More on Harsanyi's utilitarian cardinal welfare theorem (Q1083994)

If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by \textit{J. Harsanyi} [J. Polit. Econ. 63, 309-321 (1955)] who made implicit assumptions in the proof not actually needed for the result [see \textit{M. D. Resnick}, Theory Decis. 15, 309-320 (1983; Zbl 0519.90015)]. This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.