"Handsome men are jerks"

[Klaus]

I found this example of the "paradox" particularly interesting and worthy of trying it out:

[Horace]

Interesting.

[Loki]

@horace said in "Handsome men are jerks":

Interesting.

Indeed

[Klaus]

For those who are not familiar with distributions visualized as in the first example:

The dots are individuals. Their x- and y-coordinates measure how handsome and how nice they are, respectively.
The "round" shape indicates that these properties are not correlated. The correlation is illustrated with the blue bar, which is computed to go through "the middle" of the dots.

This is what correlation of such dot clouds looks like:

The middle shows "uncorrelated", as in our example. To the left, it shows more and more correlation. For instance, if you measure height and weight of people, you'd get a graph like the 0.8 one. To the right, we see more and more inverse correlation. For instance, if you'd measure HP vs MPG of engines, you'd get a picture like the -0.8 one.

The point of the "paradox" is that if you filter the population by two positive traits (you date men who are nice and hot), then in that subset there's an inverse correlation, as illustrated by the diagonal blue line on the right picture. It doesn't look as "clean" as the "-0.8" picture I posted above, but mathematically it is still clearly a negative correlation.