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The corollary to that is analyzing what students want. The majority of Caltech applicants doesn't really seem to attend a purely meritocratic school. It is an inescapable fact that the majority (59%) of al admittees to Caltech choose not to go, and an even stronger majority of scholarship-offered admittees choose not to go. The implication to that is that a lot of students choose Caltech only because it was the best school they got into (or could afford), but they would still have preferred to go elsewhere. My brother went to Caltech on a President's Scholarship, and he freely admits that he chose Caltech over other schools just for the money. I am fairly sure that there are a lot of Caltech students who would rather be going to the 'less meritocratic' HYPSM, but just didn't get in (or couldn't afford it). On the other hand, I rarely hear of the converse - somebody at HYPSM who would rather be at Caltech.
But the point is this. Caltech argues that its great strength is its purely meritocratic system. Yet it seems to me that that's not what even the majority of its own admittees want. The majority of Caltech admittees choose to go to other peer schools, and I suspect that many more would like to. Or, in other words, Harvard is clearly not purely meritocratic. But that hasn't stopped Harvard from yielding about 83% of its admittees - far and away the highest yield among non-specialized schools (i.e. not counting academies). In other words, it seems to me that Caltech is sticking to a principle that not even many of its applicants really want.
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Correlation does not imply causation unless all other factors are ruled out.
Most applicants don't even consider a school's admissions policies on whether they matriculate into the university or not. Instead, they think about the student life there. Many of them have heard about the substantial number of discontent students there - as well as the heavy workloads that stress students out. The school must resort to meritocratic admissions becasue its workload is an intense one that not many students can handle. Now, is this workload the reason why Axlines decline their scholarships? We don't know. While they may be confident in handling the core material - they still may wish to have more experiences and not to spend so much time on problem sets (some of their goals are not so much a specialized education as it is a more well-rounded goals). I cannot speak comprehensively for Axlines, of course. Caltech's curriculum isn't the most flexible curriculum, and it may be that the Axlines desire more flexible curriculums (the most intelligent and self-motivated tend to be that way).
Why is it that Axlines turn down their scholarships at higher numbers than the general Caltech admit population at large? The Axlines are likely to have other opportunities, whereas the general Caltech admit population is not.
It's not Caltech's admissions policies that Caltech prides itself on. It's the research, the rigor, the core, the honor code, the science. The rigor and the core demand a strictly meritocratic admissions policy. Does it work? Not perfectly. But it's better than any other admissions policy for its own specific education goals, because worse off students will not fulfill such goals.
The definition of "meritocratic admissions" has changed with respect to time as well. It used to be that "meritocratic" meant selecting the most scientifically talented people of a particular race. It's now changed to the "most scientifically talented people of any race whatsoever". Because the societal conception of "meritocratic" has changed, this overall change relieves Caltech and other universities from the responsibility of modifying their mission statements as such.