Wednesday, February 3, 2010

Snow Days and Keynesian Beauty Contests

The view from outside my apartment this morning.

Overnight, 2 to 4 inches of snow fell in the D.C. area, and most local schools are closed (see this Washington Post story for more details).

For school administrators and others, deciding whether to shut down school is something of a Keynesian beauty contest. Old newspaper contests asked readers to select the most beautiful women among a series of photos. Entries were graded on how they fared against popular opinion. So, the game was to pick not the women whom the reader personally thought were the prettiest, but the ones the reader thought that most other people would judge as the prettiest.

What is the worst outcome for the school administrator? If he allows school to go on, someone might get injured or not be able to make it to school. However, if all the other local schools in the area are open, the onus shifts to the students. In contrast, a good case for negligence could be made if the other schools are closed and a student gets hurt at the one open school.

But school heads shouldn't always err on the side of closing, either. While students may appreciate such a school, parents and lawmakers will not. But a school cannot be blamed for closing on a day when all the other schools are closed as well.

In the sum, the school head's best play is to follow everyone else, as illustrated in the below payoff matrix (assuming that all the other schools more or less coordinate). In the game, the school head has a payoff of 0 if he follows the other schools and -1 if he doesn't, while the other schools are not affected by the choice of this one school. This is a version of the coordination game in game theory.

Other schools: cancel Other schools: don't cancel
Your school: cancel 0, 0 -1, 0
Your school: don't cancel -1, 0 0, 0

Of course, if school is canceled, the more advanced the notice, the better. Canceling a 7:20 p.m. class at 7 p.m. isn't going to help anyone. So a school administrator is wise to wait and see how the field plays out but make a decision in enough time for students and parents to react.

Down the street.