Harsanyi's Aggregation Theorem: multi-profile version and unsettled questions

Harsanyi's Aggregation Theorem states that if the individuals' as well as the moral observer's utility functions are von Neumann-Morgenstern, and a Pareto condition holds, then the latter function is affine in terms of the former. Sen and others have objected to Harsanyi's use of this result as an argument for utilitarianism. The present article proves an analogue of the Aggregation Theorem within the multi-profile formalism of social welfare functionals. This restatement and two closely related results provide a framework in which the theorem can be compared with well-known characterisations of utilitarianism, and its ethical significance can be better appreciated. While several interpretative questions remain unsettled, it is argued that at least one major objection among those raised by Sen has been answered.The author is grateful to V. Barham, J. Broome, M. Fleurbaey, D. Hausman, S. Kolm, J. Roemer, and P. Suppes, for useful discussions and suggestions. Special thanks are due to C. d'Aspremont, N. McClennen, J. Weymark, and an anonymous referee for detailed comments on an earlier version. The usual caveat applies. The author also gratefully acknowledges financial support from the SPES programme of the Union Européenne.