Optimality of the expert rule under partial information

We study the uncertain dichotomous choice model. In this model a group of d ecision makers is required to select one of two alternatives. The applicati ons of this model are relevant to a wide variety of areas, such as medicine , management and banking. The decision rule may be the simple majority rule ; however, it is also possible to assign more weight to the opinion of memb ers known to be more qualified. The extreme example of such a rule is the e xpert decision rule. We are concerned with the probability of the expert ru le to be optimal. Our purpose is to investigate the behaviour of this proba bility as a function of the group size for several rather general types of distributions. One such family of distributions is that where the density f unction of the correctness probability is a polynomial (on the interval [1/ 2,1]). Our main result is an explicit formula for the probability in questi on. This contains formerly known results as very special cases.