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, but a special case nevertheless. Kleinberg et al. deal with the more common and slightly more general case of scores which can take any real value from 0 to 1. Also the COMPAS score, which is the topic of the ProPublica report cited above, can take other values than just 0 and 1.
By the way, also the introductory section of the Kleinberg-et-al-paper is definitely worth reading. It gives an overview over the relevance of the problem for other areas of application. So only their attempt at a formal proof is kind of a waste of time to read.
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, but a special case nevertheless. Kleinberg et al. deal with the more common and slightly more general case of scores which can take any real value from 0 to 1. Also the COMPAS score, which is the topic of the ProPublica report cited above, can take other values than just 0 and 1.
By the way, also the introductory section of the Kleinberg-et-al-paper is definitely worth reading. It gives an overview over the relevance of the problem for other areas of application. So only their attempt at a formal proof is kind of a waste of time to read.