The generalized homogeneity assumption and the Condorcet jury theorem

The Condorcet jury theorem (CJT) is based on the assumption of homogeneous voters who imperfectly know the correct policy. We reassess the validity of the CJT when voters are homogeneous and each knows the correct decision with an average probability of more than a half.     

Is diversity in capabilities desirable when adding decision makers?

When the benefit of making a correct decision is sufficiently high, even a slight increase in the probability of making such a decision justifies an increase in the number of decision makers. Applying a standard uncertain dichotomous choice benchmark setting, this study focuses on the relative desirability of two alternatives: adding individuals with capabilities identical to the existing ones and adding identical individuals with mean-preserving capabilities that depend on the states of nature. Our main result establishes that when the group applies the simple majority rule, variability in the capabilities of the new decision makers under the two states of nature, which is commonly observed in various decision-making settings, is less desirable in terms of the probability of making the correct decision.     

On the significance of the prior of a correct decision in committees

The current note clarifies why, in committees, the prior probability of a correct collective choice might be of particular significance and possibly should sometimes even be the sole appropriate basis for making the collective decision. In particular, we present sufficient conditions for the superiority of a rule based solely on the prior relative to the simple majority rule, even when the decisional skills of the committee members are assumed to be homogeneous.     

A nonasymptotic Condorcet jury theorem

This paper provides first the condition under which the majority of an odd number of jurists is more likely to choose the better of two alternatives than a single jurist selected at random from the jurists, given that each jurist has a probability larger than one half of choosing correctly, and second that the same inequality holds for a subset of an odd number of jurists chosen at random from the original group. Received: 16 November 1998/Accepted: 8 January 1999     

The robustness of optimal organizational architectures: A note on hierarchies and polyarchies

In this note we study the robustness of optimal organizational architectures, focusing on hierarchies and polyarchies. These two specific architectures are often applied in economic systems and have received considerable attention in the literature. It turns out that the application of these architectures usually involves inefficiency, namely, the use of suboptimal organizational systems. This is demonstrated by proposing a measure of size robustness of optimal architectures and by analyzing the implications of its magnitude for hierarchies and polyarchies. Received: 4 January 1999/Accepted: 10 January 2000     

Is specialization desirable in committee decision making?

Committee decision making is examined in this study focusing on the role assigned to the committee members. In particular, we are concerned about the comparison between committee performance under specialization and non-specialization of the decision makers. Specialization (in the context of project or public policy selection) means that the decision of each committee member is based on a narrow area, which typically results in the acquirement and use of relatively high expertise in that area. When the committee members’ expertise is already determined, specialization only means that the decision of each committee member is based solely on his/her relatively high expertise area. This form of specialization is potentially inferior relative to non-specialization under which the decision of each committee member is based on different areas, not just his/her relatively high expertise area. Given that the expertise of the committee members is already determined but unknown, our analysis focuses on non-specializing individuals whose decision is based on a decision rule that does not require information on the decision-making skills. Under these realistic assumptions, non-specialization is shown to be preferable over specialization, depending on the aggregation rule applied by the committee. The significance of our approach is not limited to the specific results that we obtain. Rather, it should be viewed as a first step toward a deeper examination of the role of individual decision makers in enhancing the performance of collective decision making.     

First and second best voting rules in committees

A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases.

“Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller, Catch-22

     

Are Referees Sufficiently Informed About The Editor'S Practice?

This paper clarifies why editors of academic journals should share with their referees the information about the number of referees they consult and the decision rule they apply. Our analysis also rationalizes the common questionable phenomenon of editors who seem to distort the yes or no recommendations of their referees. The editors request a recommendation of whether to accept or reject the paper as well as an assessment of the paper. The editors need the complete reports to make the appropriate correction of the referees' final recommendations.     

Optimal decision rules for fixed-size committees in polychotomous choice situations

This paper derives optimal decision rules for fixed-size committees in polychotomous choice situations. Earlier studies focus on the dichotomous choice model and thus the present extension broadens the scope of applications of the theory of collective decision making. Received: 10 November 1999/Accepted: 13 April 2000