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Matching in College Admissions?


Even though most us are well along into our academic careers here at Cornell, many of still remember the dreadfulness of (the first half of) senior year of high school, having to deal with college admissions.


In theory, the Common App is supposed to make the process less stressful by making it simpler to apply to many colleges. However, the low admissions rate of many schools makes students want to keep many backup options, leading to an increased number of applications per student, facilitated by “easy to use” tools like Common App. The growth rate of applications outpaces that of the number of seats a college has and – voilà – admissions rates look even lower for students applying the following year.


The other words, college admissions is devolving into a numbers game. And with so many students applying to so many colleges, it’s hard for colleges to tell whether students are genuinely interested or not in a particular school. Colleges have had to resort to proxies in order to gain information about preferences of students. For example, some colleges are now low looking at financial aid apps to see if they are the student’s first choice. Attending events held by the school and coming to the campus to visits are also indicators that are used. So while the Common App may have made it easier to hit “send” on the application, it could have made students lives more difficult, having to travel to all the colleges that they applied to demonstrate that they’re not just playing the numbers game. Of course, this makes it harder for lower-income students to compete.


The Vox article proposes some ideas about what could be done about this. The main one is doing a trial with the top 30 wealthiest schools in the US and try a program similar to medical school residency matching. The problem is quite similar to matching markets in our class. In class we discussed matching markets, where there are entities that all have preference lists for certain items. However, there is a limit to using this approach. We can’t use this exactly to model college admissions since students have preferences and colleges have preferences as well.


The medical school residency matching program uses updated algorithms now, and perhaps those algorithms could be applied to undergraduate college admissions. The modern day algorithms are complex so it might be worth taking a look at a simpler algorithm used in the past: Gale-Shapley. Gale Shapley, the algorithm used to solve stable marriages, can be used to investigate how to pair N colleges with N students each with preference lists of size N.


Take a look at this previous blog post for more:


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September 2018