Decision theory,linear partial information and statistical dominance

The paper deals with decision making under conditions of linear partial information, i.e. when probabilities of states of nature are not known precisely, but are subject to linear constraints. Conditions ensuring strict and weak statistical dominance of one strategy over another are derived. It is also shown that weak dominance in terms of payoffs is equivalent to weak dominance in terms of regrets. The new results are more general than those obtained by Fishburn and by Kmietowicz and Pearman for weak and strict ranking of probabilities, and include them as special cases. The new results can be employed in practical decision making in several ways.