Matching with Lotteries

College admissions are more competitive than ever. Thousands of high school students play the selection game perfectly and meet the highest standards of even the most sought-after universities. The elite schools face an interesting matching problem of the bipartite graphs of schools and students. The issue is that there are too few schools and too many applicants that desire to be matched with the school of their choice. This is a market where prices do not necessarily clear the competition. Even with astronomical tuition prices, the market still faces a glut of immaculate potential students. The institution needs to decide which students to accept in a fair way.

The institutions choose to solve the problem with a lottery where a random selection from the pool of distinguished applicants actually gains admission. Barry Schwartz discusses the injustice that this creates to the students that lose out because of random selection and through no fault of their own. (See Footnote)

The increased competition is probably good for the quality of education overall. The limited number of spots at elite colleges displaces high quality students to lower-tier schools where they can provide positive influence to their fellow students. Overall, the university system can accomodate all students and the lottery merely serves to break the competing ties when price and admission standards prove inadequate.

Easley and Kleinberg do not discuss lotteries in their analysis of matching bipartite graphs. Why is this the case?



2 thoughts on “Matching with Lotteries”

  1. Extreme competition is beneficial for the universities in the sense that they get to pick and choose the students they want to admit, while simultaneously driving up tuition prices. That being said, that same extreme competition is bad for the students because it increases tuition prices, and makes it more difficult to get into the school of their choice if that school is considered elite (think Harvard, Yale, Berkley etc). One thing I noticed in this post is the statement made, “Overall, the university system can accommodate all students and the lottery merely serves to break the competing ties when price and admission standards prove inadequate.”, seems to be a contradiction in itself. If the system can accommodate all students that means that they could, in the context of the statement, accept all students and there would be no need for a lottery. More likely what you meant to say is that it cannot accommodate all students, and the lottery system just makes selection fair in regards to biases, clearing the university of liabilities that they are picking favorites. But I think you aren’t seeing the bigger picture of networks here. If you think that one of these elite schools receives an application from the child of a successful alumni, who most likely gives generous donations to the school, will put that kids name in a lottery instead of accepting him right away, you definitely aren’t seeing the bigger picture of networks. The reason these schools are considered elite is not for the education, Temple offers roughly the same level of education as these schools, its for the networks you are automatically included in upon attendance of these institutions. Harvard and Yale crank out students who start at $100,000.00/yr because their alumni are all CEO’s, CIO’s, COO’s lawyers, doctors etc. and they take pride in hiring other Harvard grads that may have belonged to the same frat for example. So I’d say if these schools claim to be using lotteries to admit students, that they aren’t being totally truthful. If they don’t accept children of their alumni directly, I’d say that every kid entered into this “lottery” who has a parent that is an alumni, miraculously gets picked. I’d say that the lottery is for the kids that do not have ties at Harvard already, because who cares if they get in or not if mom or dad didn’t attend or donate to the school. These schools aren’t selling some education that only 20 other elite schools can provide, they’re selling the status and the network that comes with graduating with a Harvard or similar schools degree.

    1. Firstly, when I reference the “university system”, I mean every four year institution in this country. You misinterpreted what I had intended to say when you jumped to the conclusion that I wanted to assign fairness to the lottery. In the sentence that you quoted, my point was that there are enough institutions (“elite” or otherwise) in this country to accommodate every student that is willing and able to attend any college. This fact supports the argument that the strong students rejected by top schools will be displaced into other institutions, with positive benefits for all. Even though everyone can go to school if they can achieve and pay, students still compete fiercely for the top schools, and therefore my statement is NOT contradictory. The exclusivity that requires the lottery is not in the entire system, but in the “elite” schools.

      I agree with you that the difference in actual educational value between Temple and Harvard is less than advertised and that the name and history of the elite institution contributes unfairly to higher salaries. I appreciate the additional analysis of the lottery as a laundering technique for unflattering legacy admissions as an addition to the ways in which students compete. I am certainly not so naive as to think that the elite colleges do not consider legacies or other networking ploys in their decisions, but I certainly do believe that there are many high-achieving low-connected students that enter into an earnest lottery. The actual situation might very well be a nuanced middle road between covering cronyism and dealing a fair shake to brilliant, but otherwise poorly-networked students.

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