The Optimality of the Expert and Majority Rules Under Exponentially Distributed Competence

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.     

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.     

The significance of independent decisions in uncertain dichotomous choice situations

The main concern of this paper is the selection of optimal decision rules for groups of individuals with identical preferences but diverse and dependent decisional skills. The main result establishes that within the uncertain dichotomous choice situation independent voting is always weakly superior to any pattern of interdependence among individual decisions. For the special class of total interdependence patterns the optimal rule is explicitly identified.     

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.     

Partial information on decisional competences and the desirability of the expert rule in uncertain dichotomous choice situations

The paper analyzes the expert resolution problem by employing extended versions of the uncertain dichotomous choice model. The main purpose of this study is to illustrate how the analysis of optimal decision rules can be carried out while dispensing with the common restrictive assumption of full information regarding individual decisional competences. In contrast to most previous studies in this field we here evaluate the expert rule under alternative assumptions regarding the available partial information on judgmental competences rather than compare it in an ad hoc manner to some common alternative rules, such as simple majority rule. A fuller optimality analysis allowing the evaluation of all relevant decision rules, and not merely the expert rule, is attempted for a five-member panel of experts assuming a uniform distribution of individual competences. For three-member groups the optimality issue is resolved by assuming no information on individual competences and interpreting the expert rule as an even-chance lottery on skills.     

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 Application of Multiattribute Utility Theory to Models of Choice

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are in conflict with either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example.      

Re-examining the law of iterated expectations for Choquet decision makers

Yoo (Economic Letters 37:145–149, 1991) argues that the law of iterated expectations must be violated if the probability measure of a Choquet decision maker is non-additive. In this article, we prove the positive result that the law of iterated expectations is satisfied for Choquet decision makers whenever they update their non-additive beliefs in accordance with the Sarin and Wakker (Journal of Risk and Uncertainty 16:223–250, 1998) update rule. The formal key to this result is the act-dependence of the Sarin–Wakker update rule, which does not hold for the update rules considered by Yoo (1991).     

A general theorem and eight corollaries in search of correct decision

The main theorem established in this study and its corollaries summarize and generalize the existing results on optimal aggregation of experts judgments under uncertain pairwise choice situations. In particular, we explicate the link between the optimal decision procedure and the decision maker's preferences and biases and the judgmental competences of his consultants. The general theorem directly clarifies under what circumstances the optimal decision rule should be the democratic simple majority rule, the elitist expert rule, an intermediate weighted simple majority rule or a biased weighted or simple qualified majority rule.     

A Method for Eliciting Utilities and its Application to Collective Choice

Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action. The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s action, infers the decision maker’s utilities over several alternatives. This paper studies an example of such a mechanism and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’ utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes Harsanyi’s social utility function and is Pareto-efficient.     

On the Robustness of the Winner’s Curse Phenomenon

We set out to find ways to help decision makers overcome the “winner’s curse,” a phenomenon commonly observed in asymmetric information bargaining situations, and instead found strong support for its robustness. In a series of manipulations of the “Acquiring a Company Task,” we tried to enhance decision makers’ cognitive understanding of the task. We did so by presenting them with different parameters of the task, having them compare and contrast these different parameters, giving them full feedback on their history of choices and resulting outcomes, and allowing them to interact with a human opponent instead of a computer program. Much to our surprise, none of these manipulations led to a better understanding of the task. Our results demonstrate and emphasize the robustness of the winner’s curse phenomenon.      

Metapreferences and the reasons for stability in social choice: Thoughts on broadening and clarifying the debate

The standard model of collective choice looks at aggregation procedures which take individual preferences as existing for a specified set of alternatives. In this paper we propose that actors also have preferences for rules of choice or characteristics of choice processes (e.g., the perceived fairness of procedures or the popularity of outcomes) rather than simply for alternatives (outcomes) themselves. We argue that the positing of the existence of meta-preferences can illuminate a number of areas of choice theory. Here we focus on one such area: the problem of “too much” stability in majority rule decision making - a stability which belies the standard theoretical results on the generic instability of majority rule processes. We also show that discussion of the prevalence of stability in collective decision making needs to be clarified because there are at least six distinct types of stability which are sometimes confounded in the literature.     

Competence effects for choices involving gains and losses

We investigate how choices for uncertain gain and loss prospects are affected by the decision maker’s perceived level of knowledge about the underlying domain of uncertainty. Specifically, we test whether Heath and Tversky’s (J Risk Uncertain 4:5–28, 1991) competence hypothesis extends from gains to losses. We predict that the commonly-observed preference for high knowledge over low knowledge prospects for gains reverses for losses. We employ an empirical setup in which participants make hypothetical choices between gain or loss prospects in which the outcome depends on whether a high or low knowledge event occurs. We infer decision weighting functions for high and low knowledge events from choices using a representative agent preference model. For gains, we replicate the results of Kilka and Weber (Manage Sci 47:1712–1726, 2001), finding that decision makers are more attracted to choices that they feel more knowledgeable about. However, for losses, we find limited support for our extension of the competence effect.     

Potential and ‘Power of a Collectivity to Act’<Superscript>*</Superscript>

This paper connects two notions: Hart and Mas-Colell’s ‘potential’, related to the value of coalitional games, and Coleman’s earlier notion of ‘power of a collectivity to act’, related to the easiness to make decisions by means of a voting rule. ^*This research has been supported by the Spanish Ministerio de Ciencia y Tecnología under project BEC2000-0875, and by the Universidad del País Vasco under project UPV/EHU000031.321-HA-7918/2000. The first author acknowledges financial support from the Spanish Ministerio de Ciencia y Tecnología under the Ramón y Cajal programme.     

Individual and couple decision behavior under risk: evidence on the dynamics of power balance

This article reports results of an experiment designed to analyze the link between risky decisions made by couples and risky decisions made separately by each spouse. We estimate both the spouses and the couples’ degrees of risk aversion, we assess how the risk preferences of the two spouses aggregate when they make risky decisions, and we shed light on the dynamics of the decision process that takes place when couples make risky decisions. We find that, far from being fixed, the balance of power within the household is malleable. In most couples, men have, initially, more decision-making power than women but women who ultimately implement the joint decisions gain more and more power over the course of decision making.     

Decision theory with prospect interference and entanglement

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested.     

Deterrence, expected cost, uncertainty and voting: Experimental evidence

We conduct laboratory experiments to investigate the effects of deterrence mechanisms under controlled conditions. The effect of the expected cost of punishment of an individual’s decision to engage in a proscribed activity and the effect of uncertainty on an individual’s decision to commit a violation are very difficult to isolate in field data. We use a roadway speeding framing and find that (a) individuals respond considerably to increases in the expected cost of speeding, (b) uncertainty about the enforcement regime yields a significant reduction in violations committed, and (c) people are much more likely to speed when the punishment regime for which they voted is implemented. Our results have important implications for a behavioral theory of deterrence under uncertainty.     

On a concept of representative democracy

Political theory distinguishes between two concepts of representative democratic decisions. Under the first concept, representatives do not decide issues as independent individuals but merely reflect the will of their constituencies; under the second, the decisions are made by the elected representatives themselves on the basis of their independent judgments on political issues. In the literature of democratic choice, the first concept has been formalized by Murakami, Fishburn, Pattanaik among others, in terms of decision procedures where the representative is identified with the preference-pattern emerging from the aggregation of the preferences of individual voters in a given constituency. Here we formalize the second type of representative democracy and show that it comes into conflict with certain essential features of a democratic group decision rule. In particular decisiveness and monotonicity are violated. The violation of monotonicity is of particular significance because it has come to be regarded as one of the fundamental principles for the ethical acceptability of democratic decision procedures.I am also grateful to the University Grants Commission of India for the financial assistance in carrying out this study.I wish to acknowledge my great debt to Professor Prasanta K. Pattanaik, my supervisor, both for initiating me to this problem and for his invaluable comments, criticisms and guidance. The paper acquired much of its present status through the discussions I had with him. Responsibility for any error, of course, rests with me.