A Reformulation of the Axiomatic Foundations of Relative Utilitarianism

We consider the aggregation of individual agents’ von Neumann-Morgenstern’s utility functions into a societal von Neumann-Morgenstern utility function. We start from Harsanyi’s [7] axiomatization of utilitarianism, and ask under which conditions a social preference order that satisfies Harsanyi’s axiom uniquely reveals society’s marginal rates of substitution between the probabilities of any two agents’ most preferred alternatives. We then introduce three axioms for these revealed marginal rates of substitution. 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 [5] and Dhillon and Mertens [6], 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. [email protected] [email protected]