Revealed Relative Utilitarianism

We consider the aggregation of individual agents’ von Neumann-Morgenstern preferences over lotteries into a social planner’s von Neumann-Morgenstern preference. We start from Harsanyi’s axiomatization of utilitarianism, and ask under which conditions a social preference order that satisfies Harsanyi’s axiom uniquely reveals the planner’s marginal rates of substitution between the probabilities of any two agents’ most preferred alternatives, assuming that any increase/decrease in the probability of each agent’s most preferred alternative is accompanied by an equally sized decrease/increase in that agent’s least preferred alternative. We then introduce three axioms for these revealed marginal rates of substitution. The only welfare function that satisfies these three axioms is the relative utilitarian welfare function. This welfare function, that was introduced in Dhillon and Dhillon and Mertens, normalizes all agents’ utility functions so that the lowest value is 0 and the highest value is 1, and then adds up the utility functions. Our three axioms are closely related to axioms that Dhillon and Mertens used to axiomatize relative utilitarianism. We simplify the axioms, provide a much simpler and more transparent derivation of the main result, and re-interpret the axioms as revealed preference axioms.