I think your broad point about "elite" schools being a matter of reputation rather than objective measurement is basically right. But some of your analysis seems weird.
On the graduation rate: why shouldn't a school be penalized for a low graduation rate? The point of those rankings (beyond selling magazines, of course) is to give prospective students an idea of how each school will help them in life. If I have a choice of going to school A from which I'm 90% likely to graduate and an otherwise equally ranked school B which is 50% likely to kick me out without a diploma, which am I going to choose?
And the bit about CalTech seems a little like sour grapes. I was at one of those "East Coast elite" schools in the 90's and don't remember anyone thinking anything but good things about CalTech (Pasadena, on the other hand...). Basically within its fairly narrow realm of focus CT is absolutely one of the "elite" schools everyone looks to.
"If I have a choice of going to school A from which I'm 90% likely to graduate and an otherwise equally ranked school B which is 50% likely to kick me out without a diploma, which am I going to choose?"
The "otherwise equally ranked school" part shows where a single-dimension ranking system falls on its face. Does it mean they accept the same quality of applicant? If so, graduating from the school with the lower graduation rate might be a much more impressive accomplishment. Or does it mean that the quality of education graduates receive is considered to be basically the same? Does that then mean the second one is just easier to get into?
How would all colleges having high graduation rates avoid pigeon-holing people even further into the box that their high-school performance marked them for? If everybody can graduate, the potential signaling is reduced from "got into and graduated from school x" to just "got in to school x."
> On the graduation rate: why shouldn't a school be penalized for a low graduation rate? The point of those rankings (beyond selling magazines, of course) is to give prospective students an idea of how each school will help them in life.
Its easy to look at this from the other side though.
I think a lot of people look at these rankings as the value of a degree earned from that institution. That is, they are looking at it from the side of the alums as opposed to the prospects. Suppose two schools have the same admissions criteria and everything else, but the graduation rate of one is much higher. I would think the school with the lower graduation rate would be viewed as more rigorous and therefore "better".
Even in high school, I never thought differently. >10 years later this is the first time I ever even thought that someone would consider the probability of their graduating (totally within their control). It was always 100% which would be the best school to be from...or which one would be the most fun. Graduation rate has nothing to do with either.
IMHO what weights are the right weights is very subjective - reducing all these colleges to a single comparison is stupid.
For example, if there is 100% graduation, I consider that very suspect and probably a bad sign. It's natural that some people don't finish college. WRT Caltech, they are desirable BECAUSE they offer such a challenging environment.
On the graduation rate: why shouldn't a school be penalized for a low graduation rate? The point of those rankings (beyond selling magazines, of course) is to give prospective students an idea of how each school will help them in life. If I have a choice of going to school A from which I'm 90% likely to graduate and an otherwise equally ranked school B which is 50% likely to kick me out without a diploma, which am I going to choose?
And the bit about CalTech seems a little like sour grapes. I was at one of those "East Coast elite" schools in the 90's and don't remember anyone thinking anything but good things about CalTech (Pasadena, on the other hand...). Basically within its fairly narrow realm of focus CT is absolutely one of the "elite" schools everyone looks to.