Yuval Salant

On the learnability of majority rule

Abstract We 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. We 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.

How to Buy Advice with Limited Instruments

A decision maker, whose payoff is influenced by an unknown stochastic process, seeks the advice of an advisor, who may be informed about the process. We establish that there exists a strategy of the decision maker that will yield him an almost first-best payoff in every period when interacting with an informed advisor. An important feature of this strategy is that it only requires a fixed budget - regardless of the realizations of the stochastic process and whether or not the advisor is actually informed about it, the total payoff to the decision maker will never fall below a fixed threshold. The strategy also has the property that per-period compensation to the advisor is independent of the present realization of the process, and depends solely on the expected value of the advice as reported by the advisor.