A Theory Of Bayesian Groups

A group is often construed as a single agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated contribution “Groupthink”, Russell et al. (2015) apply the Bayesian paradigm to groups by requiring group credences to undergo a Bayesian revision whenever new information is learnt, i.e., whenever the individual credences undergo a Bayesian revision based on this information. Bayesians should often strengthen this requirement by extending it to 'non-public' or even 'private' information (learnt by 'not all' or 'just one' individual), or to non-representable information (not corresponding to an event in the algebra on which credences are held). I propose a taxonomy of six kinds of 'group Bayesianism', which differ in the type of information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, and so on. Six corresponding theorems establish exactly how individual credences must (not) be aggregated such that the resulting group credences obey group Bayesianism of any given type, respectively. Aggregating individual credences through averaging is never permitted. One of the theorems – the one concerned with public representable information – is essentially Russell et al.'s central result (with minor corrections).