The general theory of decisions

Abstract

The majority of the existing decision theories, starting from von Neumann and Morgenstern Expected Utility theory, are based on sound mathematical background and yielded good results. However, they are developed for solving particular decision situations. Consequently, nowadays there is no theory to unite main directions of decision analysis. The existing main theories suffer from several important disadvantages: (i) use of numerical techniques which contrast with real-world imperfect information; (ii) the assumptions of well-structured knowledge about future objective conditions; (iii) the use of probability measures whereas real-world probabilities are imprecise; (iv) the use binary logic-based preference relations, whereas real preferences may be vague; (v) no account for the fact that a human being reasons with linguistic description of information; (vi) parametrical modeling of behavioral determinants without account for interaction; (vii) missing partial reliability of real decision-relevant information. Thus, it becomes needed to develop a general theory of decisions that would be free of the limitations outlined above. In this paper, we propose the fundamentals of the new general theory of decisions which is based on complex consideration of imperfect decision-relevant information issues and behavioral aspects. We illustrate that the existing theories including Expected Utility of von Neumann and Morgenstern, Prospect Theory, Choquet Expected Utility, Cumulative Prospect Theory and other theories are special cases of the suggested general theory of decisions. We provide axioms and principles, the corresponding mathematical methodologies of decision analysis and auxiliary formal techniques. The application of the suggested theory is illustrated with the aid of a benchmark complex decision problem.