When an Event Makes a Difference

Abstract

For (S, Σ) a measurable space, let ${\cal C}_1$ and ${\cal C}_2$ be convex, weak^* closed sets of probability measures on Σ. We show that if ${\cal C}_1$ ∪ ${\cal C}_2$ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min_μ1∈${\cal C}_1$ μ₁(A) > max_μ2 ∈ ${\cal C}_2$(A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.