.

Asking girls at the SCHOOL'S PROM which boys they danced with, then the boys which girls they danced with, will (in theory) be G(equals)B. Why? Obviously, no other boys or girls could have been danced with, since they were all at the same SCHOOL'S PROM. A closed population.

An open population is what the sex surveys (let me say dance, since that’s what the analogy I’m talking about concerns) actually studied a group of girls who went to the prom (had a sex history) and a group of boys who went to the prom (had a sex history), but not necessarily THE SAME PROM (could have or did have sex with every person taking the survey). Attending A PROM (ie… having sex with how many #’s) is not the same as dancing at the SCHOOL’S PROM (ie… how many from this very specific group did you have sex with?). The results, since there will be boys and girls who were at a prom who are not being asked who they danced with, would from an open population be G(greater than)B, or G(less than)B, or G(equals)B.

Academically, which is all the use of statistics are good for IMHO, the result from a CLOSED population survey can not be overlaid onto an OPEN population with the hopes that the comparisons mesh.

But math aside, its bumpkis about who are statically the bigger sluts, the men or the women. That number will never be found, but hey, if someone can make a career and get a paycheck out if, then more power to them.

Posted by Phenics | August 13, 2007 4:28 PM

Phenics@27: I don't know if your explanation is correct or not, but it's the only thing around this "issue" that has ever made sense to me.

Posted by Soupytwist | August 13, 2007 4:48 PM

Can we please talk about the sex more than the statistics?

regardless of this math crap, 4 and 7 is pitifully small. For an unmarried 36 year old I would hope it's more like 50 or 80 (ie 4/year times 20 yeats).

Posted by unPC | August 13, 2007 5:00 PM

Duh! Dumb guys are fucking trannies!

Seriously, this was sorted out about ten years ago. There are a small number of female prostitutes who sleep with hundreds of men. It's hard for researchers to get them in the data set, because they're in prison, half-way houses, squats, etc. And probably don't know if the number is 50 or 100 or 1000.

Posted by chris | August 13, 2007 5:35 PM

Clausti = rockclimber?

If so, then what a small world it is...

Posted by Bison | August 13, 2007 5:47 PM

@29 - actually that's around my "score". I was surprised it was so low, but Americans are a bit scared of sex, IMHO.

Posted by Will in Seattle | August 13, 2007 6:49 PM

@29 and @32, there are those of us who married young and have been faithful to our partners. I'm in my thirties and my 'score' is 2.
Ain't no shame.

Posted by grumpypants | August 13, 2007 7:15 PM

to all of you -

Read this whole thing and gotta say over the afore mentioned number, 20 years, I have slept with hundreds of males and almost as many women - very bi - happily married as well and cheating like hell for 13 years - still friends with the ex, who never married again and admits she had a lot of fun - and still enjoying sex 4-5 times a week with different people.

Wonderful libido, very good looks, and not shy at all and lots of money .... never pretend it is more than lust, but romance has colored some affairs.

So what is this one and two baloney ... where is biology in your life?

Seattle is a haven for bi people - you can pick up someone on every corner of the Hill to say nothing of the hip downtown clubs. Any gay bar at 1:00 am is ripe for a carload if you have space, some booze and smoke ... the party most of the guys were hoping for all night long ... rolling on and on.

Posted by Rudy from New York | August 13, 2007 10:44 PM

@34 your not running for president are you?

Posted by Giffy | August 13, 2007 11:37 PM

David@26: You're making a good point, but I believe that in your example, the woman who had (heterosexual) sex 18,250 times in a town of 10,000 men raised the total number of partners for men by just 1, herself. They may have each had sex with her 1.825 times, but she's just the one additional partner.

I have always thought it would be fascinating if there were an led readout thingie showing when the last time a person had sex (with another person) was, numbered in days. Like a car that counts how many days since its last oil change. I'll bet it would be very very surprising and illuminating.

Posted by Diana | August 14, 2007 2:22 AM

I'm kind of surprised that so many people are pushing the "sex worker" button on this one.

I mean I know that prostitution exists (duh) but really, what percentage of the population actually patronizes them? I really don't see this pushing the average up by much at all.

Posted by Ken Ketchum | August 14, 2007 8:13 AM

@37 - they don't necessarily have to be actual prostitutes, just a small # of women who sleep with lots of men.

Consider an extreme example: 100 men and 100 women, married to each other. Each man sleeps with his wife and one other woman - we'll call her the town whore (NTTAWWT).
The women are faithful to their husbands. The average number of partners for both sexes here is about 2.

But if you try to get the average number of partners by sampling, say, 10 men and 10 women, you'll get the right answer for the men and the wrong one for the women. Either you'll get the town whore in your sample and overestimate women's average number of partners, or (more likely) you'll miss her and underestimate it.

Something like that could be causing the disparity.

Posted by tsm | August 14, 2007 9:36 AM

the high school prom theorum does not work on a logical basis. Basic explanation: 1 girl comes to prom and dances w/ the 4 boys at prom. Therefore, 1 girl danced w/ 4 boys and 4 boys danced w/ 1 girl. That'
s 4 to 1, not G=B 4=4.

Posted by brad | August 14, 2007 11:29 AM

I recall a radio program a few years ago where they talked about such surveys, and when the person doing them tried to understand that phenomenon by pressing the women she found they did indeed underestimate their number of sexual partners - not consciously to appear chaste, but in a "well I suppose there was that other guy but he didn't really count" kind of way.
Whereas presumably the men would include every last hooker and one-night stand.

So even aside of all the mathematical issues (and it seems to me there might be some confusion between medians and means in there) one doesn't need to suppose everybody's lying.

Posted by rozzen | August 14, 2007 4:34 PM

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