But that isn’t necessarily about reputational halo effects. That instead could be a rational assessment of internal competitiveness.
Indeed, there is no doubt that many sorts of next-step gatekeepers are willing to go “deeper into the class” at Princeton as opposed to Arizona. We can see that in many different placement studies. These effects are diminished but can survive controls just for next-step placement tests, like the LSAT or MCAT. But if we also controlled for reasonable internal competition adjustments, would there be anything left to explain?
It is very hard to really do that sort of control, but plausibly not. Even more plausibly, if there is anything left to explain, it could be a variable effect, and sometimes nonexistent in specific cases, and in most other cases relatively small.
The reason this is important is the reputational halo theory suggests you can get this effect just by matriculating, and then chilling for the next four years while waiting to collect that benefit. If it is rational adjustments for internal competition, you instead can’t just stop with matriculation, you need to actually compete for the next four years. And in fact, if it is a rational internal competition factor, it will be quite hard to get to that required level at Princeton, as hard as it would be to get to the higher required level at Arizona, such that many Princeton students will try but fail.
Which of course is the reality Princeton students discover after matriculation. The need to keep competing if you want the most selective next step positions is not over. And your competition is now other people who also matriculated at Princeton. And that is a very hard competition.
ETA: Some quick numbers. According to College Transitions’s law school feeder study, right around 60% of the Princeton grads going to a law school went to a T14 law school. That’s a very high percentage, in fact. At Arizona, it was 7%. That’s probably not an entirely fair comparison as about 19% went to Arizona for law school, which could be a great deal and more than sufficient for many purposes. But even holding out those people, the others went to T14s at under a 9% rate.
But then here is the question. Is it easier to be among the top 9% of Arizona law-bound students, or top 60% of Princeton law-bound students?
Again, I don’t think there is an obvious answer to this question. LSATs alone will explain a lot of that, and then whatever is left could at least mostly be internal competition adjustments.
Like this is very crude, but per 2024-25 CDS data, the 75th percentile SAT at Princeton is a 1500. Only 16% at Arizona had over a 1400. 72.9% had 4.0 HS GPAs at Princeton, 14% at Arizona.
Again acknowledging this is very crude, that is consistent with the idea that a top 60th percentile law bound student from Princeton could be seen as roughly equivalent on average to a top 9th percentile law bound student from Arizona, just based on LSATs and then internal competition adjustments.