 Again, linear pooling (except in its degenerate dictatorial form) does not generally satisfy this requirement (often called ‘external Bayesianity’), and so we would also get an impossibility result if we added it to our list of conditions, together with non-dictatorship (Madansky 1964). Subsequent work has shown that if we aggregate probabilities by geometric rather than linear averaging, we can make aggregation and revision commute (Genest 1984; Genest et al. 1986), though we must then lift the independence requirement on the opinion pooling rule. This finding has been picked up in more recent work and has sparked a small but growing philosophical literature on Bayesian group beliefs (e.g., Dietrich 2010, 2019; Russell, Hawthorne, and Buchak 2015; and Baccelli and Stewart 2020). The key question here is this: under what conditions can a group whose opinions are given by aggregating its members’ opinions constitute a rational Bayesian agent?