Sunday, August 22, 2010

The optimal level of ability sorting

Our system of higher education is designed heavily to achieve ability sorting. States and municipalities create institutions that cater to different academic backgrounds. Flagship state universities are intended to attract the best students, other state universities serve a wider swath of the student population, and community colleges attract unconventional students who often lack the preparation necessary to enter four-year universities right away. Universities are differentiated in other ways as well—for instance, in my home state of Oregon (as in many states), Oregon State University has engineering departments while the University of Oregon does not—but the general design almost always involves a hierarchy of institutions. And within institutions there are clear hierarchies as well.

In general, I think this is a good idea. My experience tells me that I am far more likely to learn when placed alongside people at a similar (or slightly higher) level. For an academically capable person, there is nothing more infuriating than being trapped in an environment with no real peers.

Needless to say, however, our current system of ability sorting is far from complete. There are some very smart (and very dumb) people almost everywhere. Students choose universities for financial or personal reasons rather than academic strength alone. This makes me wonder: what is the optimal level of ability sorting?

Many models will say that we should have perfect ability sorting. But regardless of whether perfect sorting would be desirable, it's clearly unrealistic: there will always be frictions and informational asymmetries that keep us from achieving it. A better question, then, is this: if some imperfection in ability sorting is inevitable, what is the optimal policy given that imperfection?

The intuitive answer is that we should come as close as possible to perfect ability sorting. But depending on our model, this isn't necessarily true at all; even if perfect sorting is the first-best solution, once imperfections exist it may be optimal for us to add additional noise to the sorting process.

To see why, suppose that there are two universities in the world, A and F, and two types of students, Good and Bad. In an ideal world, all the Good students attend university A while all the Bad students attend university F. Imperfections in the sorting process, however, mean that at best 1% of the students at university F will actually be Good. Now consider a policy that shifts students so that 2% of university F will be Good. Obviously, the students who moved from university A to university F will be worse off. The Good students who were already at university F, however, will be better off—they have a larger group of Good peers to learn from. It's entirely possible that the second effect will exceed the first. In other words, as long as university F has some Good students, it's possible that the benefits from providing a "critical mass" of Good students outweigh the harm to the additional Good students moved to university F.

Broadly speaking, this is an example of how the second-best policy solution may involve deliberately moving away from the first-best solution.

1 comment:

Darf Ferrara said...

When you say that higher education is designed to achieve ability sorting, I assume that you mean designed that through some sort of evolutionary process. And I guess you think that ability is a linear ordering. I think both of those assumptions are somewhat difficult to justify in the real world, but the model is interesting. In my experience, I learn best when I'm with people that are smarter than me, but in the same league, so to speak. Von Neumann might move too fast for me be pulled up by him. On the other hand, I've also learned quite a bit from people that might not be as smart (score well on standardized tests, that is), but with a completely different way of looking at the world than I do. Artistic types and creative types mostly.