Groups of people are uncannily accurate at guessing the number of beans in a jar, the weight of a steer, and the like. In fact, the bigger the group, the more accurate its collective guess — a principle known as the Condorcet Jury Theorem. There’s a significant limitation, though: This only works if each person in the group has a better than 50% chance of getting the right answer. If the individuals in the group have a less than 50% chance — for instance because they know absolutely nothing about the question at hand — then increasing the size of the group will decrease the likelihood of their getting the right answer.

I learned this today by reading Ethan Zuckerman’s interesting review of Infotopia by Cass Sunstein. The converse of Condorcet — that groups of ignorant people make worse decisions as the size of the group increases — is Ethan’s formulation. I’m not sure if either version of the theorem is borne out (other than in pure theory and in relatively abstract test cases) but they sure make a compelling argument for the importance of a voting public being educated and well-informed — and it’s a significant proviso to glib statements about “the wisdom of crowds.” Ignorant voters make bad decisions — worse the more of them there are. Informed voters make good decisions — and better ones the more of them there are.