A critical reinterpretation of Shacklean decision theory

Shackle was one of the representative critics of probability calculus. His alternative decision theory was mathematically reformalized by Katzner till 1990s. Following the Katzner's reformalized framework, this paper presents a new interpretation of Shacklean theory by focusing on the common stage structure of the decision-making. This paper shows that the characteristics of Shackle-Katzner framework can be explained as: (1) the non-distributive and non-additive ordinal measure of subjective uncertainty, (2) the incomplete list of imaginable future states, (3) the valuation of "importance" reflecting various types of loss-psychology, and (4) the final choice of the action is made on the set of importance intervals. The purpose of this paper is to investigate how the foundational stance of Shackle-Katzner framework about the decision-making elicits the different formal structure, and to provide a new interpretation of Shacklean decision theory.