“You erroneously are assuming they are applying to UCLA and not Cal because they think they have a better chance of getting in.”
No I said that more lower stat applicants are applying to UCLA. Since there are more of them in both % terms and absolute numbers, some of those lower stat applicants also decided not to apply to Cal, for whatever reason.
I then went on to hypothesize that (“it looks to me like”) one possible reason might be that lower stat students have a misleading impression of the relative difficulty of getting into the two schools. There may be others, like the weather being nicer in Westwood, more local students, or simply the on-campus housing situation at UCLA being better, as noted in post #39. But IF one contributing factor is a misleading impression of relative difficulty, then those impressions could change, assisted by recent publicity.
IF those impressions were a significant factor and did change, then one consequence would be a narrowing of the gap in total numbers of applications between UCLA and UCB (all else remaining equal), as lower stat applicants were deterred from applying. Of course all else not will remain equal. Nevertheless, it will still be interesting to see how the relative number of applications to UCLA and UCB changes in the next few years.
[Mathematically, my hypothesis is that if the number of applications N = f(A,B,C,…) where A, B and C are various contributing factors, with A being the perceived difficulty of getting in, the derivative df/dA is negative at least in the region of the current values of A, B, C,… (It won’t be necessarily be negative for all values of A - if a school becomes very unselective, a lot of students may then decide it’s not worth applying, but when most high stat California students do already apply, there are probably more to be lost at the low end as A increases than there are to gain at the high end). We can’t observe (let alone prove) what the precise shape of f() is, or really even characterize the various factors precisely. However, it would be fun to run some multivariate regressions across the number of applications to a large number of colleges to see what some of those factors might be (remembering that correlation does not prove causation).]