MIT doesn't do legacy admissions: http://mitadmissions.org/blogs/entry/just-to-be-clear-we-don...
That sets a pretty high bar. The last time I checked, which was before the Great Recession changed the game and increased applicants, MIT was getting 13,000 applications a year despite the extreme amount of self-selection, of which they judged 3,000 could do the work. From that they construct a class of around 1,100 students.
Transparency on the alumni relations of each student is the only way to go I guess...
For instance, when I was a student there (class of '82), the biggest demographic problem within the student body was the severe imbalance between men and women. The undergraduates were only around 15% women. That's frustrating for pretty much everyone.
Caltech addressed this by trying hard to (1) get more qualified women to apply, and (2) convincing more of those who were accepted to choose Caltech over the other schools that accepted them. Essentially, they would treat a bright high school girl with a talent for math, science, or engineering the way schools with effective sports programs treated outstanding high school athletes.
Nowadays, around 40% of undergraduates there are women.
Even Harvard, Stanford, and Yale each admitted 3 people that year (which, interestingly were different people -- it's as if they colluded to induce enrollment).