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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". Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility 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 Archimedean-like assumption, they may always be represented using a simple numerical model.
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  • Bouyssou, Denis & Pirlot, Marc, 2004. "A note on Wakker's Cardinal Coordinate Independence," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 11-22, July.
    • Handle: RePEc:eee:matsoc:v:48:y:2004:i:1:p:11-22
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    1. Fishburn, Peter C., 1989. "Non-transitive measurable utility for decision under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 187-207, April.
    2. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    3. Fishburn, P. C., 1984. "SSB utility theory and decision-making under uncertainty," Mathematical Social Sciences, Elsevier, vol. 8(3), pages 253-285, December.
    4. 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.
    5. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
    6. Wakker, Peter, 1988. "Derived strengths of preference relations on coordinates," Economics Letters, Elsevier, vol. 28(4), pages 301-306.
    7. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    8. Fishburn, Peter C. & Lavalle, Irving H., 1987. "State-dependent SSB utility," Economics Letters, Elsevier, vol. 25(1), pages 21-25.
    9. Irving H. Lavalle & Peter C. Fishburn, 1987. "Decision Analysis Under States-Additive SSB Preferences," Operations Research, INFORMS, vol. 35(5), pages 722-735, October.
    10. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    11. Nakamura, Yutaka, 1998. "Skew-symmetric additive representations of preferences," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 367-387, October.
    12. Fishburn, Peter C., 1990. "Continuous nontransitive additive conjoint measurement," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 165-193, October.
    13. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
    14. Wakker, Peter P. & Zank, Horst, 1999. "A unified derivation of classical subjective expected utility models through cardinal utility," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 1-19, August.
    15. Iverson, G. & Falmagne, J. -C., 1985. "Statistical issues in measurement," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 131-153, October.
    16. Fuhrken, Gebhard & Richter, Marcel K, 1991. "Additive Utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 83-105, January.
    17. Fishburn, Peter C., 1990. "Skew symmetric additive utility with finite states," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 103-115, April.
    18. 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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    1. Denis Bouyssou & Marc Pirlot, 2008. "On some ordinal models for decision making under uncertainty," Annals of Operations Research, Springer, vol. 163(1), pages 19-48, October.
    2. Bouyssou, Denis & Pirlot, Marc, 2005. "Following the traces:: An introduction to conjoint measurement without transitivity and additivity," European Journal of Operational Research, Elsevier, vol. 163(2), pages 287-337, June.

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