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?