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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. 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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