Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a "multi-profile" context. Harsanyi was contented with showing that if the individuals' utilities u_i are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u_i. We provide a related conclusion by considering u as functionally dependent on the u_i, through a suitably restricted "social welfare functional" (u₁,..., u_n)→u=f(u₁,..., u_n). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's "single-profile" theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the u_i discussed by Fishburn as a corollary to harsanyi's theorem.