Aaron Clauset, Samuel Arbesman, and Daniel B. Larremore have published a paper in Science Advances: Systematic inequality and hierarchy in faculty hiring networks. The long and the short of it is that you’ve got to go somewhere really good for your PhD if you want a faculty job. They develop a “prestige network” by assuming that schools rarely “hire down” — that is, generally faculty in subject X at a given university got a PhD in subject X at some better university. So to put schools in order, you find a list of schools that minimizes the number of such hires. (The number of faculty at institutions more prestigious than their doctorate ends up being about 9 to 14 percent.)
I’ve been thinking this would be a good idea for a while, but building the data set isn’t exactly easy. The supplement indicates that “all information was collected manually from public data sources on the World Wide Web, typically from the faculty member’s curriculum vitae or biography on their homepage”, and that a total of about 20k faculty (in three subjects: CS, business, and history) were in the study. The rankings are Figure S10 of the supplement.
Schools, then, work differently than people, at least according to the quote of Andre Weil as reported by Paul Halmos, from I Want to be a Mathematician: An Automathography : “André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters.”