We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is (...) optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns. (shrink)

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.

The focus here is on analytical and instrumental requirements for those collective decision exercises that lend themselves to a judgment-driven resolution. These have not as yet received much concerted technical attention from either of the two main movements in the field. They remain somewhere beyond the purview of the objectively-predicated instruments that mainstream GDSS (Group Decision Support System) designs tend to favour. Yet neither are they so inherently ill-structured as the situations with which the GDNSS (Group Decision and Negotiation Support (...) System) community is concerned, these usually allowing only a subjectively-predicated, compromisive or consensus-based conclusion. If the technical requirements peculiar to judgment-driven decision exercises are to be well met, it will be through the offices of analytical instruments that can help assure the rationality of the resolutions at which they arrive. The primary purpose of these pages is to offer some suggestions about the types of analytical instruments that might serve this end. (shrink)

We study the uncertain dichotomous choice model. In this model a set of decision makers is required to select one of two alternatives, say ‘support’ or ‘reject’ a certain proposal. Applications of this model are relevant to many areas, such as political science, economics, business and management. The purpose of this paper is to estimate and compare the probabilities that different decision rules may be optimal. We consider the expert rule, the majority rule and a few in-between rules. The information (...) on the decisional skills is incomplete, and these skills arise from an exponential distribution. It turns out that the probability that the expert rule is optimal far exceeds the probability that the majority rule is optimal, especially as the number of the decision makers becomes large. (shrink)