This suggests that the right formalization of “bargaining power” would give a nonnegative scaling factor to each member of the group, and the group will act to maximize the sum of the agents’ expected utilities weighed by their respective scaling factors. … Of course, at this point this is merely an intuition, and I do not have a worked-out proposal nor a careful justification.
There is a justification for that intuition. Some have objected to the axiom that the aggregation must also be VNM-rational, but Nisan has proved a similar theorem that does not rely on the VNM-rationality of the collective as an axiom.
There is a justification for that intuition. Some have objected to the axiom that the aggregation must also be VNM-rational, but Nisan has proved a similar theorem that does not rely on the VNM-rationality of the collective as an axiom.