MAllgoewer

Actually, Kleinberg et al. 2016 isn't all that bad. They have a small paragraph at the beginning of section 2 which they call an "informal overview" over the proof. But it's actually almost a decent proof in and of itself. You may accept it as such, or you may write it down a bit more formally, and you end up with a short, sweet proof. The reason they can't use a graphical approach like the one in this blog entry is that the above diagram with the squares only applies to the special case of scores that either output 0 or 1, but nothing in between. That is an important special case,... (read more)

I like the idea of clearly showing the core of the problem using a graphical approach, namely how the different base rates keep us from having both kinds of fairness.

There is one glitch, I'm afraid: It seems you got the notion of calibration wrong. In your way of using the word, an ideal calibration would be a perfect score, i.e. a score that outputs 1 for all the true positives and 0 for all the true negatives. While perfect scores play a certain role in Kleinberg et al's paper as an unrealistic corner case of their theorem, the standard notion of calibration is a different one: It demands that when you look... (read more)