Decision Making with Qualitative Utility: A Model for Generalizing Expected Utility Maximization

Title: Decision Making with Qualitative Utility: A Model for Generalizing Expected Utility Maximization

Abstract: This research proposes a deviation from the von Neumann-Morgenstern (vNM) postulates paradigm in decision theory. It suggests that it may be rational to judge alternatives according to the issues in their main focus. If these issues are deemed as equal, the alternatives will continue to be judged as equal even if they are mixed with different side-effects. This contradicts the vNM Independence axiom. Moreover, outcomes of issues in the main focus may completely overshadow the outcomes of the side-issues, so alternatives of the former may be judged as infinitely more (or infinitely less) preferable than those of the latter. This contradicts the vNM Continuity axiom. The research provides examples to illustrate these points and introduces a new model for decision making: Expected Qualitative Utility Maximization. This model encompasses the Maximin criterion and relaxes both the Independence and Continuity postulates. It uses the definition of a qualitative order on nonstandard models of the real numbers and considers nonstandard utilities. The research characterizes Expected Qualitative Utility Maximization by an original weakening of von Neumann-Morgenstern's postulates. Subjective probabilities can be defined from these weakened postulates, similar to Anscombe and Aumann's approach. Subjective probabilities are numbers, not matrices as in the Subjective Expected Lexicographic Utility approach.

Implications: The research has implications for various fields, including economics, psychology, and artificial intelligence. It challenges the traditional vNM approach to decision theory and provides a more flexible model that better reflects human decision-making processes. The research also has practical applications in areas such as healthcare, finance, and policy-making, where decisions often involve weighing different factors and considering qualitative aspects alongside quantitative ones.

Link to Article: https://arxiv.org/abs/0202023v2 Authors: arXiv ID: 0202023v2