> If students and staff have to fill out some kind of viewpoint survey, the only rational strategy is for them to randomize their answers to minimize the chance of being in the group that gets told “sorry, we have too many of your type this year”.

University students love messing with surveys.

My prediction: They'd coordinate to answer according to the groups they don't belong to. Right-leaning people would claim to be on the left. Left-leaning people would claim to be on the right.