Bryan Caplan  

Collusion in the Classroom

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I grade on a curve. So if all of my students studied 50% less, they might learn less economics, but their grades would stay the same. The students keep studying because they are in a Prisoners' Dilemma - their lives would be easier if they all studied 50% less, but if one student unilaterally did so, his grade would suffer.

After calling attention to their plight, I often advise my students to try collusion. Call a meeting, work out study quotas, and see how much easier their lives get. To date - and as far as I can tell - no class has ever called my bluff (though once I taught a class with four students, and got a little nervous!).

Frankly, I'm not worried. I'm not afraid to put bad ideas in my students' heads because I'm confident that attempted collusion would fail. And in the process, my students would learn a valuable economic lesson.

Why am I so confident that collusion would fail? Here are my four big reasons:

1. Hold-outs. In any class with more than a few students, there are bound to be a few contrarians who refuse to join the cartel. They might be Mormons, or lovers of economic wisdom, or just very disagreeable. But they will exist, and they will ruin the curve for students who abide by any collusive agreement.

2. Cheating. Many, perhaps most, of the students who formally adhere to the cartel won't live up to its terms. If much of the class is slacking off, students who put in a little extra work can get an easy A. When the other colluders accuse them of cheating, they'll just deny it: "No, I didn't study at all. I'm just smart/lucky/etc."

3. Division of spoils. It's easy to say "Let's all work 50% less." But 50% less than what? 50% less than you worked last semester? Students who intend to start raising their GPAs won't like that deal. Similarly, the studious won't appreciate an offer like "Let's all study a maximum of two hours per semester," because that is a much bigger sacrifice for them than it is for the slackers. These tensions make it hard to reach a collusive agreement.

4. New entry. If word gets out that I grade on the curve and my students are colluding to take advantage of the system, I bet a lot of students will want to add my class. (I always sign add forms... everyone's entitled to my opinion!) And what is the cartel to do with these new students? Invite them in? Exclude them? Buy them off? There's no good solution.

The point of all this isn't primarily to convince my students that their collusive plans are bound to fail. The real point is to illustrate why forming and maintaining a successful business cartel is so much easier said than done.

In fact, in many ways my students have it easy. In my classroom, there is an upper bound on how much one hold-out can raise the class average; once a student has 100% of the possible points, he can't make the curve any harder. In business, on the other hand, a firm facing an artificially high price might expand its output by a factor of ten, a hundred, or more.

Furthermore, if my students' cartel doubles the size of my class, I automatically double the number of A's and B's that I hand out. But in business, it doesn't work that way - doubling the number of firms doesn't double demand; in fact, the number of firms normally won't affect demand at all.

Question: Has anyone ever observed classroom collusion? If so, how successful was it in reducing students' average level of effort?

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COMMENTS (14 to date)
Bill Millan writes:

You don't have a standard of performance you expect a person to reach in order to achieve a certain grade in the class?

So a student is at the mercy his classmates having the average talent you expect. In a bright class, one might study hard and recieve a "B" when if they had been in an average class they would have got an "A."

I don't like your standard of value.

Jessica writes:

An American history teacher at my high school posed essentially the same challenge to each class of his students, albeit focusing more on the link to organized labor than business cartels. My husband's AP class finally pulled it off on their final by filling in every multiple choice answer with "E" and answering the essay questions with an identical sentence. They all got A's.

There was - of course - the one reluctant holdout (whom we found out later was beaten for poor grades, hence the concern) who was eventually bullied into submission. Which ended with her in tears and the school psychiatrist yelling at the rest of the class and comparing them to Nazis....

Bob writes:

Relax Bill. Curves make sense when the distribution of student ability is more stable than the level of difficulty of your exams. In a large class, this is almost always true unless you give very basic (same problems with different numbers) tests. In a class of four you have a valid point, but I assume that Bryan recognizes the exceptions.

If I were in Bryan's class I would propose that the entire group skip the final. In a small class I think that would work.

TD Kendall writes:

I regularly do the same thing with my undergraduate game theory class -- invite them to try colluding, that is, and there have been some very good attempts to do so.

Last year all of the students showed up for the exam, but when I got there with the exams in hand, the "ringleader" handed me a "contract", which all of the students had signed, in which they promised to sit there the entire class period without writing anything on their exam papers. I was sweating bullets for about five minutes until finally the first student defected and picked up an exam. Within two minutes, they were all hard at work on the exam. In that case, I believe it was student heterogeneity that did them in. The first defector happened to be one of three terminal MA students taking the class. Since he wasn't an undergraduate, the rest of the students wouldn't have an easy way to punish him after class.

Mark Nau writes:

My high-school Economics teacher similarly graded on a curve. An "A" was at least 90% of the maximally scoring student, etc. He made this policy very clear at the beginning of the term.

Midway through, I was approached and asked to stop accumulating points by a group of fellow students. I did so simply by failing to turn in any homework.

The second-highest-scoring student was evidently unmoved by their pleas, a situation we didn't discover until just before the final. The teacher clearly enjoyed sharing that news with everyone. There were only 2 "A"s that term, and I barely got mine by acing that final.

dWj writes:

I got a kick, a few months ago, when OPEC was discussing output cuts, and one of the countries was up-front enough about its cheating to ask that the reduction be applied pro-rata to what they were actually producing rather than to their quota. If you needed evidence OPEC's a paper tiger....

Incidentally, can someone explain to me why the baseball players' union would object to having a steroid ban enforced? If we suppose baseball players are graded on the curve, this seems like the kind of collusion they should be glad to engage in.

Pat writes:

I have been in part of a one-time collusion in a class of six people. While we talked about the final, we first tried it on a homework assignment. It might of been easier to control since half the class shared a house. Also, the homework was hard enough that we generally worked together (teacher-approved). We all decided to skip one of the questions (It was a graduate quantum mechanics class and a week-long assignment had 2 or 3 problems). The result: The professor simply assigned it again the next week. And again the week after that. Finally, we all yielded. That being said, I now know Clebsch-Gordon coeffiecients and perturbation theory backwards and forwards.

flix writes:
albeit focusing more on the link to organized labor than business cartels.

Same thing.

Carl Marks writes:

The correct course for collusion would be to have all students answer only one question of their choice, assuming equally weighted questions. If there is no minimum sit time for the exam, cheaters could be identified by another group decision that everyone must leave the room within the first 15 minutes.

Of course if you want to turn it into a real Prisoner's Dilemma then the curve should be based on the average score, and setting that grade equal to a B.

jf writes:

In college I was once in a course with, well, just me by the middle of the semester. The entire grade was a paper. I got busy with other things, some of which were academic, and didn't write the paper. I prepared to take an extra course the next year to make up for the inevitable F. I got an A. Monopoly beats collusion any day.

Bill writes:

I would have had so much fun destroying any plans for collusion. Hearing of such a plan would have only made me study harder. I had zero respect for slackers (even when I was one, on occasion).

John writes:

Interesting that almost all of the comments deal with the efficiency of different collusion plans rather than with the pedagogical inefficiency of grading on a curve.

ACS writes:

As a student of economics I have witnessed many attempts made by my classmates to collectively cut back studying. Unfortunately all of the collusion efforts, as predicted by Professor Caplan, ended in failure. When my high school economics teacher encouraged the class to organize a boycott against his final, no one believed that he was serious, for we all thought forming a cartel would be easy—at least easier than studying for a cumulative exam. Had we understood the four big reasons, we would not haven been so optimistic. I must admit that I am a “hold-out,” always reluctant to participate in the collusion because I love studying economics. I act as a consumer deriving satisfaction from my education rather than as a firm trying to maintain high price, or high grade in this case. My level of utility does not depend solely on my grade in a positive and linear relationship; instead I have indifference curves mapped on two axes—“economic wisdom accumulated” and “points received on the exam.” I would enjoy the same level of utility if I learn the material but fail the exam or if I learn nothing but receive an A. If I study and earn an A as a result, however, my indifference curve and thus my level of happiness would be much higher than under the two previous conditions. Of course not all of my classmates share my interest. So I agree that heterogeneity is an important cause of the failure of collusion in the classroom.

Susan writes:

In most of my major classes we are given a curve. I like the idea of having a class that tries to come up with a plan so that everyone would benefit, but I’m not sure if I am the type of person who could let go and not try to study or to lower my personal standards to match others in the class. What I see as acceptable others would probably think is too much work. Honestly I have tried to be lazy and it never works out well. I have been told that I cannot truly enjoy free-time even though I could always use it. My major classes only have 11 people in them and I know that it would have been very difficult to get everyone to answer the same way or try for the same level because there are two of us who probably could not handle knowing if someone else was going to mess up the curve for their own benefit. There is only one class that I have taken this year that I can see everyone agreeing to mark the same answer, and that was if we were offered the curve that Bryan offered because we were so board in class that we did not pay attention and studied very little for the test as it was. I like the idea of trying to get the class to participate together but I think those who learn by failing would say that it is easier said than done and would not appreciate the lesson. Some people do not have to study; they show up to class, listen and do well on the test. Even if you did not try to ruin the curve it would stink if you did and it could cause huge problems among the students.

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