On the Learnability of Majority Rule, Journal of Economic Theory
I establish how large a sample of past decisions is required to predict future decisions of a committee with few members. The committee uses majority rule to choose between pairs of alternatives. Each members vote is derived from a linear ordering over all the alternatives. I prove that there are cases in which an observer cannot predict precisely any decision of a committee based on its past decisions. Nonetheless, approximate prediction is possible after observing relatively few random past decisions.
Salant, Yuval. 2007. On the Learnability of Majority Rule. Journal of Economic Theory. 135(1): 196-213.