Abstract: A group is often construed as a single agent with its own probabilistic beliefs, where these beliefs are obtained by aggregating those
of the group members. In a celebrated contribution, Russell et al. (2015) apply the Bayesian paradigm to groups by requiring group beliefs to change via Bayes’ rule whenever new information becomes publicly available, i.e., whenever the members’ beliefs all change via Bayes’ rule given that information. The Bayesian paradigm in fact suggests a stronger requirement: Bayes’ rule should constrain group beliefs not just in the face of public information (learnt by all members), but also in the face of non-public information (learnt by only some members), including private information (learnt by just one member). I propose a taxonomy of types or degrees of group Bayesianism. Each type requires group beliefs to obey Bayes’ rule for a certain type of information. The types of information (hence, of group Bayesianism) are obtained by differentiating according to (i) how widely information is accessible in the group, and (ii) whether of not information is representable within the algebra where credences are held. Six theorems will establish how exactly (and whether) group credences can obey any given type of group Bayesianism. As it turns out, group credences must be formed using `weighted geometric averages’ of individual credences, with certain constraints (on the weights) that depend on the kind of group Bayesianism.One of these theorems – the one concerned with public and representable information – is essentially Russell et al.’s central result (with some necessary minor qualifications).