Decision theory and strict ranking of probabilities

This paper is concerned with the derivation of guides to decision making in a set of circumstances intermediate between the classic extremes of pure risk and pure uncertainty. It is assumed that the decision maker can specify a subjective strict ranking of the probabilities of states of nature, in which case, given knowledge of the payoffs of a strategy, it is possible to find in a straightforward fashion, maximum and minimum expected payoffs for the strategy. If the information contained in the strict ranking is available to the decision maker, then to fail to take it into account must adversely affect the quality of decision making. The paper discusses both the interpretation and the possible practical uses of extreme expected values in decision making and includes a numerical example, based on an investment decision problem, to demonstrate the ease of use of the results obtained.