Sex-partner math revisited

Reader Ritchie Simpson challenges me to consult a mathematician on my assertion that “one should always be sceptical of surveys that show heterosexual men had more partners, on average, than women, since this is a mathematical impossibility.”

While I do not fundamentally disagree with your observation about “heterosexual men,” I am dubious about your math.

My go-to guy on matters arithmetic is retired Cape Breton University professor Doug Grant, now living in exile in Kitchener. His response after the jump.

After pointing out the obvious potential for sample bias inherent in self-selecting groups like the membership of the OK Cupid dating site, Grant turned to the arithmetic issue. It seems that, for my statement to be true, the number of men and women in the population must be equal:

[Your assertion about] the average number of sex partners is not correct unless one assumes the number of males and females in the subject population are equal, which is certainly not true in fact.  To take an extreme example, suppose there were 100 heterosexual men and one heterosexual woman on an isolated island.  If all 100 men had sex with the single woman, the average number of sex partners in the male population would be one, while the average in the female population would be 100. What is true is that the total of all the male partners in male-female pairings must equal the total of the female partners, but, since the denominators may be different, the averages can differ considerably.

I asked for clarification:

When a survey that purports to sample the general population in a country where population variation between males and females is small, say < 5%, then a survey showing males have eight partners on average and females four should be viewed skeptically, no?

Grant replied:

Yes, indeed, skepticism would be warranted under those circumstances.  In fact, the test would be that if you multiply the number of males by the average number of partners claimed, that should equal the analogous product for the females.  If there is a big discrepancy between the two products, then someone is fibbing.

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