The Revealed Preference Approach to Welfare Judgments

We consider the aggregation of individual agents ’ von Neumann-Morgenstern’s util-ity functions into a societal von Neumann-Morgenstern utility function. We start from Harsanyi’s [14] axiomatization of utilitarianism, and ask under which conditions a so-cial preference order that satisfies Harsanyi’s axiom uniquely reveals society’s marginal rates of substitution between the probabilities of any two agents ’ most preferred alter-natives. We then introduce three axioms for these revealed marginal rates of substitu-tion. Our main result is that the only welfare function that satisfies these three axioms is the relative utilitarian welfare function. This welfare function, that was introduced in Dhillon [7] and Dhillon and Mertens [9], normalizes all agents ’ utility functions so that the lowest utility value is 0 and the highest utility value is 1, and then adds up the utility functions. The three axioms that we introduce are closely related to axioms that Dhillon and Mertens used to provide foundations for relative utilitarianism, but our axioms allow a much simpler and more transparent derivation of the main result. We are grateful to Lars Ehlers for comments and to Philippe Mongin and John Weymark for pointers regarding the formal literature on utilitarianism. We owe special thanks to Jim Belk who suggested to us the idea on which the proof of Proposition 3 is built