Range of asymptotic behaviour of the optimality probability of the expert and majority rules

Daniel Berend, Luba Sapir

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)16-31
Number of pages16
JournalJournal of Applied Probability
Volume43
Issue number1
DOIs
StatePublished - 13 Dec 2006

Keywords

  • Decision rule
  • Dichotomous choice
  • Expert rule
  • Majority rule
  • Optimality probability
  • Partial information

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Range of asymptotic behaviour of the optimality probability of the expert and majority rules'. Together they form a unique fingerprint.

Cite this