Conditions for the optimality of simple majority decisions in pairwise choice situations

Recently it has been proved in a number of studies, that, under a proper set of assumptions, the optimal group decision rule in pairwise choice situations is a weighted majority rule, with weights that are proportional to the logarithms of the decision makers' odds of choosing the correct alternative.The purpose of the present note is to specify the necessary and sufficient conditions for this rule to coincide with the simple majority rule, and with restricted simple majority rules (which are defined as rules of simple majority, based on some subset of the most competent group members). These conditions are formulated in terms of inequalities between the group members' weights, thereby permitting easy verification of the optimality of the above mentioned rules.     

Comparison of the Polar Decision Rules for Various Types of Distributions

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is optimal if it maximizes the probability of the group to make 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 team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns.     

Majority rule and general decision rules

For ann-member body making dichotomous decisions, decision rules can be formulated as simple games. Of all possible decision rules, majority rule maximizes the average reponsiveness of the body to individual preferences. It is the unique decision rule which does this whenn is odd, but not whenn is even. Other conditions limit the choice of decision rules whenn is even.     

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.     

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.     

Order relations among efficient decision rules

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.     

Preference aggregation and statistical estimation

This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference patterns into various pattern classes and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues.     

Bayesian decision theory,rule utilitarianism,and Arrow's impossibility theorem

The first part of this paper reexamines the logical foundations of Bayesian decision theory and argues that the Bayesian criterion of expected-utility maximization is the only decision criterion consistent with rationality. On the other hand, the Bayesian criterion, together with the Pareto optimality requirement, inescapably entails a utilitarian theory of morality. The next sections discuss the role both of cardinal utility and of cardinal interpersonal comparisons of utility in ethics. It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates avoiding the celebrated impossibility theorem by making use of information which is unavailable in Arrow's original framework. Finally, rule utilitarianism is contrasted with act utilitarianism and judged to be preferable for the purposes of ethical theory.     

A Characterization for the Spherical Scoring Rule

Strictly proper scoring rules have been studied widely in statistical decision theory and recently in experimental economics because of their ability to encourage assessors to honestly provide their true subjective probabilities. In this article, we study the spherical scoring rule by analytically examining some of its properties and providing some new geometric interpretations for this rule. Moreover, we state a theorem which provides an axiomatic characterization for the spherical scoring rule. The objective of this analysis is to provide a better understanding of one of the most commonly available scoring rules, which could aid decision makers in the selection of an appropriate tool for evaluating and assessing probabilistic forecasts.      

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.     

Evidence for Learning to Learn Behavior in Normal Form Games

Evidence presented in Salmon (2001; Econometrica 69(6) 1597) indicates that typical tests to identify learning behavior in experiments involving normal form games possess little power to reject incorrect models. This paper begins by presenting results from an experiment designed to gather alternative data to overcome this problem. The results from these experiments indicate support for a learning-to-learn or rule learning hypothesis in which subjects change their decision rule over time. These results are then used to construct an adaptive learning model which is intended to mimic more accurately the behavior observed. The final section of the paper presents results from a simple simulation based analysis comparing the performance of this adaptive learning model with that of several standard decision rules in reproducing the choice patterns observed in the experiment.JEL Classification: C92, C72     

A theorem for Bayesian group decisions

This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we impose a multiattribute utility independence condition on the preferences of the group with respect to the expected utilities of its actions as appraised by its members. The result is that the expected utility of an alternative for the group is a weighted average of the expected utilities of that alternative for its members. The weights must be determined collectively by the group. Pareto optimality is not assumed, though the result is consistent with Pareto optimality.     

Between‐ and within‐person predictors of children’s information management following rule violations

The purpose of this study was to better understand both why some children disclose more about their misbehavior to their parents than do other children, as well as why a child discloses to parents about misbehavior in some situations but not in others. Analyses test parental warmth, children's beliefs regarding the legitimacy of parental authority and their own obligation to disclose misbehavior, and parent's responses to children's disclosure of disagreement with parents’ rules and children's misbehavior as predictors of both between‐person and within‐person variations in disclosing and revealing forms of information management. Parent‐child dyads (n = 218) were interviewed during the summers following the child's 5th (M age = 11.9 years) and 6th grade school years. Feeling obligated to disclose rule violations and believing that parents have legitimate authority to impose rules across more topics explained why some children reveal more and conceal less from parents than do other children. Children were more likely to conceal information about the specific topics for which they felt less obligated to disclose rule violations and following rule violations in areas in which their parents previously punished rule violations.     

公众对转基因作物的接受度及其影响因素:基于六城市调查数据的社会学分析

本文利用一项大规模的入户抽样调查数据,分析了中国公众对转基因作物的接受度问题。与以往基于“消费者行为研究”框架而采取“个体决策行为模型”的研究不同,本文从风险社会学的理论视角出发,试图发展一个“社会行动模型”的理论框架,以解释个体在“风险社会”中面对一项新技术时的决策行动受到哪些社会性因素的影响。结果显示,中国公众对推广种植转基因大米的接受度不高,与2002年相比有明显下降;传统的“个体决策行为模型”有一定的解释力,但其决策行为是基于有限知识基础上的“有限理性选择”,大众媒体的影响、对“专家系统”的制度性信任都是重要的影响因素。     

Tempered Regrets Under Total Ignorance

Several decision rules, including the minimax regret rule, have been posited to suggest optimizing strategies for an individual when neither objective nor subjective probabilities can be associated to the various states of the world. These all share the shortcoming of focusing only on extreme outcomes. This paper suggests an alternative approach of tempered regrets which may more closely replicate the decision process of individuals in those situations in which avoiding the worst outcome tempers the loss from not achieving the best outcome. The assumption of total ignorance of the probabilities associated with the various states is maintained. Applications and illustrations from standard neoclassical theory are discussed.     

Thirteen theorems in search of the truth

We review recent work on the accuracy of group judgmental processes as a function of (a) the competences (judgmental accuracies) of individual group members, (b) the group decision procedure, and (c) group size. This work on individual competence and group accuracy represents an important contribution to democratic theory and a useful complement to the usual emphasis in the social choice literature on individual preference and preference aggregation mechanisms. The work reported on is rooted in a tradition which goes back to scholars such as Condorcet, Poisson, and Bayes.     

What can the regression model of human judgment learn from multi-attribute decision theory?

Zeleny's recent conjecture that multi-attribute decision theory may help to overcome the inadequacies of the linear regression model is incorrect. Recognition of the information processing advantages inherent in multiple -attribute decision situations combined with a requirement of transitivity itself implies linear objective functions. This follows from some recent developments by a psychologist and an economist in the analysis of individual and collective decision processes, developments which do not take as their starting point the paradigm of choice offered in utility theory.     

Strict proportional power in voting bodies

It is a widely known fact among game theorists as well as political scientists that the distribution of voting weights in a voting body is generally a poor proxy for the distribution of voting power within the body. It has been proposed to equate the distribution of a priori voting power and actual seat distribution by randomizing the decision rule of the voting body over various majority rules. In this paper, some implications of this procedure will be discussed.     

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.     

Towards a Multi‐level Approach on Frontline Interactions in the Public Sector: Institutional Transformations and the Dynamics of Real‐time Interactions

This study develops a multi‐level approach on frontline interactions in the public sector. Previous research suggests that detailed analyses of frontline interactions are essential to our understanding of how welfare services take shape when policies and rules are applied and negotiated in individual cases. The dynamics and performances of real‐time interactions have, however, rarely been analyzed as such. This study shows how the methods developed in the field of Conversation Analysis can contribute to this research. Our multi‐level approach integrates analyses of the policy‐ and institutional transformations that shape conditions for frontline interactions; and analyses of how policies and rules are evoked, negotiated and reshaped in the turn‐by‐turn organization and performances of interaction. The approach is applied on an analysis of how rules regarding financial aid are applied in an authority highly affected by changes in welfare policy towards standardization and detailed regulations. The empirical case is the Swedish Board for Study Support. The empirical study includes analyses of documents, interviews and analyses of taped telephone conversations. The study shows how institutional arrangements of standardization, detailed regulations, monitoring and depersonalization, structure the frontline work and shape narrow frames for officials' discretion in interactions with clients. The study also shows how rules are invoked and negotiated in recurrent practices in the interaction: in the careful design of decisions; in the investigations of alternatives and exceptions from the rules in order to find solutions to the client's problems. The analyses of concrete interactional practices clearly indicate that also a rule‐governed work dominated by task discretion involves recurrent negotiations, flexibility and local policy‐making.