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<p>I don’t think these comparisons are nearly as meaningful as some people think. That’s because, in choosing between a highly selective school (e.g., Stanford) and a somewhat less selective school (e.g., any of the the UCs), those who prefer the less selective school are, by and large, not going to bother to apply to the highly selective school. If UCLA is your dream school, why would you apply to Stanford? But if Stanford is your dream school, you might very well apply to UCLA as a back-up, thinking if you don’t get into Stanford, UCLA might make a reasonable second- (or third, or fourth, or tenth-) best fallback. So it stands to reason that the cross-admit pool is going to be heavily skewed toward those who prefer the more selective school from the outset. And that’s why, in virtually every case, the cross-admit "revealed preferences’ come out in favor of the more selective school.</p>
<p>Bottom line, then, the cross-admit comparison only tells you which school is more selective. Try it a few times, and tell me about any counter-examples you find.</p>
<p>I know in my own case, my absolute first choice was the University of Michigan. My HS GC encouraged me to think about applying to some highly selective private schools, and I knew I had the stats to be competitive. But I just wasn’t interested. So I only applied to one school, Michigan, I was accepted, I attended, and I never looked back. Most of the Michigan residents I met in college also had the University of Michigan as their number one choice. Many, but not all, of the OOS students had applied to more selective private schools and had not gotten in; if they had ended up in the cross-admit pool with one or more of those more selective alternatives, most would have chosen the more selective private school–but that’s because the more selective school was their preferred choice all along. People like me who preferred Michigan don’t choose more selective schools as their back-up. That would just be irrational.</p>
<p>And this is not just a public-private thing. My D1 had very good stats and could have been competitive almost anywhere. She really wanted a small, intimate LAC, and after looking at a bunch of them, she fell in love with Haverford. Now Haverford’s pretty selective, but there are LACs that are more selective. But since Haverford was her first choice, it made no sense to her to include more-selective LACs as back-ups. So her list of schools consisted almost entirely of schools that were either about as selective as Haverford, or less selective. As it turns out she applied to Haverford ED and was accepted, so she never even applied anywhere else. But someone whose number one choice is Swarthmore might easily decide to also apply to Haverford, reasoning that it’s slightly easier to get into Haverford than to Swarthmore and so it might make sense to apply to Haverford as a back-up, while students like my D1who prefer Haverford are by and large not going to apply to Swarthmore as a back-up. So the Swarthmore-Haverford cross-admit pool will consist mainly of people who prefer Swarthmore from the outset.</p>
<p>It’s just an obvious selection bias problem, if you think about it. So the cross-admit data mean virtually nothing, except which school is more selective.</p>