Probabilities in Decision Rules

Abstract

Principles of rational decision making are important in the behavioral sciences such as economics (especially microeconomics) and psychology (especially cognitive psychology). The principles use subjective probabilities because these probabilities are accessible. This paper explains how the requirement of accessibility regulates probability laws and decision principles. It proposes relativizing probabilities to ways of grasping propositions (in addition to relativizing them to times and agents). The relativization promotes psychological realism. Pronouns, demonstratives, proper names, and other expressions refer directly without the intermediary of a concept. Hence two sentences may express the same proposition although an ideal agent who understands both sentences is unaware of their synonymy. An ideal agent may thus assign two probabilities to a proposition. Relativization to ways of grasping propositions resolves the inconsistency. It generalizes the usual version of the probability laws and yields it as a special case. Relativizing probabilities to ways of grasping propositions makes a decision’s rationality relative to the way the agent frames the decision. Most framing effects arise from logical mistakes and misunderstanding propositions. However, because of multiple ways of grasping the same proposition, they may also arise from lack of empirical information. Then they influence the rationality of decisions made by cognitively ideal agents. Acknowledging this influence revolutionizes normative decision theory.