## The Curse of Curves

One of the major issues in an academic setting is cheating. And, there is significant evidence that it is more widespread than most would imagine. According to this source: http://www2.newsadvance.com/lifestyles/2011/sep/19/lifetime-cheating-ar-1321580/ 82% of alumni admit to having cheated in college. Why is this?

Most students at Cornell are familiar with the curve system. Grades in many classes are assigned based on the statistical distribution of the scores of students in the class. This, in essence, means that students here are being graded against their peers.

One of the fundamental ideas of Economics is that of unintended consequences. While the transfer to curved grades makes a lot of sense logically, I believe that there is an unexpected side effect that many people wouldn’t necessarily predict – it encourages cheating.

Let’s look at cheating under the “normal” system, where students are graded on a 100 point scale. This is essentially a game of “player vs. system” and isn’t very easy to model directly through game theory. However, it’s very easy to understand intuitively. Let’s say the student we are considering is a “b” student. That is, if the student does the best he or she can, he will earn a B in the class. Now, if the student cheats, he earns an A if not caught, but is penalized if he is caught. There’s some percentage chance of being caught, and some penalty for it. In this system, it is relatively easy to stiffen the penalty proportional to the percentage chance of being caught, and therefore make it, on average, disadvantageous to cheat by simply adjusting the average payoff of cheating to a C.

Now, let’s consider the curved class. This is a much more interesting example, because there are multiple players in this game. For the sake of simplicity, let’s say that the class consists of two students, and is curved to a B. IE, if both students did the best they could, without cheating, they would each earn a B. If, however, student A cheats and student B doesn’t, student A will earn an A, and student B will earn a D. If both students cheat, with the same penalties as in the previous example, they will, on average with respect to the consequences, receive a C. The payoff matrix for this could be appropriately modeled as follows: (Up, Left is neither player cheating, Down, Right is both players cheating.

3,3 1,4
4,1 2,2

Those familiar with game theory will recognize this as “The Prisoner’s Dilemma.” For those not familiar with this case, a decent explanation can be found here: http://pespmc1.vub.ac.be/PRISDIL.html

The interesting thing here, is that for both players, cheating is a strictly dominant strategy, where as with the non-curved class, playing against the odds, it was a strictly dominated strategy. This means that, (as long as these payoffs hold) the optimal thing for students in a curved class to do would be to cheat. In addition, even when cheating, the average GPA of the students would drop. I believe that there is a significant chance that the grade curving system does, in fact, have an unintended consequence of incentivizing cheating and penalizing honesty in the classroom.