A confounding problem with your method is that schools such as Amherst and Williams accept circa 50 percent of their classes with a 100 percent yield rate, but a significantly higher acceptance rate (40 percent for ED versus slightly less than 20 per cent for RD).
So your method doesn’t look at the quality of the self-selected pool.
I think desirability would also look at to which schools high stat students apply versus those to which they don’t apply.
Incidentally, if you rank schools by SAT alone Cal Tech is number 1 on both the Math + CR list (Forbes) and the Math + CR + Writing list (Business Insider).
http://www.businessinsider.com/colleges-with-the-highest-sat-scores-2013-4?op=1
@GMTplus7 I’d hypothesize a high correlation between the SAT scores of spouses. To test this, we’d have to control for meeting your spouse at college, and look at marriages between people who attended different colleges.