Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 2, Pages 79-99
doi:10.1155/S1173912602000068
Expert rule versus majority rule under partial information, II
1Departments of Mathematics and of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
2Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
Copyright © 2002 Daniel Berend and Luba Sapir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.