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<p>I just don’t buy the “revealed preference” idea for college selection. Apart from the flaws in parchment.com’s extremely limited, self-selected, and unverified “data,” the whole idea doesn’t make sense to me. I think if you run a few of these comparisons, you’ll quickly find that in almost every case, the more selective school “wins” the “revealed preference.” </p>
<p>A lot of people want to jump on that as confirmation of the rightness of revealed preference: of course everyone wants to get into the most selective schools, because they’re the most desirable, right? </p>
<p>Well, no, not necessarily. I think all it means is that applicants whose first choice is the more selective school A will often also apply to a somewhat less selective school B as a back-up; if they get into both, that group will almost always choose A. But those for whom the less selective school B is their first choice are much less likely to apply to the more selective school A as a back-up; they calculate that if they don’t get into their first choice, B, then they should have an even less selective school C as their back-up. It would be a senseless waste of time and effort for them to apply to A, because if they’re not going to get into their less selective first choice B, they have little or no chance of getting into the more selective alternative A.</p>
<p>Thus the pool of cross-admits to A and B will be heavily skewed toward applicants predisposed toward A, the more selective school. So basically all the “revealed preference” is telling us is which is the more selective school.</p>
<p>Just as an illustration, the University of Michigan and Michigan State aggressively compete with each other for the state’s top students. Their rivalry runs deep, and in some families is multi-generational. As between the two schools, Michigan is much more selective. And guess what: parchment.com says Michigan wins 80% of the cross-admits. Well, doh! That’s because a significant number of applicants for whom Michigan is their first choice also apply to Michigan State as a back-up. But applicants for whom Michigan State is their first choice are much less likely to apply to Michigan as a back-up; why bother? The “revealed preferences” of cross-admits tell us only about the preferences of cross-admits, who are a subset of cross-applicants. It tells us nothing at all about the actual preferences of the bulk of applicants to either school. I’d be willing to bet that, of students who end up at Michigan State, an overwhelming majority had Michigan State as their first choice, and most of them didn’t bother to apply to the University of Michigan. In fact, I can almost guarantee it. In 2012, Michigan had only 9,700 in-state applicants, to go with 32,000 or so OOS applicants. That same year, Michigan State had 30,000 applicants, of whom probably 80% or more were in-state. Relatively few of Michigan’s OOS applicants also apply to Michigan State. That means an overwhelming majority of each school’s applicant pool didn’t even apply to the other school. So who were the cross-applicants, from whom the cross-admits were drawn? Well, I submit they came primarily from Michigan’s 9,700 in-state applicants, who generally had Michigan as a first choice (otherwise they’d have simply applied to Michigan State) but in many cases also applied to Michigan State as a back-up. Very few of the 25,000+ Michigan residents who applied to Michigan State also applied to the University of Michigan as a back-up. So, given this skew in the cross-applicant pool, it should be no big surprise that when we tally up the cross-admits, 80% chose Michigan. That tells us nothing more than that, as between the two schools, Michigan is the more selective.</p>
<p>Try it with a few pairs of schools. You may find some outliers where the less selective school “wins,” but it’s rare.</p>
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