Oh Augustus, Now I Know Why They Call You "The Strong"

The blogerati are still having fun with a New York Times story on sexual partners—who gets how many (a Google blog search for "male female sex partners mean median" yields 200 hits as of 911 am pst Ag 22 (link; cf. link)). Surveys suggest that men claim more sexual partners (of the opposite sex) than women. But wait, object the arithmeticians: every time a man has sex with a woman, then by definition a woman must have sex with a man. So the number must be exactly the same.

Model it this way:

M1	F1, F2		F1	M1, M5
M2	F2, F3		F2	M1, M2
M3	F3, F4		F3	M2. M3
M4	F4, F5		F4	M3, M4
M5	F5, F1		F5	M4, M5

So, two each, and an average of two for everybody, and the green grass grows all around, all around. Call it the “frat boy” model: a boring, moderately promiscuous, society, where the guys do a lot of lying.

But contrast:

M1	F1, F2, F3,		F1	M1, M2, M3, M4, M5
M2	F1, F2		F2	M1, M2, M3, M4
M3	F1, F2		F3	M1
M4	F1, F2		F4	0
M5	F1		F5	0

Call this the “Victorian” model, with a lot of virginity and a lot of prostitution (though not, it seems, any pure monogamy). There are still 10 relationships on each side, so, an average of two each as before.

But while the mean is the same (definitionally), note the median. The midpoint on the male side is two relationships; on the female; only one. So measuring with the median, men do, in fact, have more relationships than women—solely because one or two poor girls are doing most of the work.

So far this is stuff that any good high school student could figure out, and a lot have. But now consider this case which doesn’t seem to have received so much attention:

M1	F1, F2, F3, F4, F5		F1	M1
M2	0		F2	M1,
M3	0		F3	M1
M4	0		F4	M1
M5	0		F5	M1

Call this the “Augustus the Strong” case, after the Elector of Saxony alleged to have fathered 385 children (link). One guy gets all the action. This is more or less what you would expect in a polygamous society, and it is what guys forget when they think that polygamy would be such a great idea. Note that we still have an equal number of M and F relationships-now, five and five—so the means remain equal. But the median for women is now actually higher (one) than it is for men (zero).

Fn.: A private communcation cautions that Augustus is called "the Strong" not because of his progenitive capacity as because he was capable of breaking horeshoes with his bare hands. Sorry, my bad. He was 5 9 1/2 and weighed 242 pounds. Oof. Also liked eggshell porcelaine. Sissy boy.

Fn2: I recall reading in The Economist many years ago that many more Turkish women report that they are married, than men. I assumed then that it was lying or, ahem, misunderstanding. Course it could be illegal polygamy.

Fn3: Apologies for the quirky formatting. I have spent far too much time trying to get it right; be glad that it works at all.