In my eyes, the ratio visually represents the relative prestige differences between two schools. So just by looking at the ratio, I would assume that Cornell has a long way to go before it will catch up to Stanford in terms of prestige, however shallow that might sound. Again this has nothing to do with the quality of the institution, its just the way the schools are perceived by students/parents right now. A decade from now that could all change. Who knows. Post #25, gives an interesting historical perspective on how the position of these universities has changed over just a few years. That is itself an interesting visual.
That is precisely the point. The ratio doesn’t tell you why, it just tells you right now Harvard and Stanford have a more powerful brand and prestige relative to Princeton and Yale. Again it says nothing about quality of education, just perception. As you can see from Post #25, this was not the case even a few years ago. Stanford, Yale and Columbia were more tightly bunched together.
Pretty much any metric is gameable, if by gameable, you mean the University can take concrete measures to move the numbers. Even output based measures are eminently gameable. If a University decides tomorrow that it wants to increase the number of Nobel Prize winners on its faculty, it can just allocate a budget and go poach these winners from other universities. With enough money, resources and motivation, you can move any metric in the direction you want. I think this term is thrown around rather pejoratively in CC. as in, “Oh, that’s gameable, so it has no value”. The fact is Universities are reacting to “metrics” that seem to drive decisions of one of their important stakeholders, like any rational actor would or should.