Abstract This article proposes a welfare criterion for economies in which agents have heterogeneously distorted beliefs. Instead of taking a stand on whose belief is correct, our criterion asserts that an allocation is belief-neutral efficient (inefficient) if it is efficient (inefficient) under any convex combination of agents’ beliefs. Although this criterion gives an incomplete ranking of social allocations, it can identify positive- and negative-sum speculation driven by conflicting beliefs in a broad range of economic environments.