Draft:Harsanyi's utilitarian theorem

In social choice theory and ethics, Harsanyi's utilitarian theorems are a set of closely-related results showing that under certain conditions, the only coherent social choice function is given by the utilitarian rule.^[1] The theorem was first proven by John Harsanyi in 1955 and has important implications for political, moral, and economic philosophy, as well as electoral systems and welfare economics.

The theorem states that any social choice function is given by a weighted sum of individual utility functions, so long as the social choice function satisfies three conditions:^[1]

• Social rationality—the social choice function satisfies von Neumann-Morgenstern rationality (or equivalently, philosophical coherence).
• Individual rationality—individual preferences (i.e. measures of well-being) satisfy the von Neumann-Morgenstern axioms.^{[note 1]}
• Pareto efficiency (unanimity)—if the entire population prefers A to B, the social choice function will prefer A to B. In other words, if an action would hurt someone but help no one, the social choice function will reject it.

The theorem implies that if society and individuals behave rationally and consistently under uncertainty, and society respects individual preferences, then society must adopt a utilitarian rule for social decision making.

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