Economics of the Transhuman Condition
Ross Douthat Writes a Truly Terrifying Horror Story

Selective Colleges as Tito-Era Yugoslavian Firms Once Again

In an email message this morning, paraphrased:

I think the diversity" reason for selective college admissions is weak from a moral point of view. It suggests admissions is about creating an interesting experience for students. Most Americans, by contrast, think of selective college admissions as a ticket to the American Dream: they want the kids who are most deserving to get in. Americans reject all sorts of preferences. The one exception is class: they support... giving a leg up to hard working and talented low income students who have overcome obstacles because they think such students deserve to get in...

I cannot help but feel that there is something totally wrong here. Admission to a good college should not be like a tournament--it should not be a valuable prize that makes its recipients especially better off awarded to those most deserving, with those slightly below the cutoff turned into social losers in some important way. Admission to a good college should be like a matching market--if society would benefit the most from having student X attend an CalTech-like and CalTech-caliber place, there should be enough places at CalTech-like institutions so that all of those students get to go. And similarly all the way on down the line.

The simplest model I can think of of how to match a number of students with different levels of preparation--say, evenly distributed over the interval [0,1] to n different colleges each of which has level of rigor Ri--is to say that the value of education to society V for a student with particular preparation P attending college i is:

V = V* - (P - Ri)2 + gP*i

That is, students benefit from going to college (V*), and they benefit less from going to a college where the level of instruction is not calibrated to their preparation--they lose if the college is either too advanced or too elementary--- ((P - Ri)2), but they benefit more from being around better students (gP*i, where g is a constant and P*i is the average preparation level of the students at their college).

In this framework, with a small finite number of colleges, admissions decisions matter: in the best equilibrium the colleges' rigor levels are evenly spread over the range from zero to one (with four colleges at 1/8, 3/8, 5/8, and 7/8) and the student whose test scores indicate a preparation level of 400001/800000 and so gets to go to alma mater 5/8 is significantly better off in some sense than the student whose test scores indicate a preparation level of 399999/800000 and so is sent to alma mater 3/8. These effects are to some degree a small-numbers problem: as the number of colleges grows large they diminish. And these effects are to some degree a mismatch problem: those who are through matching error admitted to an institution attended by the better prepared are better off for it (and their roommates are worse off for it), and those who are through matching error sent to an institution attended for the worse prepared are worse off for it (and their roommates are better off for it)

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