Skill, power and marginal contribution in committees

Power is an important basic concept in Political Science and Economics. Applying an extended version of the uncertain dichotomous choice model proposed, the objective of this paper is to clarify the relationship between two different types of power a voter may have: skill-dependent (s-d) power and marginal contribution (mc). It is then shown that, under the optimal committee decision rule, inequality in skills may result in higher inequality of the two types of power and that the distribution of the second type of power (mc) can be even more unequal than the distribution of the first type of s-d power. Using simulations, and assuming evenly spread skills, this possibility is proved to be robust. The significance of the finding is due to the effect of power on reward, whether it is defined in terms of status or in terms of monetary payment.

Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making 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 group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.

Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making 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 group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.