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Modelling dependence in simple and indirect majority systems

Published online by Cambridge University Press:  14 July 2016

Philip J. Boland ,
Frank Proschan  and
Y. L. Tong
Philip J. Boland*
Affiliation:
University College, Dublin
Frank Proschan*
Affiliation:
The Florida State University
Y. L. Tong*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: Department of Statistics, University College, Dublin, Belfield, Dublin 4, Ireland.
∗∗Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 32306-3033, USA.
∗∗∗∗School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

Keywords

DECISION THEORYRELIABILITY THEORYCONDORCET JURY THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 81 - 88
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research partially sponsored by AFOSR Contract 82-K-007.

Research sponsored by AFOSR Contract 82-K-007.

Research sponsored by the U.S. National Science Foundation under grant DMS-8502346.

References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring, Md.Google Scholar
Condorcet, N. (1785) Essai sur l'application de l'analyse à la probabilité des voix. Paris.Google Scholar
Grofman, B. and Owen, G. (1986) Review Essay: Condorcet Models, Avenues for Future Research. Information Pooling and Group Decision Making: Proceedings of the Second University of California Irvine Conference on Political Economy. JAI Press, Greenwich, CT.Google Scholar
Karlin, S. (1968) Total Positivity , Vol. 1. Stanford University Press, Stanford, California.Google Scholar
Miller, N. R. (1986) Information, electorates and democracy: some extensions and interpretations of the Condorcet Jury Theorem. Information Pooling and Group Decision Making: Proceedings of the Second University of California Irvine Confernece on Political Economy. JAI Press, Greenwich, CT.Google Scholar
Mood, A. M. (1950) Introduction to the Theory of Statistics. McGraw-Hill, New York.Google Scholar
Srihari, S. N. (1982) Reliability analysis of majority vote systems. Informat. Sci. 26, 243–256.Google Scholar