So just to continue with a little bit more standard competition law analysis:
One of the standard defenses to an accusation of anti-competitive cartel behavior is that the similar actions in question were not the result of an agreement, they were the result instead of something called conscious parallelism. As the name implies, conscious parallelism involves competing companies observing each other and adopting similar practices, but without any agreement to do so.
Determining whether parallel behavior was the result of an agreement or just conscious parallelism can be extremely difficult, not least because competitors typically have very powerful incentives to try to hide agreements (like, they may be illegal, and are usually at least very bad for PR). One approach, though, is to see if there are identifiable cases of where it appears individual competitors are acting against their unilateral interests. Another is to look for opportunities for collusion, such as regular meetings of competitors (even if they are nominally for other purposes). And so on.
OK, so in that context, you note that many competing private colleges do not offer merit scholarships. However, some do. So, it is not a universal norm, and therefore it at least cannot be assumed that offering merit scholarships is necessarily always against a college’s unilateral self-interest.
And then as I noted above, although some of these private colleges offer merit scholarships and some don’t, none of the Ivy League do. At least at first blush, this seems like a pretty odd fact. Like, you were suggesting the frequency is .333–which we should actually adjust by taking out the Ivy League since they are the subject of this analysis and therefore should not be part of the “control” group. And that would make it .42 in the control group.
If there were independent chances of any given Ivy League college offering merit scholarships at a .333 frequency, then the odds that none of them would is about 4%. At .42, it drops to about 1.3%. Hmmm.
What this suggests is that something about being in the Ivy League specifically is making it much less likely that a private college will offer merit scholarships. Indeed, this evidence is at least consistent with the odds of such a college doing so being a flat zero.
Now, this is not an absolute proof that the Ivy League is operating as a cartel and has adopted this as one of the cartel’s rules. Nonetheless, that is one possible explanation for why over 40% of the non-Ivy colleges in your sample offer merit scholarships, and yet none of the Ivies do.