Optimality of the Expert Rule Under Partial Information |
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Authors: | Daniel Berend Luba Sapir |
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Institution: | (1) Department of Mathematics, Ben-Gurion University, Beer-Sheva, 84105, Israel;(2) Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel |
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Abstract: | We study the uncertain dichotomous choice model. In this model a group of decision makers is required to select one of two alternatives. The applications 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 members known to be more qualified. The extreme example of such a rule is the expert decision rule. We are concerned with the probability of the expert rule to be optimal. Our purpose is to investigate the behaviour of this probability as a function of the group size for several rather general types of distributions. One such family of distributions is that where the density function of the correctness probability is a polynomial (on the interval 1/2,1]). Our main result is an explicit formula for the probability in question. This contains formerly known results as very special cases. |
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Keywords: | dichotomous choice model experts decision rule expert rule optimality probability expertise partial information |
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