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I present for you a ranking of major American universities by prestige:
7. UC - Berkeley
9. University of Chicago
10. University of Pennsylvania
11. Cornell University
12. Duke University
13. Brown University
14. Johns Hopkins University
15. Georgetown University
17. University of Texas
18. University of Michigan
23. UNC - Chapel Hill
24. University of Illinois
25. University of Wisconsin
26. Rice University
27. University of Maryland
28. Carnegie Mellon
30. Notre Dame
Now, for my methodology. The ranking is based on 3 different measurements: academic prestige (40%), prestige among students (30%), and prestige among members of the general public (30%).
Academic prestige is measured by the combination of the US News Peer Assessment score, which indicates the prestige given to a university by administrators at other universities (5%). The second factor is the Wall Street Journal rankings of admissions to elite professional schools, measuring prestige for professional school admissions committees (10%). The third factor is the average score for the universities graduate programs according to the US News survey (25%), this measures what professors (and thus graduate school admissions committees) think of schools.
Prestige among students is measured on the basis of the revealed preference ranking of colleges, scores from which were standardized to scores out of 100.
The third element of the ranking is prestige with members of the general public. This is difficult to measure, so as a proxy, media mentions of the school not in reference to sports were used - drawing from a sample of 1600 US and international media sources.
The rankings produced are fairly close to other major rankings, and particularly similar to the US News ranking done by guidance counselors. Though generally similar to the standard US News rankings, certain schools perform much better (e.g., Berkeley) while some do much worse (e.g., Northwestern at #22, WUSTL at #33).
I welcome your feedback, and I have all of the raw data in an excel sheet, so if you'd like to see what the rankings look like given a different weighting, just let me know.
Edit: One final note. There's a very significant drop off in prestige between the top and the bottom. MIT earns a prestige score of 91.4 and Harvard one of 86.9, but #30 Notre Dame scores a 47.1.