There is something more important that the students learned by organizing themselves this way: that they are not each other's enemies. I am sure a few students received high marks that they did not deserve as a result, but I suspect that would have been the case even had the students taken the exam (judging by what I saw as a TA in my first year of grad school).

The professor now offers students a choice between an exam and a project, and the students voted for a project. The project is a better way to measure their aptitude. On the whole, I think this was positive for all involved.