<p>I really disagree that competition within top schools is a negative factor for students.</p>
<p>Sure, at a top school, many or most students want to do research. But the resources are there for all students to do research, so there’s limited or no competition for research spots. Everybody wants to do research, and everybody can do research.</p>
<p>And grad schools are pretty uninterested in picking students from diverse backgrounds, unlike undergraduate programs, which prefer not to take all of their students from a handful of high schools. As I mentioned upthread, 10 of the 70 students in my entering PhD class came from MIT (and more were admitted but chose to go elsewhere). There was no attempt to take only the top one or two applicants from a particular school.</p>