A thought about college admissions

The July-August issue of The Atlantic contains the 2012 "Ideas Report". One of the ideas, proposed by Barry Schwartz, is to admit students to college by lottery. The idea would be to identify all of the qualified people from the complete list of applicants, and then randomly choose from among the qualified as many as the college could accept.

I rather like the idea. As Schwartz points out, it would have the advantage that the process would not tell qualified candidates that they were not good enough for the college.

I have done a lot of selection from large lists of applications. Indeed, I once did a computer program to rank order college applicants in order to admit the highest ranking ones. I have come to the conclusion that we are seldom good enough at recognizing quality that our rankings can be assumed accurate. Assume that you get 1000 applications and will be able to accept only the 100 best. Think how unlikely any ranking procedure would be to accurately discriminate among the applications grouped around the decision point. What is the probability that the application ranked 101st is actually better than that ranked 100th? I would suppose it is pretty high.

The suggestion however opens a world of possibilities. Selecting randomly does not mean that the acceptances would be drawn with equal probability from the qualified. Lets think about 150 applicants out of the 1000 judged as qualified. It would be a pretty weak ranking system if the first ranked application was not significantly better than that ranked 150th. So maybe there should be a higher probability of admitting the first ranked than the 150th ranked applicant. One could, for example assign a probability of one that the first ranked candidate would be selected and a probability of zero that the 151st ranked applicant would be picked, decreasing the probability linearly over the range. This would be very easy to implement on a computer.

Alternatively, you could choose those ranked 1 to 110 with probability one, and then those from 111 to 120 with probability one-half. Indeed, there are many, many ways that you could choose 100 candidates from a ranked list of 150 qualified candidates.

In reality, there are a lot of things a college might want in an entering class in addition to qualified students. For example, it might not want a class with 90 women and 10 men, or it might choose to have a class with some diversity in life experiences. It might want to be sure that there was a variety of academic interests, so that it did not have a class composed entirely of drama students or math students.

The Schwartz suggestion opens the field for some good thinking about how best to select an entering class from a large number of applicants.