More on Harsanyi's utilitarian cardinal welfare theorem

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 Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.