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Here is an interesting ranking of the ivies that I stumbled upon.
The author looked at USNews, Forbes and Niche rankings and averaged out the positions of each ivy. He reasoned his choice of rankings as follows: USNews focuses on reputation & inputs, Forbes focuses on outcomes, Niche focuses on quality of student life.
The ranking was he following (average rank in parentheses)
1. Princeton University (2.5)
2. Harvard University (3)
3. Yale University (3.75)
4. University of Pennsylvania (8.75)
5. Columbia University (9.5)
6. Brown University (11.5)
7. Dartmouth College (13)
8. Cornell University (22)
He also broke the ivies into tiers and included what are the ivy-equivalents, in his opinion, for each tier: