Fully Bayesian Aggregation

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only prefefence aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, and achieves only static rationality. Our characterisation of linear-geometric preference aggregation implies as corollaries a characterisation of linear value aggregation (Harsanyi's Theorem) and a characterisation of geometric belief aggregation.