When n individuals satisfy the axioms of subjective expected utility (SEU) theory and these individuals' probabilities or/and utilities are sufficiently diverse, it is impossible to aggregate the individuals' preferences into a (n + 1)-preference which is both Paretian and in agreement with SEU...

Mixture sets were introduced by Herstein and Milnor (1953) into decision theory, where they are still widely used. This note clarifies the formal connection between mixture sets and convex sets. The results suggest that the former concept might be unnecessary for decision-theoretic purposes.

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (D.S.) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the...

The paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of Neighbourhood semantics. This axiomatization of common belief is the weakest of all those currently available : it dispenses with even the Monotonicity...