Stochastic Dominance Decision Rules when the Attributes are Utility Independent

In multivariate decisions under risk, assessing the complete utility function can be a major obstacle. Decision rules are investigated which characterize uniformly better alternatives with respect to a whole class of utility functions. In this paper independence assumptions are imposed on the preference structure while the levels of attributes may be stochastically dependent in an arbitrary way.

The utilities considered are additive, multiplicative, or multilinear. Necessary and sufficient conditions are developed for uniform decisions over utilities with common substitutional structure and where the univariate conditional utilities show qualitative properties such as risk aversion. The rules are direct extensions of known univariate rules and easy to evaluate.