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Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules

Part of: Operations research and management science Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Daniel Berend  and
Luba Sapir
Daniel Berend*
Affiliation:
Ben-Gurion University
Luba Sapir*
Affiliation:
Ben-Gurion University
*
∗ Postal address: Departments of Mathematics and of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email address: berend@cs.bgu.ac.il
∗∗ Postal address: Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email address: lsapir@bgu.ac.il
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Abstract

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We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making 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 group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.

Keywords

Dichotomous choicedecision ruleexpert rulemajority ruleoptimality probabilitypartial information

MSC classification

Primary: 91B06: Decision theory
Secondary: 91B12: Voting theory 90B50: Management decision making, including multiple objectives
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 16 - 31
Copyright
© Applied Probability Trust 2006 

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