Jordan Ellenberg writes:
"You may have noticed that, among the men in your dating pool, the handsome ones tend not to be nice, and the nice ones tend not to be handsome.You can see that the "niceness" distribution of the "uglies" is totally bunched up at nice while the "niceness" distribution of the "handsomes" is not dissimilar to the overall population norm.
"Is that because having a symmetrical face makes you cruel? Does it mean that being nice to people makes you ugly? Well, it could be. But it doesn’t have to be. ...
"The handsomest men in your triangle, over on the far right [the green line], run the gamut of personalities, from kindest to (almost) cruelest. On average, they are about as nice as the average person in the whole population, which, let’s face it, is not that nice. ..
The ugly guys you like, though—they make up a tiny corner of the triangle [the red line], and they are pretty darn nice. They have to be, or they wouldn’t be visible to you at all.
The negative correlation between looks and personality in your dating pool is absolutely real. But the relation isn’t causal. "
It follows that the average of the most handsome people [centre of green line] is going to be meaner than the average of the ugly ones [centre of red line].
Niceness suddenly negatively correlates with handsomeness, whereas in the overall population - by hypothesis - there is no correlation at all.
Notice you could equally ask, "Why are the nicest ones so ugly?" - and then the green and red lines are interchanged and horizontal.
This is called Berkson's paradox and is a general feature of populations where a selection is made jointly on two weakly-correlated or uncorrelated variables. The selection process itself can induce correlations where none existed previously, or even reverse previous correlations.
The effect is particularly pernicious in academic admissions (and also medical trials).
[h/t: Razib Khan].