Decision Making with Linear Partial Information (L.P.I.)

This paper deals with decision making in a set of circumstances intermediate between the classical extremes of pure risk and pure uncertainty. It extends the Cannon-Kmietowicz-Pearman methods of finding maximum and minimum expected values of strategies, when probabilities of occurrence of future states of nature can be ranked, to the more general case investigated by Kofler and Menges, in which a set of linear constraints is imposed on the probabilities. A general solution to the problem is obtained, and its relationship to earlier results is discussed. A new criterion for strategy choice, in the condition mentioned above, is also proposed. It recommends selection of a strategy with the highest minimum expected utility (max E_min). The criterion arises naturally from the extension of the von Neumann-Morgenstern utility theory to the case of incomplete knowledge about the probabilities. These developments greatly enhance the attractiveness of the earlier results for applied work and lay foundations for further theoretical advances.