On the self-(in)stability of weighted majority rules

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.

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Effectiveness of Weighted Majority Rules with Random Decision Power Distribution

Journal of Public Economic Theory ◽

10.1111/j.1467-9779.2008.00370.x ◽

2008 ◽

Vol 10 (3) ◽

pp. 423-439 ◽

Cited By ~ 1

Author(s):

DANIEL BEREND ◽

YURI CHERNYAVSKY

Keyword(s):

Power Distribution ◽

Weighted Majority ◽

Majority Rules ◽

Decision Power

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Ranking of Weighted Majority Rules

Journal of Applied Probability ◽

10.1239/jap/1231340229 ◽

2008 ◽

Vol 45 (4) ◽

pp. 994-1006

Author(s):

Daniel Berend ◽

Yuri Chernyavsky ◽

Luba Sapir

Keyword(s):

Decision Making ◽

Decision Rule ◽

Decision Rules ◽

Collective Decision ◽

Correct Decision ◽

Weighted Majority ◽

The Family ◽

Effective Decision ◽

Majority Rules ◽

Rule Out

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.

Download Full-text