The Angry Statistician

My friend Jordan Ellenberg wrote an article for the Wall Street Journal recently describing a metric to roughly measure the least read books, which he calls the Hawking Index (HI). As he describes it, take the page numbers of a book's five top highlights, average them, and divide by the number of pages in the whole book. On a discussion thread on Facebook, this led to a proposal from me for measuring the general quality of a quote. Assume a user has some level of discrimination $D$; the higher the value of $D$, the more likely they are to quote a passage. Now assume each passage has some measure of quality $Q$; the higher the value of $Q$, the more likely a passage is to be quoted. Let's try a classic Bradley-Terry-Luce model - if a user with discrimination $D$ quotes at least one passage from a particular work, the probability $p$ that they'll quote a given passage with quality $Q$ from that same work is roughly $$p = \frac{Q}{Q+D}.$$ Nice, but where ca...