<p>^sevmom(post #160) makes a good point. Cross-admit numbers are only one part of the decision tree. Most applicants pre-screen schools, and don’t even bother to apply to those schools that don’t interest them–especially highly selective schools that don’t interest them. </p>
<p>From the numbers I cited in post #159, it looks like Duke has relatively little appeal to Michigan residents, and more particularly to Michigan residents who also have their eye on elite private schools. For a Michigan resident who prefers Michigan to Duke, there’s little point to applying to Duke; if their admissions credentials are strong enough to make them competitive at the most selective private institutions, they have a very strong chance of admission to Michigan, so why even bother to apply to a school that they like less than Michigan? So at least for Michigan residents, who I venture to guess make up, if not an outright majority, then at least a strong plurality of those cross-applying to Michigan and Duke, the cross-admit pool is mostly going to reflect those who would prefer Duke to Michigan if they get in, because of self-selection.</p>
<p>Look at it this way: no Michigan resident in his right mind is going to say, “I’ll apply to Michigan and Harvard with Michigan as my first choice, but if I don’t get into Michigan then I’d settle for Harvard as my second choice.” No, if Michigan is that student’s first choice, chances are he’s not going to bother to apply to Harvard. He’ll be looking for other match and safety schools in case he doesn’t get into his first choice. On the other hand a Michigan resident who really prefers to go to Harvard but would settle for Michigan if her first choice doesn’t work out will apply to both; and some fraction of those like her are more likely to end up in the cross-admit pool, already pre-programmed to choose Harvard if accepted to both. So just looking at the cross-admit figures is going to give you a pretty distorted picture of student preferences, because there’s self-selection as to who ends up cross-applying and who ends up in the cross-admit pool.</p>
<p>I’ll generalize this claim: I’m going to say that with few exceptions, the school that is perceived to be more selective in admissions is going to win the bulk of the cross-admit battles. But that’s not because the more selective schools are inherently more desirable; its because fewer people are going to be using them as back-ups. The students who have a clear preference for the less selective school will in most case not bother to apply to the more selective school, knowing they’d choose the less selective school if offered the choice; whereas those preferring the more selective school will apply to both, intending to attend the more selective school if admitted, and if not then to consider the less selective school. Since the cross-admit pool is therefore biased by the inclusion of more applicants who have pre-selected the more selective school as their first (or a higher) choice, the more selective school should win most of the cross-admit battles.</p>
<p>Let’s test my hypothesis, using Fall 2010 acceptance rate as a proxy for selectivity (I know, it’s imperfect):</p>
<p>Brown (9%) v. Michigan (51%): Brown wins 73-27
Brown (9%) v. Duke (16%): Brown wins 73-27
Duke (16%) v. Emory (29%): Duke wins 75-25<br>
Vanderbilt (18%) v. Emory (29%): Vanderbilt wins 70-30
Brown (9%) v. Cornell (18%): Brown wins 74-26
Columbia (10%) v. Cornell (18%): Columbia wins 69-31
Penn (14%) v. Cornell (18%): Penn wins, 69-31
Penn (14%) v. Chicago (19%): Penn wins, 89-11
Dartmouth (12%) v. Northwestern (23%): Dartmouth wins 75-25
Cornell (18%) v. CMU (33%); Cornell wins 86-14
Cornell (18%) v. Johns Hopkins (21%): Cornell wins, 63-37
Chicago (19%) v. WUSTL (21%): Chicago wins 67-33
Chicago (19%) v. Notre Dame (29%): Chicago wins 67-33
Tufts (24%) v. Brandeis (35%): Tufts wins 67-33
Case Western Reserve (67%) v. Ohio State (68%): Case wins 72-28
Michigan (51%) v. Case Western Reserve (67%): Michigan wins 82-18
Rice (21%) v. Texas (47%); Rice wins 82-18
Texas (47%) v. Texas A&M (69%): Texas wins 83-17
U Maryland-College Park (44%) v. Penn State (55%): U Maryland wins 63-37
UVA (33%) v. VaTech (67%); UVA wins 91-9
Michigan (51%) v. Michigan State (70%); Michigan wins 77-23 </p>
<p>What’s impressive is how lopsided most of these are. And it’s not about prestige or desirability-- or not exclusively about those things. Whatever your top choice is, you’re generally not going to choose more selective schools as back-ups. If your first choice is Michigan State, you don’t apply to Michigan as a back-up; so you self-select out of the Michigan-Michigan State cross-application pool. But if your first choice is Michigan, you might apply to Michigan State as a back-up. So the Michigan-Michigan State cross-application pool is going to self-select with a bias for those whose top choice between the two schools is Michigan; and that preference will also be reflected in the cross-admit pool. Similarly between Michigan and Harvard; if your first choice is Michigan, you’ll likely apply to Michigan and schools of similar or lesser selectivity; you’re not likely to apply to Harvard (even if you have credentials that might make you competitive). But if your first choice is Harvard, you might also apply to Michigan–or Duke–as a back-up, knowing either school has a higher admit rate. But more people in the cross-applicant pool will have Harvard as their first choice, and it only stands to reason that more of the cross-admits will have already pre-selected Harvard as their top choice.</p>
Latin is awesome. I was also one of 2 juniors to get a 5 on AP Latin last year in MI. But only 35 people total took it here… Not much Latin goin’ on in this state it seems ;(</p>