Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T11:35:34.092Z Has data issue: false hasContentIssue false
  • English
  • Français

The Expected Likelihood of Transitivity of Preference

Published online by Cambridge University Press:  01 January 2025

WIlliam V. Gehrlein
WIlliam V. Gehrlein*
Affiliation:
Department of Business Administration, University of Delaware
*
Requests for reprints should be sent to William V. Gehrlein, Department of Business Administration, University of Delaware, Newark, DE 19716.
Get access Rights & Permissions [Opens in a new window]

Abstract

May's model of pairwise preference determination is used to assess the expected likelihood that a subject's pairwise preference comparisons on three alternatives will be transitive. A closed form representation for this expected likelihood is obtained for each situation considered. When the subject is assumed to act precisely according to rankings on attributes with May's model, the computed expected likelihoods the relatively large. When the subject becomes a probabilistic chooser, as defined in a specific manner, expected likelihoods of transitivity decrease significantly from corresponding values with May's model. For a probabilistic Chooser, there is a significant likelihood that the subject might yield transitive pairwise preferences substantially different than the results suggested by May's model.

Keywords

transitivityindividual preferencepairwise comparison
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 695 - 706
Copyright
Copyright © 1990 The Psychometric Society

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.)

Footnotes

This research was supported by a grant from the General University Research Program and through a fellowship from the Center for Advanced Study, both of the University of Delaware. Very helpful input from John H. Antil, Meryl P. Gardner, and James M. Munch is also acknowledged.

References

Bar-Hillel, M., & Margalit, A. (1988). How vicious are cycles of intransitive choice?. Theory and Decision, 24, 119–145.CrossRefGoogle Scholar
Berg, S., & Bjurulf, B. (1983). A note on the paradox of voting: Anonymous preference profiles and May's formula. Public Choice, 40, 307–316.CrossRefGoogle Scholar
Bettman, J. R. (1979). An information processing theory of consumer choice, New York: Addison-Wesley.Google Scholar
Coombs, C. H. (1958). On the inconsistency of preferences in psychological measurement. Journal of Experimental Psychology, 55, 1–7.CrossRefGoogle ScholarPubMed
Genhrlein, W. V. (1981). The expected probability of Condorcet's paradox. Economics Letters, 7, 33–37.CrossRefGoogle Scholar
Gehrlein, W. V. (1989a). Probability calculations for transitivity of simple majority rule with anonymous voters. Public Choice, in press.Google Scholar
Gehrlein, W. V. (1989). The probability of intransitivity of pairwise comparisons in individual preference. Mathematical Social Sciences, 17, 67–75.CrossRefGoogle Scholar
Gehrlein, W. V., & Fishburn, P. C. (1976). The probability of the paradox of voting: a computable solution. Jounal of Economic Theory, 13, 14–25.CrossRefGoogle Scholar
Gehrlein, W. V., & Fishburn, P. C. (1976). Condorcet's paradox and anonymous preference profiles. Public Choice, 26, 1–18.CrossRefGoogle Scholar
Luce, R. D. (1979). Individual choice behavior, Westport, CT: Greenwood Press.Google Scholar
Luce, R. D., & Suppes, P. (1965). Preference, utility and subjective probability. In Luce, R. D., & Bush, R. R., Galanter, E. (Eds.), Handbook of mathematical psychology, Volume 3 (pp. 249–410). New York: Wiley.Google Scholar
May, K. O. (1954). Intransitivity, utility, and the aggregation of preference patterns. Econometrica, 22, 1–13.CrossRefGoogle Scholar
Russo, J. E., & Dosher, B. A. (1983). Strategies for multiattribute binary choice. Journal of Experimental Psychology: Learning, Memory and Cognition, 9, 676–696.Google ScholarPubMed
Selby, S. M. (1965). Standard mathematical tables 14th ed.,, Cleveland, OH: Chemical Rubber.Google Scholar
Wright, P., Barbour, F., & M., Zeleny (1977). Phased decision strategies: Sequels to an initial screening. In Starr, M. K. (Eds.), Multiple criteria decision making (pp. 91–109). Amsterdam: North-Holland.Google Scholar