Revealed Preferences and College Rankings

I just read a fascinating "revealed preferences" paper on college rankings, in which the rankings are based on decisions of students admitted to multiple schools (e.g., Harvard beats Brown if an applicant is admitted to both but chooses to enroll at Harvard). They consider each decision as a "match" (as in chess) between pairs of schools, and use the mathematically sophisticated Elo system (invented by a physicist and used in chess) to determine a ranking. These revealed preference rankings are at odds with the U.S. News results in interesting ways.

Harvard is number one by a big margin - no surprise given its 70% admissions yield. The authors list Yale, Stanford and Caltech as the rest of the top four, although if you look carefully at their regional data it seems clear that Caltech is number two (their admissions yield is around 50% and no other schools do much better than 30%).

Another interesting piece of data is that at certain schools like Princeton the probability of admission is not monotonic with SAT score. Probability of admission is higher at around 91 percentile than at 95 percentile, although then it goes up again. The authors claim this is evidence of Princeton "managing" its admissions to improve yield - they don't want to fight over the candidates who will be admitted to multiple top schools, except the very exceptional ones. I'm not fully convinced, but the oddly shaped probability curve is very striking.

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