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Ranking of Weighted Majority Rules

Part of: Mathematical economics

Published online by Cambridge University Press:  14 July 2016

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

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A decision-making body may utilize a wide variety of different strategies when required to make a collective decision. In principle, we would like to use the most effective decision rule, that is, the rule yielding the highest probability of making the correct decision. However, in reality we often have to choose a decision rule out of some restricted family of rules. Therefore, it is important to be able to rank various families of rules. In this paper we consider three classes of decision rules: (i) balanced expert rules, (ii) the so-called single expert rules, and (iii) restricted majority rules. For the first two classes, we show that, as we deviate from the best rule in the family, the effectiveness of the decision rule decreases. For the last class, we obtain a very different phenomenon: any inner ranking is possible.

Keywords

Decision ruleweighted majority rulebalanced expert rulerestricted majority ruledichotomous choice model

MSC classification

Secondary: 91B06: Decision theory 91B02: Fundamental topics (basic mathematics, methodology; applicable to economics in general) 91B12: Voting theory
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 994 - 1006
Copyright
Copyright © Applied Probability Trust 2008 

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