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A note on Wakker's Cardinal Coordinate Independence

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  • Bouyssou, Denis
  • Pirlot, Marc

Abstract

Peter P. Wakker has forcefully shown the importance for decision theory of a condition that he called “Cardinal Coordinate Independence” (CCI). Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility (SEU) model with a finite number of states. He has furthermore explored in depth how this condition can be weakened in order to arrive at characterizations of Choquet Expected Utility and Cumulative Prospect Theory. This note studies the consequences of this condition in the absence of any transitivity assumption. Complete preference relations satisfying Cardinal Coordinate Independence are shown to be already rather well-behaved. Under a suitable necessary order denseness assumption, they may always be represented using a simple numerical model.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 48 (2004)
Issue (Month): 1 (July)
Pages: 11-22

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Handle: RePEc:eee:matsoc:v:48:y:2004:i:1:p:11-22

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Fuhrken, Gebhard & Richter, Marcel K, 1991. "Additive Utility," Economic Theory, Springer, vol. 1(1), pages 83-105, January.
  2. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
  3. Nakamura, Yutaka, 1998. "Skew-symmetric additive representations of preferences," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 367-387, October.
  4. Fishburn, Peter C., 1989. "Non-transitive measurable utility for decision under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 187-207, April.
  5. Fishburn, Peter C., 1990. "Continuous nontransitive additive conjoint measurement," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 165-193, October.
  6. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  7. Fishburn, P. C., 1984. "SSB utility theory and decision-making under uncertainty," Mathematical Social Sciences, Elsevier, vol. 8(3), pages 253-285, December.
  8. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
  9. Fishburn, Peter C, 1991. " Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-34, April.
  10. Wakker, Peter, 1988. "Derived strengths of preference relations on coordinates," Economics Letters, Elsevier, vol. 28(4), pages 301-306.
  11. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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