Abstract. The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution (Madansky, 1964;Lehrer and Wagner, 1981;McConway, 1981;Bordley, 1982;Genest and Zidek, 1986;Mongin, 1995;Clemen and Winkler, 1999;Dietrich and List, 2014;Herzberg, 2014). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities (IP) by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi (1985), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.