This. This is the one. If you view everything Harvard does as supporting this goal, it all makes perfect sense.
You don't necessarily want the smartest kids. You want the kids that are most likely to go on to make the most money AND the kids who are most likely to have a strong emotional connection to the university so they write big checks.
1. I'm have yet to be convinced that Harvard is trying to maximize its benefit to society.
2. Even if we stipulate that Harvard's sole goal is to maximize its benefit to society, it may be that increasing the number of Jeff Deans or Jim Kellers, even by a small amount, is more beneficial to society than better educating a lot of average people.
... or it may not be. My point is that the approach you suggest is not obviously correct.
Most likely to graduate is interesting. Almost everyone I know who didn’t graduate, it was due to finances. Purely academic reasons, at least anecdotally, seem relatively uncommon now.
That's probably true for the Ivy's since they get the cream of the crop.
The community colleges near me have a 25% 6 year graduation rate. I guarantee you that's not all due to finances.
The most obvious criteria is: most likely to graduate.
Some others that aren't bad:
* Highest expected value of future donations
* Highest expected value of impact (publication)
* Highest expected value of future salary
* Highest expected value of holding public office (the weighting here might be contentious)
As long as all of the criterion are achievement based, I expect them to screen for roughly the same people, demographically.