This has been voted into the negatives, but I'm not sure its so basically bad as an idea. If we can set up a system where all of the students, teachers, and any other staff, are all in continuous rationality competitions with each other, then this would quickly cause one to hone their skills.

For example, maybe the teacher of a class is chosen from within a class and has to fight (metaphorically) to maintain that position. Maybe the choice of whether you are teacher, student, principal, cafeteria cook, or janitor depends on the outcomes of numerous rationality contests between members.

And note that I don't necessarily mean that cafeteria cook or janitor would be positions that go to the losers...