Sustainable social choice under risk

The question addressed in this paper is what kinds of welfare criteria are sustainable, when the future states of the world evolve according to a stochastic process. A stochastic process determines an infinite sequence of ex-ante probability distributions over the states of the world. It is shown that when a social welfare order over such sequences is complete, transitive, continuous, and gives no dictatorship either to the present or the future, then it is represented by a convex combination of an integral over a countably additive measure and an integral over a purely finitely additive measure. The notions of symmetric treatment of the present and the future, stationarity for the present and anonymity for the future are introduced. According to the symmetric treatment, the distributions of the states of the world in the present, when constant in time, and in the distant future can be interchanged without affecting the welfare. The sustainable social welfare order that treats the present and the future symmetrically and satisfies stationarity for the present and anonymity for the future is a sum of the discounted average of the expected utility and the expected utility over the occupation measure of the stochastic process. (C) 2018 Elsevier B.V. All rights reserved.