Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T08:07:46.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Between the expert and majority rules

Part of: Operations research and management science Mathematical economics

Published online by Cambridge University Press:  01 July 2016

Daniel Berend  and
Luba Sapir
Daniel Berend*
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.
∗∗ Postal address: Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva 84105, Israel. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Sapir (1998) calculated the probabilities of the expert rule and of the simple majority rule being optimal under the assumption of exponentially distributed logarithmic expertise levels. Here we find the analogous probabilities for the family of restricted majority rules, including the above two extreme rules as special cases, and the family of balanced expert rules. We compare the two families, the rules within each family, and all rules of the two families with the extreme rules.

Keywords

Dichotomous choice modelexpertdecision rulebalanced expert rulerestricted majority ruleprobability being optimallogarithmic expertise levelpartial information

MSC classification

Primary: 91B06: Decision theory 91B12: Voting theory 90B50: Management decision making, including multiple objectives
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 941 - 960
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Berend, D. and Harmse, J. (1993). Expert rule versus majority rule under partial information. Theory Decision 35, 179–197.CrossRefGoogle Scholar
[2] Berend, D. and Sapir, L. (2001). Optimality of the expert rule under partial information. Acta Appl. Math. 69, 141–162.CrossRefGoogle Scholar
[3] Berend, D. and Sapir, L. (2002). Expert rule versus majority rule under partial information. II. J. Appl. Math. Decision Sci. 6, 79–99.CrossRefGoogle Scholar
[4] Berend, D., Harmse, J. and Sapir, L. (2003). Range of asymptotic behaviour of the optimality probability of the expert and majority rules. Preprint.Google Scholar
[5] Condorcet, J.-A.-N. (1785). Essai sur l'Application de l'Analyse à la Probabilité des Décisions Rendues à la Pluralité des Voix. Imprimerie Royale, Paris.Google Scholar
[6] Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.Google Scholar
[7] Fishburn, P. C. and Gehrlein, W. V. (1977). Collective rationality versus distribution of power of binary social choice functions. J. Econom. Theory 15, 72–91.CrossRefGoogle Scholar
[8] Gradstein, M. and Nitzan, S. (1986). Performance evaluation of some special classes of weighted majority rules. Math. Social Sci. 12, 31–46.CrossRefGoogle Scholar
[9] Isbell, J. R. (1959). On the enumeration of majority games. Math. Tables Aids Comput. 13, 21–28.CrossRefGoogle Scholar
[10] Karotkin, D. (1993). Inferiority of restricted majority decision rules. Public Choice 77, 249–258.CrossRefGoogle Scholar
[11] Karotkin, D. (1994). Identification of the simple majority games and weighted majority rules. Unpublished manuscript.Google Scholar
[12] Karotkin, D. (1998). The network of weighted majority rules and weighted majority games. Games Econom. Behavior 22, 299–315.CrossRefGoogle Scholar
[13] Muroga, S., Toda, I. and Kondo, M. (1967). Enumeration of threshold functions of eight variables. Res. Rep. 245, Department of Computer Science, University of Illinois, Urbana.Google Scholar
[14] Nitzan, S. and Paroush, J. (1982). Optimal decision rules in uncertain dichotomous choice situations. Internat. Econom. Rev. 23, 289–297.CrossRefGoogle Scholar
[15] Nitzan, S. and Paroush, J. (1984). A general theorem and eight corollaries in search of a correct decision. Theory Decision 17, 211–220.CrossRefGoogle Scholar
[16] Nitzan, S. and Paroush, J. (1985). Collective Decision Making. Cambridge University Press.Google Scholar
[17] Sapir, L. (1998). The optimality of the expert and majority rules under exponentially distributed competence. Theory Decision 45, 19–35.CrossRefGoogle Scholar
[18] Sapir, L. (1999). Expert rule versus majority rule under partial information. III. In Proc. Conf. Heavy Tails, American University, Washington, DC, June 1999 (CD-ROM).Google Scholar
[19] Sapir, L. (2003). Comparison of the extreme decision rules for various types of distributions. To appear in Theory Decision.Google Scholar
[20] Von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.Google Scholar