“So rich and (apparently) smart kids are actually pretty common.”
Of course. On average, rich people are smarter than poor people. They have higher IQs. It’s genetic. (On average smarter people accumulate more money and pass their genes on to their offspring, although of course there is always some regression to the mean, so that two very smart parents are likely to have children who are less smart than they are.) However, there are a lot more kids out there whose parents cannot afford $60K+ per year than those whose parents can. Probably by an order of magnitude. You won’t run out of less well off kids to admit who are smarter than the full pay cohort, that’s for sure.
BTW, the correlation between intelligence and income is positive and significant, but not enormous. Someone could correct me, but from memory I think it is roughly 0.25. (For reference, the correlation between intelligence of a parent and child is roughly 0.80 - again this is just from memory, so I welcome corrections.)
"Poor kids are less likely be high performing at age 13. So how would it be fair to not admit them? "
Well, first you need to identify them, It’s actually quite easy to do, although not palatable for political reasons. IQ tests or at least high g-loaded achievement tests will identify them. Remember, we are not looking to reinvent the wheel here or start from scratch. A high school student needs to have had some education previously. So each student has a record, and public schools have been free for over a hundred years in the US. One of the huge problems we have in education is that we refuse to structure elementary education in such a way as to identify talented students. Tracking, IQ testing, acceleration, grade skipping, etc. have all been under assault for the better part of 50 years. Grade inflation has now progressed to the point that a transcript is practically meaningless. But this is what we have, and we have to work within the system. Given what we have I would look at SSAT scores, particularly the analogies portion of the verbal section and the mathematics sections. Those should be most highly g-loaded (correlated with general intelligence), although I agree they are very imperfect measures.
Perhaps poor students should be offered the possibility of taking an IQ test when they interview. At least one extremely elite Boston day school does this for every applicant prior to the interview (they use a shortened test). Rich kids could offer IQ test results as well, although this would generate enormous backlash from parents for obvious reasons (they didn’t groom their bright but relatively average kid for elite admission only to be shown the evidence that the kid just isn’t that off the charts).
I see no need for elite schools to be “evangelists” looking to identify the small group of kids who are unprepared for rigorous secondary education but do in fact have the native intelligence to do it. That strikes me as an exercise in virtue signalling that is more appropriate for elite primary schools (since the public system refuses to do it).
Last, I argue that the financial aid kids should be smarter than the full pay contingent so that the kids are better able to deal with their unequal economic status. It’s also a good reality check for the full pay kids that life throws the dice and you can’t buy smarts.