Belief-Averaging and Relative Utilitarianism: Savage Meets Arrow

Working paper (January 2021)
[pdf]

We consider social welfare functions when the preferences of individual agents and society maximize subjective expected utility in the tradition of Savage. A system of axioms is introduced whose unique solution is the social welfare function that averages the agents’ beliefs and sums up their utility functions, normalized to have the same range. The first distinguishing axiom requires that an act about which beliefs agree becomes socially more preferred if it gains support among the agents. The second is a weakening of Arrow’s independence of irrelevant alternatives that only applies to non-redundant acts.