A follow up on ranking strategies.
This approach was first used for college rankings by Avery, Glickman, Hoxby, and Metrick. I forgot to acknowledge them in the first post.
What we use is an algorithm that says, "For this desirable student (objectively 'desirable' to the schools that were impressed enough to admit them), which school did they choose?" I see this as the "virtuous" approach. In a sense, in this model, schools are rewarded for admitting desirable students and winning the competition for them.
This hinders gaming of the system because most things that you can do to game this generally helps students. Want to game it by admitting students who won't get admitted to your competitive peers? You'll fall in the rankings, because those students will pit you against 'weaker' opponents, giving you less of a chance to rise in the rankings even if you always win.
There's another ranking approach that is fun but naughty. I'll call it the "vicious" approach. This one takes all colleges that admitted a student and all colleges that rejected them. The ones who rejected the student are modeled as the winners, and the ones who accepted them are modeled as the losers. In this way, the colleges that are most selective in admitting a student rise to the top.
I've actually run this "vicious" algorithm, but we don't publish its results. (Gaming this one would hurt students: imagine you're City College. You could do well for yourself by getting all the future freshmen of your rival, State College, to apply to your institution, then rejecting all of them. The kids wasted money on their application, you probably rejected some great candidates just to game the rankings, and State College unfairly drops in the rankings.)