论文信息 - On the existence of a probability measure compatible with a total preorder on a Boolean algebra

On the existence of a probability measure compatible with a total preorder on a Boolean algebra

Abstract If an economic agent's beliefs about the relative likelihood of events are characterized by a total preorder ≲ on the algebra A of events, the problem arises to know under which conditions, ≲ is representable by a probability measure. Here we show that there exists a probability measure compatible with a total preorder on a Boolean algebra, if and only if, the Boolean algebra is well bounded, weakly Archimedean, and perfectly separable, this last condition substituting for Villegas' monotone condition used in Chateauneuf and Jaffray (1984); if σ-additivity is required. Villegas' monotone condition, must merely be added.

Alain Chateauneuf | A. Chateauneuf

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