Stochastic Orderings from Partially Known Utility Functions

In an expected utility analysis of a decision problem, knowledge of the utility function at a few selected points may be available. When combined with general properties such as monotonicity or concavity, the limited knowledge of the utility function may be sufficient for ranking a pair of probability distributions unambiguously. Necessary and sufficient conditions for such stochastic orderings are presented for the following cases of partially specified utility functions: nondecreasing functions, and nondecreasing concave functions. Examples of these orderings are presented.