Drora Karotkin

Optimum committee size: Quality-versus-quantity dilemma

Abstract. According to Condorcet, the larger the team of decision-makers using the simple majority rule, the more likely they are to reach correct decisions. This paper examines the validity of this claim under the condition of reduced team competence with size. Determining committee size always involves quality-versus-quantity dilemma. This study provides criteria, as well as an algorithm, for deciding on the optimum size of boards and committees.

Robustness of optimal majority rules over teams with changing size

This work investigates the robustness of optimal restricted majority rules under a changing size of a decision group. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. This is most likely to be the case when information about the competence of the members of the decision team is not costless. One of the useful findings of this study is that optimal restricted majority rules are robust over reductions of the decision team.

Inferiority of Restricted Majority Decision Rules

The case in which a group of decision makers appoints a committee to choose between two symmetrical alternatives by a simple majority vote, namely restricted majority decision rule, is one member of the set of weighted majority decision rules. It is shown that for any group of decision makers one of the restricted majority decision rules is always the worst of all weighted majority decision rules. This inferiority exists both in terms of the efficiency and in terms of effectiveness of the decision rule.The importance of this finding should be kept in mind when deciding the size of the committee because a seemingly irrelevant change in the number of decision makers may result in the inferior rule, instead of the optimal rule, being used.Moreover, because of the widespread use of restricted majority decision rules and the relatively small number of such rules, the probability of the inferior rule being used is relatively high.

Variability of decisional ability and the essential order of decision rules

Abstract The paper examines how the optimal decision rule changes as one varies the decision-making ability of a group of individuals who have common preferences over two alternatives but who potentially differ in their ability to detect and identify the better alternative. The analysis is restricted to sets of rules which possess the property of an essential order. The main finding is that when the team members do not have their full ‘competency’ for choosing the better alternative, the optimal decision rule approaches the simple majority rule via the different stages on the ladder of the essential order.

Incentive schemes for investment in human capital by members of a team of decision makers

Abstract This paper shows that in the dichotomous collective choice model, there is a Pareto improvement if individual rewards are contingent on both the individuals and the teams correct decision, and not solely on the latter. Each of the teams members would invest more in human capital than he would without such an incentive.

On two properties of the marginal contribution of individual decisional skills

Abstract Employing the symmetric uncertain dichotomous choice model, we establish in this note two properties of the marginal contribution of an individuals decisional skill to the collective decisional quality. First, this marginal contribution is independent of the individuals decisional skill and, second, it increases with his relative ranking by decisional skill.

The network of weighted majority rules and its geometric realizations

Abstract In a previous work the first author considered the network G ( n , p ) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p =( p 1 ,…, p n ) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G ( n , p ) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.

Optimality among restricted majority decision rules

When a group of decision makers with common interests faces a dichotomous choice, the task of deciding may be delegated to a committee consisting of a subset of the original group. This procedure is called a restricted majority decision rule. If each member of the original group is characterized by the probability of his deciding correctly, the expected utility from the decision is determined by which members are appointed to the committee. The conditions between enabling the comparison of alternative restricted majority rules are based on the voting profiles of the decision makers. The purpose of the current study is to propose an algorithm for identifying the optimal restricted majority rule amongst all restricted majority rules.

Robustness of optimal decision rules where one of the team members is exceptionally qualified

This work investigates the robustness of optimal decision rules under a changing size of a decision group where the competence of one member is outstanding while the others possess an identical competence. More specifically, we focus on the expert rule, the almost expert rule and the tie-breaking chairperson rule. We first establish criteria for the optimality of each of these rules and then use it to investigate their robustness. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. Our findings are that the expert rule and the chairperson rule are robust while the almost expert rule is not.

Two remarks on the effect of increased equalitarianism in decisional skills on the number of individuals that maximizes group judgmental competence

Employing the symmetric uncertain dichotomous choice model, this paper is concerned with the effect of two types of changes in individual decisional competencies on the optimal collective decision rule and, in particular, on the optimal number of essential decision makers (individuals who are effectively involved in the decision-making process). The first change is simply a decrease in the decisional skills of some of the existing more competent essential decision makers. The second change is a rank and mean-preserving equalization of decisional skills. We show that the number of essential decision makers is not necessarily positively related to both of these changes. This surprising observation implies that a more egalitarian distribution of decisional skills may justify a reduction in the optimal number of individuals effectively participating in the collective decision-making process.