On the relationship between individual and group decisions

Abstract

Each member of a group receives a signal about the unknown state of the world and decides on a utility-maximizing recommendation on the basis of that signal. The individuals have identical preferences. The group makes a decision that max-imizes the common utility function assuming perfect pooling of the information in individual signals. An action profile is a group action and a recommendation from each individual. A collection of action profiles is rational if there exists an information structure under which all elements in the collection arise with posi-tive probability. With no restrictions on the information structure, essentially all action profiles are rational. In fact, given any distribution over action profiles, it is possible to find an information structure that approximates the distribution. In a monotone environment in which individuals receive conditionally independent signals, essentially any single action profile is rational, although some collections of action profiles are not.