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Published September 19, 2017 | Submitted
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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.

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I wish to thank Stephen Selinger for pointing out Resnick's argument to me and, W. A. J. Luxemburg for a useful discussion which simplified the argument. Published as Border, Kim C. "More on Harsanyi's utilitarian cardinal welfare theorem." Social Choice and Welfare 1.4 (1985): 279-281.

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