Abdulkadiroğlu, Atila. “College Admissions with Affirmative Action.” International Journal of Game Theory; 2005, Vol. 33 Issue 4, p535-549, 15p
The College Admissions game is very similar to the real estate game that we discussed in class. The difference is that in the real estate game, each buyer has a set valuation for every house in the market and the sellers have no preference over buyers other than whether they can give them a high price for the house. As we briefly mentioned in class, games where there are valuations over specific buyers/sellers on both sides get much more complicated. Some real-world examples of these scenarios that Abdulkadiroglu mentions in his article include college admissions, the job market (for certain fields), and even marriage.
Abdulkadiroglu’s objective in this publication is to prove that Affirmative Action (the author denotes as AA) measures are actually beneficial to both students and colleges in the college admissions game. The argument that many have had against AA measures in the past is that it prevents colleges from choosing the most qualified students based solely on academic criteria. Take a simple scenario where there are two females and two males and a college has the capacity for two students. Let’s say that if the college were blind to the gender of these students, they would choose the two females based on credentials. Then, exercising a quota in which the college must choose from a {male, female} set would be unfair to the second-ranked female. Intuitively, this model could be applied to a larger scale and Affirmative Action would be an unfair practice.
This paper proves differently. The heart of Abdulkadiroglu’s argument lies in something called “dominant strategy incentive compatible” (DSIC). This means that revealing one’s true preference is the dominant strategy. The author proves by counterexample that when colleges have substitutable preferences, no stable mechanism is DSIC for every student. In his example, there is one college (out of two) with a substitutable set of preferred students, one of the students (out of three) is accepted by a college when he misrepresents his preferences, and denied by both when he shows his true preferences. This scenario arises when a college equally prefers two sets of students.
In the competitive college admissions game of today, it is very difficult to distinguish students and so the case of substitutable accepted-student sets is a reasonable model. The most competitive colleges are faced with an applicant pool of straight A students all with high SAT scores and ranking these students can, at times, become arbitrary. This is the difference between the real world and the example above where there was a concrete ranking of students. The author implies that many sets of accepted students are equally preferred.
The paper then goes on to demonstrate that when the college’s preferences satisfy AA and RR (a measure of whether or not a student respects the college’s type-specific quotas), the game is DSIC for the students. This means that the students’ best strategy is choosing the true ranking of their preferred colleges. This is a good thing since it complicates the process less. Similar to many of the auctions we saw in class, both parties can choose their true preferences without worrying about anticipating the moves of other players in the game. The true value is the dominant strategy.
This paper is pretty dense in the sense that there is a lot of notation used that we haven’t really learned in class. It is however, very applicable to our own lives 1-4 years ago and very applicable to the job markets many of us will be entering in the future. It is very relevant so I highly recommend that you all take the time to read it. J
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