Decision Making Under Ambiguity: A Belief-function Perspective

Abstract

In this article, we discuss problems with probability theory in representing uncertainties encountered in the "real world" and show how belief functions can overcome these difficulties. Also, we discuss an expected utility approach of decision making under ambiguity using the belief function framework. In particular, we develop a proposition for decision making under ambiguity using the expected utility theory. This proposition is based on Strat's approach of resolving ambiguity in the problem using belief functions. We use the proposition to explain the Ellsberg paradox and model the decision making behavior under ambiguity. We use the empirical data of Einhorn and Hogarth to validate the proposition. Also, we use the proposition to predict several decision making behaviors under ambiguity for special conditions. Furthermore, we discuss the general condition under which the "switching" behavior, as observed by Einhorn and Hogarth, will occur using the concept of "precision measure" in the expected utility theory.