Sufficient Conditions for Multivariate Almost Stochastic Dominance under Dependence Uncertainty (Revision 2 )

Most often important decisions involve several unknown attributes. This produces a double challenge in the sense that both assessing the individual multiattribute preferences and the joint distribution of the attributes can be extremely hard. In this respect, it would be useful to have sufficient conditions for the dominance of one random vector over another under dependence uncertainty, when only partial information on the joint distributions of the two vectors is available, for instance, when only the marginals or just the first two marginal moments are known. Sufficient conditions for multivariate stochastic dominance under dependence uncertainty can be obtained only in very special cases. In this paper the authors develop sufficient conditions for multivariate almost stochastic dominance based on marginal distributions of the attributes or just on their means and variances. To make use of multivariate almost stochastic dominance, preferences are elicited either in terms of bounds on marginal utilities or via transfers. The authors apply the theoretical results to comparing the efficiency of photovoltaic plants.