Expected utility for decision making with subjective models

Abstract

According to Savage “a state of the world is a description of the world, leaving no relevant aspect undescribed”. This paper presents an analysis of decision situations in which the decision maker feels he may be unaware of some aspects which are relevant for the determination of the consequences of his actions, and therefore does not think that the model on which his decision is based is a faithful representation of reality. In the present interpretation, in such situations the decision maker need not believe that all actions which are perceived as resulting with certainty in one consequence will necessarily do so. Hence the decision maker contemplating such an action — represented in the model by a constant map from the state space into the consequence space — will not necessarily rank it as indifferent to the corresponding consequence itself. A representation result is presented in which the decision maker evaluates actions not directly through the maps which represent them but through maps corrected by bringing extreme consequences closer to a central one. The latter reflects a first-approximation evaluation of the set of competing alternatives available in the given decision situation.