Arrovian Aggregation via Pairwise Utilitarianism.

We consider Arrovian aggregation of preferences over lotteries that are represented by skew-symmetric bilinear (SSB) utility functions, a significant generalization of von Neumann-Morgenstern utility functions due to Fishburn, in which utility is assigned to pairs of alternatives. We show that the largest domain of preferences that simultaneously allows for independence of irrelevant alternatives and Pareto optimality when comparing lotteries based on accumulated SSB welfare is a domain in which preferences over lotteries are completely determined by ordinal preferences over pure alternatives. In particular, a lottery is preferred to another lottery if and only if the former is more likely to return a preferred alternative. Preferences over pure alternatives are unrestricted. We argue that SSB welfare maximization for this domain constitutes an appealing probabilistic social choice function.