The fact that Facebook, Airbnb, and Dropbox came out of other places suggests there isn't anything inherently special about Stanford, except that there's a lot of talent there.
I think the question comes down to, does the school give the unfair advantage or does the school attract smart people that are more likely to accomplish something great. I think its already accepted that there is a correlation.
There's a correlation, but rich kids can also buy their way into schools like Stanford: http://www.paulgraham.com/hs.html
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It's dangerous to design your life around getting into college, because the people you have to impress to get into college are not a very discerning audience. At most colleges, it's not the professors who decide whether you get in, but admissions officers, and they are nowhere near as smart. They're the NCOs of the intellectual world. They can't tell how smart you are. The mere existence of prep schools is proof of that.
Few parents would pay so much for their kids to go to a school that didn't improve their admissions prospects. Prep schools openly say this is one of their aims. But what that means, if you stop to think about it, is that they can hack the admissions process: that they can take the very same kid and make him seem a more appealing candidate than he would if he went to the local public school. [6]
[6] I don't mean to imply that the only function of prep schools is to trick admissions officers. They also generally provide a better education. But try this thought experiment: suppose prep schools supplied the same superior education but had a tiny (.001) negative effect on college admissions. How many parents would still send their kids to them?
It might also be argued that kids who went to prep schools, because they've learned more, are better college candidates. But this seems empirically false. What you learn in even the best high school is rounding error compared to what you learn in college. Public school kids arrive at college with a slight disadvantage, but they start to pull ahead in the sophomore year.
(I'm not saying public school kids are smarter than preppies, just that they are within any given college. That follows necessarily if you agree prep schools improve kids' admissions prospects.)
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I'm going to go with "unfair advantage," but there are a lot of smart people there too.