[throwawaymath]

I don't really follow your first two paragraphs. I don't know about the ultimate utility of this system, but I don't think it exhibits the statistical properties you're saying it does.

In a threshold-based admission lottery, everyone more than k sigma from the mean (for example) is collapsed into the same category, such that information distinguishing them is lost. But the implicit premise to this system is that you can't accurately measure the distinctions between those deviations anyway.

Given that premise, you're not adding noise to the system, though you are removing information. I think the claim under question is that trying to precisely measure people more than k sigma from the mean is intrinsically noisy and prone to spurious correlation with academic success. So then you'd also be removing noise under this system.

So I think your point of contention should be with the premise if you disagree with it, because I don't think we can really argue about statistical properties of the lottery distribution until we first settle on the underlying axioms.

[motohagiography]

The point I meant to raise was that the underlying axiom of the piece is that the lottery is fair, when the mechanism for that fairness is simply removing information. There are lots of reasons for it, but a lottery is a fig leaf.

The proportion of input students of a type will be the same as in the the output of a fair lottery. Appeals to randomness just forfeit responsibility and ownership of the decision.