Ignorance, error, and information in the classic theory of decision

Abstract

This paper introduces an additional dimension of incompleteness or inaccuracy of information held by the decision maker. Up to this time decision theory, applicable to any level of living system, most usually the organism, has looked at situations in which there were varying degrees of ignorance about the connections between actions selected by the decision maker and the occurrence of states of affairs which the decision maker values to varying degrees. Here are introduced two notions relating to the decision maker's knowledge of states of affairs which may develop. The first is ignorance. A decision maker is ignorant if there are states of affairs which may come about as a consequence of actions open to him, but about whose possibility he is ignorant. The second is error. A decision maker commits error if he makes decisions in the belief that there is a set of outcomes which may occur, but which, in fact, includes some states of affairs which can not occur. The effects of these two types of divergence between the actual and perceived state of the world are examined under some reasonable assumptions. Under conditions of certainty, risk, and uncertainty, the probability of making mistakes and the expected cost of these mistakes are investigated. The notion of irrationality, it is suggested, can be replaced by the behavioral notion of being in a state of error or ignorance.