Aggregation of Semiorders: Intransitive Indifference Makes a Difference
A semiorder can be thought of as a binary relation P for which there is a utility "u" representing it in the following sense: xPy iff u(x)-u(y) > 1. We argue that weak orders (for which indifference is transitive) can not be considered a successful approximation of semiorders; for instance, a utility function representing a semiorder in the manner mentioned above is almost unique, i.e. cardinal and not only ordinal. In this paper we deal with semiorders on a product space and their relation to given semiorders on the original spaces. Following the intuition of Rubinstein we find surprising results: with the appropriate framework, it turns out that a Savage-type expected utility requires significantly weaker axioms than it does in the context of weak orders.
(This abstract was borrowed from another version of this item.)
|Date of creation:||Feb 1990|
|Contact details of provider:|| Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014|
Web page: http://www.kellogg.northwestern.edu/research/math/
More information through EDIRC
|Order Information:|| Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Avraham Beja & Itzhak Gilboa, 1989.
"Numerical Representations of Imperfectly Ordered Preferences (A Unified Geometric Exposition,"
836, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Itzhak Gilboa & Avraham Beja, 1992. "Numerical representations of imperfectly ordered preferences (a unified geometric exposition)," Post-Print hal-00481383, HAL.
- Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
- Yew-Kwang Ng, 1975. "Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions," Review of Economic Studies, Oxford University Press, vol. 42(4), pages 545-569.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
- Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
- Itzhak Gilboa, 1987. "Expected Utility with Purely Subjective Non-Additive Probabilities," Post-Print hal-00756291, HAL.
- Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
- Gensemer, Susan H., 1987. "Continuous semiorder representations," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 275-289, June. Full references (including those not matched with items on IDEAS)