I like this way of framing it, although I find it questionable whether SATs, grades, etc measure C exclusively. Because almost all candidates are the same age

I like this way of framing it, although I find it questionable whether SATs, grades, etc measure C exclusively. Because almost all candidates are the same age when applying, C also carries information about m, in the sense that the same equation applies to their time in K-12, so candidates with a high C did so either because they had a high learning rate (m) or went to a high-quality high school or had a high-quality environment (x), or some combination. Thus I would say that SAT score measures mx. C at time t = mx + C at t - 1, or dC/dt = mx. Schools are interested in m, which is not easily measurable directly. Affirmative action is a very crude way to look for candidates that have a high m, low x, and moderate to high C at application time. My conclusion is that if it were possible, colleges would ideally look for candidates that performed substantially better on SATs etc than their peers at each high school, as that would control for x and allow you to estimate m. Affirmative action, on the other hand, is a cruder but partially functional way to do this, as it uses race as a bad proxy for x.