<p>To simplify the model, assume each of the above school will plan to enroll 2,000 student for their 2016 class. </p>
<p>The same 30,000 students applies each school. </p>
<p>Each school admits 3000 students, waitlist 300, and reject all others. </p>
<p>For some reason each school admits the same 3,000 students and waitlist the same 300 students. Other 26700 applicants are rejected from every top 15 school.</p>
<p>The final result: each top 15 school can get 3300/15=220 enrollment. Except these same 3300 students, no other applicants can go to a top 15 school.</p>
<p>Except that schools know how to predict yield and the # of people they have to waitlist. UPenn waitlists over 3000. That means that (assuming everyone takes the waitlist spot) their entire admitted class could turn them down, and they’d STILL have some waitlisted students left over (about 2500 people matriculate).</p>
<p>Yeah, you’re seriously underestimating their waitlist size. Most waitlists are enormous because (a) they assume a worst-case yield scenario; (b) only about half will accept their spot on any given waitlist; and (c) many who accepted their waitlist spot will not accept an offer of admission after committing to and getting excited about another school.</p>
<p>According to one of my SAT teachers, the Harvard, Princeton, and Yale have a secret pact to have only one school accept a qualified applicant. It makes sense, but it also sounds ridiculous.</p>
<p>At the same time, if you look at the acceptance threads, students accepted to Princeton might not have been accepted to any other Ivies (eg). The above situation couldn’t happen.</p>
<p>@Littlepenguin, there are plenty of people who have gotten into multiple of HYP. It’s just very hard because of the statistical disadvantages and because they look for different things.</p>
<p>OP is assuming that an applicant who is qualified to be accepted by one top school will be accepted by all of them, but that is rarely the case.</p>