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.

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...