I consider social welfare functions when the preferences of individual agents and society maximize subjective expected utility. A system of axioms is introduced whose unique solution is the social welfare function that averages the agents’ beliefs and adds up their utility functions, normalized so that they 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 applies only to subsets of acts that make every outside act redundant.

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