Studies in Sexuality

I have read a study once, the average number of sexual partners of a male in his life time was 9 in the U.S., it was 4 for women (let's label this as Proposition 1). Let's look at the remaining propositions:

Prop 2: In a population with equal number of men and women, the average number of partners for both sexes cannot be different.

Prop 3: If we assume that the number of men and women in the US are equal and Proposition 2 is true, Proposition 1 cannot be true.

Proposition 3 is correct without any serious objections. So, we look at Proposition 2 first. We know that for every man having sex, there has to be a woman that is engaged in the same activity. So, the number of sexual encounters in both sides of the aisle have to be equal. But, how about the average number of partners per se? With a population of 10 men and 10 women, a woman can sleep with every male, and other women may not sleep with any men at all. In this case, one woman would have had 10 sexual partners, and each man would have had 1 sexual partner. If we calculate the average number of partners of a woman in this population of 10, we need to add the total number of partners of each woman and divide it by the total number of women. So, we have:

10 x 1 + 0 x 9 = 10, 10 / 10 = 1.

For men, it is:

1 x 10 = 10, 10 / 10 = 1.

As one can see, we always achieve the same average (A more comprehensive proof of Proposition 2 is beyond the scope of this blog). Thus, proposition 1 is false.

Does this mean women lied in this study, or men? I suspect both did. However, is everything about sexual mates the same in both sexes? I don't think so. In the example above, the averages were the same, however, women had a really high standard deviation within themselves in terms of number of partners. For this, we need to look at both sexes to see if there are "exceptional" members in terms of number of partners in either sex - for instance male sultans with harems or female prostitutes. My hunch is that the standard deviation among women are higher than it is among men, just like 2 cities with the same average temperature year round: One is inland and its temperature fluctuates, but the other city is on the coast and has a more stable temperature.