It is nice now to be able to easily look up objective and sorta-objective data on any miraculous or semi-miraculous public school you read about. One thing I've noticed lately is the schools with the unimpeachable numbers are tiny. Like, 60 per grade. On one hand this would seem to confirm my preference for small schools. And I definitely like high schools with 240 kids more than 2400.
But if we're thinking of this as one big incentive system, if you want to start a school that's going to get great test scores, and gain you bonuses and fame, you have no incentive to make the school any bigger than the smallest possible school. I like small schools, but I'd say a high-scoring school with 360 kids is better than one with 240, particularly if you figure that a strong principal is key to any size school, and that they are in very limited supply. Should a school get more credit in an incentive system for serving more kids?
Here's an abstract question: let's say you could either have a "B" scoring school of 1250 students or the same teachers and student randomly broken up into five separate schools of 250. You'll probably get a bit of a distribution of scores, right, like A, B, B, B, C? Is this better or worse, assuming that everyone is doing the same thing? Can you gain fame by showing off your "A" school and close your "C" school to show how tough-minded you are, even if all the variation is essentially random?