A note on Wakker's Cardinal Coordinate Independence

Denis Bouyssou (1) , Marc Pirlot (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 Faculté polytechnique de Mons

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.

Mots clés: Nontransitive preferences.; Decision under uncertainty; Cardinal Coordinate Independence

Mots clés: Nontransitive preferences

Domaines: Economies et finances

Denis Bouyssou, Marc Pirlot. A note on Wakker's Cardinal Coordinate Independence. Mathematical Social Sciences, 2004, 48 (1), pp.11-22. ⟨hal-00004075⟩