Bayesian theory for rational individual decision making under uncertainty prescribes that the decision maker define independently a set of beliefs (probability assessments for the states of the world) and a system of values (utilities). The decision is then made by maximizing expected utility. We attempt to generalize the model to group decision making. It is assumed that the group's belief depends only on individual beliefs and the group's values only on individual values, that the belief aggregation procedure respects unanimity, and that the entire procedure guarantees Pareto optimality. We prove that only trivial (dictatorial) aggregation procedures for beliefs are possible.