Here comes my Ig Nobel

I may end up getting an Ig Nobel for this, but here goes.

According to various surveys, a typical American male has 6 sexual partners in his life and typical American female has 2. I don't see how that's possible, unless there are 3 times as many women as men, so I decided to investigate the matter a little further.

Let's consider a simple model. Suppose we have 5 men and 5 women. We make a table to show who has sex with whom by marking with an "X." How do the averages work out under various scenarios?

Scenario #1: The Stud

In this scenario, 1 man has sex with all 5 women while the remaining men have 1 sexual partner each.

..........W1.....W2...W3...W4....W5
M1.....X........X......X......X........X
M2.....X
M3...............X
M4........................X
M5.................................X

The average for the men is (5+1+1+1+1)/5 = 1.8
The average for the women is (2+2+2+2+1)/5 = 1.8

Scenario #2: The Slut

In this scenario, one woman has sex with all the men while the remaining women have one partner each.

............W1...W2...W3...W4...W5
M1.......X......X
M2.......X...............X
M3.......X........................X
M4.......X..................................X
M5.......X

The average for the men is (2+2+2+2+1)/5 = 1.8
The average for the women is (5+1+1+1+1)/5 = 1.8

Scenario #3: The Shy Guy

In this scenario, one man has no partner while each man has at least one partner.

........W1....W2....W3....W4....W5
M1
M2...X
M3.............X
M4......................X
M5................................X.........X

The average for the men is (0+1+1+1+2)/5 = 1
The average for the women is (1+1+1+1+1)/5 = 1


Scenario #4: The Plain Jane

In this scenario, one woman has no partner while the other women have at least one partner.

......W1....W2....W3....W4....W5
M1..........X
M2..........X
M3....................X
M4....................X
M5..............................X.........X

The average for the men is (1+1+1+1+2)/5 = 1.2
The average for the women is (0+2+2+1+1)/5 = 1.2

We could add more people or fill the chart differently, but that wouldn't change the result. The average number of partners for both groups must be the same, because each X adds the same amount to both groups.

This leads us to a rather unsurprising conclusion: many people lie about their sexual behavior.