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Diversification and the Market for College Admissions

By Kenneth Anderson

(Kenneth Anderson)

Help me out with thinking this through; I?m unsure about what I suggest below and would like to figure it out.

Assume that you are a student applying to college.  Your high school has a declared policy limiting the number of schools to which you can apply.  It says it does so in order that you will ?take applying seriously.?

You rather suspect that the school does so in order to be able to push particular students it favors for particular colleges, so that too many students do not create too much ?noise? and competition for a place that the high school counselor thinks is most competitively filled by a particular student.  The high school?s incentive, in other words, is first to maximize its ability to get students into particular colleges as an institution seeing the students as a cohort, not to simply support each student in his or her efforts.

One effect of this is to favor students who come from wealthy, powerful, or highly connected legacy families, since those students are most likely in the first place to be able to get into the most competitive schools.  But although you suspect this, it is rather difficult to prove without something like discovery in a lawsuit to find out exactly on whose behalf the counselors call certain colleges and discourage other students from applying at all.  But let?s leave all that aside to focus on a more generalized strategic question.

Proposition one.  If we assume that the student has more than a zero chance of getting into a top institution ? not a slam dunk, but not ruled out altogether, or at a minimum uncertain ? in an environment with many students applying, then simply as a matter of increasing the student?s odds, the student would do better to apply, say, to all the top colleges merely as a matter of odds.  This is all things equal better for the individual student even if it makes it more difficult for the high school to favor some students over others in applications to particular colleges.

Proposition two ? and this is the one that particularly interests me as to whether it is true or not.  Assume that this particular high school limits the number to which one can apply to six.  If the trend is for students at other high schools across the country to apply to a much larger number of colleges, then this high school student does not just suffer from missing the odds of applying to a greater number of colleges ? this student is penalized for not having diversified applications across colleges relative to other applicants.

It seems to me ? maybe ? akin to the condition in portfolio theory that market prices in shares assume that risk that can be eliminated through diversification will be eliminated that way and will not be compensated for in share prices; the market assumes diversification.  In college admissions, if large numbers of students diversify their risk by applying to a large number of colleges ? diversifying their holdings of lottery tickets to those colleges ? a student who fails to to diversify by applying to a large number of colleges will be penalized with lower odds of admission even beyond simply increasing the odds, other things equal.

Is this second proposition correct or is it not correct, or does proposition two merely collapse into proposition one?  If there were only one student in the world applying, and colleges were not required to take any students at all, and if the chances of admission to any one college were genuinely unknown and uncertain as to the student, then presumably the student should increase the odds and hedge against the uncertainty by applying to more rather than fewer schools.  That is proposition one.

The second proposition adds other students also applying.  Given that they are also bidding for entry, and assuming the same unknowns, they will have the same reasons to increase the number of colleges to which they apply.  So everyone ideally wants to apply everywhere.  But if for some reason everyone else automatically applies to 100 colleges and you apply to only one, are your chances worse because of the fact that everyone else has applied to every available college?  That is proposition two ? the addition of new players to the game who hold in effect a diversified portfolio while you hold only one application, and unlike stock, you haven?t bought lots and lots of application lottery tickets to that college; you can only buy one.

My point is two fold, if I?m right.  One is that there are two very good reasons, one intrinsic and the other strategic, for increasing without limit the number of colleges to which you apply.  The other is that if you fail to do so when others do, you put yourself in a distinctly worse relative position.  Is this akin to market diversification and compensation for bearing diversified versus undiversified risk?  Am I correct in this analysis or not?  If not, what am I missing or doing wrong?

Full post as published by The Volokh Conspiracy on November 18, 2010 (boomark / email).