Tuesday, 3 December 2013

Why Lloyd Shapley was Wrong

By Michaela Miller
Her author profile can be found below this article.

Lloyd Shapley (right) won the Nobel prize for economics in 2012 alongside Alvin Roth (left).
Image credits to The Guardian (UK).

Now heading into my eleventh grade year, I can finally begin to appreciate the amount of stress that accompanies students of this age. As if nine classes, the SATs, and a job weren´t enough, it is in this season that I will be forced to think about that dreadful thing they call college. Now don´t get me wrong, I´m excited for college. I want to meet people my age with the same interests and goals, I want to root for the team, and I want to figure out the rest of my life. I´m just not all that excited about the hours of stress involved with the admission process. Why do I have to worry about this now, when my time is a scarce good? If only the process was something a bit more like the 2012 Nobel prize winner Lloyd Shapley´s suggestion... right?

Shapley definitely understands the difficulties of college admissions. Of course, filling out the form itself is no piece of cake (I´m not even sure what I would do if I was asked to list my top colleges), but then there is the dreaded "waiting list". As Shapley said in his essay "College Admissions and the Stability of Marriage", students are forced to wonder if they should wait on the college they really want, or go to another one that has already accepted them. Should they accept one college and then back out later if another one they like better lets them in, or should they stick with their original choice? The economist makes what he believes is a positive statement that a great deal of these problems could be resolved if the admission process followed some pattern of the following suggestion, which is this: Colleges would rank students according to their preference of having them attend their college. A student would then apply to the colleges he prefers - disregarding colleges who had already asserted they would not accept that particular student under any circumstances - beginning with the college of his first choice. If he was accepted to that college, he would go to it. If not, he would apply to the second college of his choice, and on and on until he came to a college that would accept him. In this way, the relationship between this student and the other colleges would be stable because there would be no other college who wanted him to attend there as equally as he wanted to go there (the definition of an unstable relationship).

While this "proof" sounds good on paper, I have my doubts as to its reliability were it to be applied to real life. What if a student in this system, like one of my friends, was indecisive? He didn´t really know what he wanted to do with his life, and his only objective was to get through college with the highest amount of enjoyment and the least amount of work possible. He was accepted to the college he applied to first, but later, after deciding to go there, he discovered that the opportunity cost of his choice to go to that college was much greater than he first anticipated. All of his friends went to a different college that had better sports and a nicer atmosphere. Now there is now a student dissatisfied with his college choice and another college who would possibly be just as equally willing to accept him as he would be willing to go there. In other words, there is now an unstable relationship, the very thing this "proof" seeks to avoid.

Or take another situation that causes a dilemma for a college instead of a student. Another friend of mine, we´ll call her Macy, had outstanding grades all through high school. She was just one of those kids who´s a good test taker; never had to do much work, never had to study. She got into the college of her choice with an outstanding transcript, but as soon as she started classes there, everything began to change. Macy found that she couldn´t pass classes without studying for them, but even though she made a choice at the margin to study more, she lacked a lot of the background information she needed to succeed. Her grades continued to plummet through her first semester until she was at the bottom of almost every class. Because of this, the college was put in the position of wanting to accept a different student who had been declined because of a full quota at the beginning of the year. This again causes an unstable relationship, because there is a student who wanted to go to that college but didn´t get to and there is a college who now wants to accept that student. Though I never asked her, this situation may have caused a doubly unstable relationship because Macy may have wished to go to another college that had easier academics and that college, because of where she would be coming from and her accomplishments during high school, would most likely have been very happy to have her.

Shapley´s hypothesis may hold merit when looked at ceteris paribus, but in the real world people and situations change all the time and those changes are one of the variables that cause the process of college admission to be so difficult and stressful. In both macroeconomics and microeconomics, the latter being what Shapley is focused on, it is very hard to used the scientific method to actually test a hypothesis to see if it holds consistent with results. Therefore, even though the "proof" offered by Shapley sounds convincing, without solid, real-life evidence of it, it is really nothing more than a normative statement.

About the author:

Michaela is a high school junior who enjoys volleyball, soccer, and ballroom dancing. She has been playing the piano for almost eight years, and she greatly enjoys it. She even plays in a small band with some friends of hers! She has five cats, two parakeets, four chickens, a cockatiel, and a brother (whoops, that's not a pet...). She loves all of her classes, but her favorites are Physics and AP Calculus (math and science person!). She is currently working at her local pharmacy, and she couldn't imagine a better job. Her goal is to graduate college with a pharmacy major and either a dance or business minor.


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