Suppose that there are two decision makers, with preference relations that admit a vNM representation using utility functions u1 and u2. They communicate their utility functions to a third person, who computes a function u = 1 2 u1 + 1 2 u2. Under what conditions is u a utility function? Suppose that the third person derives a preference relation >u from u according to the vNM representation. Give an example where >u coincides with the preference relation of the first decision maker in some cases, and with the preference relation of the second decision maker in other cases.