Universal Pareto dominance and welfare for plausible utility functions

We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents' preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.