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Bipartite Graph for US News and World Report

As high school seniors begin filling out college applications for January 1st, many seniors are beginning to notice the small numbers beside the words ‘Percent Acceptance’ on the colleges’ websites.  These small numbers for competitive schools have been getting smaller and smaller each year.  A company that keeps track of all of the percent acceptance rates for the colleges across America is the US News and World Report.  US News and World Report is well known for tracking all colleges’ data that students and parents want to know: school population, rural or urban, student to teacher ratio, tuition price tag, acceptance rate and more.  Therefore, it is often a shocker to top students when they see a 7% next to Harvard and Stanford, their top choice schools.  So what does the 7% really mean? In simple terms, it means so many students are applying to schools and only a small percentage of them are accepted.  For example, for the class of 2013 at Harvard, 27,462 students applied; only 2,175 were admitted.  Similar occurrences took place at the rest of the Ivy’s and the MIT’s and Stanfords across the US as seen here:

This topic ties into our class like problem 7 in Homework 3 and has similarities to the blog post called The Job Market: Unemployment and Bipartite Graphs.  Colleges have only a certain number of dorm rooms to fill; they can only handle so many new freshman.  More than 2,175 students may have been qualified for the Harvard education, but the school could not accept all of those students.  A bipartite graph can be used to represent this idea. In this example, the sellers are the students and the buyers are the colleges. The buyers can only get a payoff from the number of students they can accept/handle.  Accepting more students would not add to the value they hope to get out; rather it would hurt the value.  Knowing that colleges only accept a small percentage of students causes students to apply to more than one school. Students can find the same (or a similar acceptable) value at Harvard or Penn State.  Therefore, when a student is not accepted to Harvard but are accepted to Penn State, then they can still end up happy attending a good school.


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