Decision theory, strict ranking of probabilities, and statistical dominance

In this paper the authors extend Fishburn's analysis of statistical dominance of one strategy by another to the case of strict ranking of probabilities of states of nature. Conditions ensuring strict dominance are derived, and it is shown that Fishburn's results for weak ranking of probabilities are a special case of the more general results presented here. Conditions for weak dominance, a criterion proposed elsewhere by the authors, are also derived. The latter results are particularly useful when strict dominance cannot be established. This happens frequently in practice. Two numerical examples, one concerned with employment planning and the other with transport investment, illustrate possible areas of application of this approach to decisionmaking and show the ease with which the calculations can be made.