Ruth Ben-Yashar

The Optimal Decision Rule for Fixed-Size Committees in Dichotomous Choice Situations: The General Result

This paper presents a general pairwise choice framework and derives the optimal decision rule for fixed-size committees. The main result generalizes a number of earlier results in the subject. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A nonasymptotic Condorcet jury theorem

Abstract. 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.

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

Abstract. 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.

First and Second Best Voting Rules in Committees

A group of people with identical preferences but different abilities in identifying the best alternative (e.g., a jury) takes a vote to decide between two alternatives. The first best voting rule is a weighted voting rule that takes into account the different individual competences, and is therefore not anonymous. Under such a rule, it is rational for group members to vote informatively, i.e., according to their private information. The use of any (non-trivial) anonymous voting rule may provide an incentive for some group members to vote strategically, non-informatively. However, this paper shows that the identity of the best anonymous voting rule does not depend on whether or not they actually choose to do so; a single, second best, rule maximizes utility in both cases.

Quality and structure of organizational decision-making

Abstract In this paper organizational quality is defined in terms of the decision criterion the organization applies. This quality determines the decisional skills of the individual decision makers and, in turn, the optimal structure of decision making. The assumption that individual decisional skills are determined endogenously is the distinctive and novel characteristic of our framework. Our analysis focuses on the relationship between quality and structure of decision making in organizations. In particular, we study the following issues: How are organizational quality, individual decision-making skills and the structure of the organization related? How does the size of the organization affect its optimal quality? Our results imply that evaluation of organizational performance and comparison of organizations solely on the basis of their quality can be misleading. This is true because the performance of organizations is determined by their quality as well as by their structure and size.

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

Abstract. 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.

Investment Criteria in Single and Multi-Member Economic Organizations

This paper compares the determination of investment criteriain single- and multi-member organizations. Individualdecisional skills are assumed to be endogenous variables thatdepend on the investment criteria. Our main result specifiesthe condition that determines the relationship between theinvestment criteria in single- and multi-member organizations,given the size of the multi-member organization, the decisionrule it applies and the function relating the individualsdecisional skills to the investment criterion. Theimplications of our main result are developed for specialorganizations such as hierarchies and polyarchies. Ouranalysis implies that the criteria in a multi-memberorganization may be stricter than the criteria set in asingle-member organization, even though in the former case theorganization may worsen the average decision-making ability ofits members. The analysis can be applied not only in singleand multi-member decision making settings, but also in somecontexts of centralized and decentralized decisions. This isillustrated in the case of decisions by editors ofprofessional journals regarding the acceptance or rejection ofsubmitted papers.

The invalidity of the Condorcet Jury Theorem under endogenous decisional skills

Abstract. The current note clarifies that Condorcet Jury Theorem cannot be generalized to the extended setting where individual decisional skills are not assumed to be exogenous parameters even when these skills are homogeneous. This is true when skills are determined endogenously either by a central planner or, in a decentralized strategic setting, by the decision makers themselves.

Optimal collective dichotomous choice under partial order constraints

Abstract This paper generalizes optimal collective dichotomous choices by including constraints which limit combinations of acceptance and rejection decisions for m projects under consideration. Two types of constraints are examined. The first type occurs when acceptance of some projects requires acceptance of others. This type reduces the choice problem to the tractable (solvable in polynomial time) problem of finding a maximum weight closed subset of a directed acyclic graph. The second type occurs when some projects must be accepted when certain others are rejected. We show that this type renders the choice problem to be NP-complete by reduction from the problem of Vertex Cover. Applicability of the generalization to information filtering is discussed.

On the Optimal Composition of Committees

This paper derives a simple characterization of how to optimally divide an organization’s experts into different decision-making committees. The focus is on many three-member committees that make decisions by a simple majority rule. We find that the allocation of experts to committees is optimal if and only if it minimizes the sum of the products of the experts’ skills in each committee. As a result, given the experts of any two committees, the product of the experts’ skills should be as similar as possible in the two committees, and it is never optimal to have the three worst experts in one committee and the three best experts in another.