Risk attributes theory: Decision making under risk

Abstract

In this paper, some limitations in the conventional theories and models of the decision making under risk are presented from a new angle. To eliminate those limitations, a theoretical framework is proposed, in which the risk preference relation is constructed on a set of risk attributes instead of risky prospects. The axioms are presented to ensure the existence of the representation function for this risk preference relation through employing the Multi-attribute Utility Theory (MAUT). In our framework, we construct a risk decision model with four risk attributes. One of these attributes measured by a newly defined attribute measurement, the Relative Maximum Absolute Value (RMAV), can be employed in our model to explain the experimental result more intuitively compared with the overweighting of small probability proposed by Kahneman and Tversky in their Prospect Theory. In addition, the validity of the model is testified by applying it to explain the Allais Paradox and the Fourfold Pattern of Risk Attitudes. The advantages of our theory are summarized to complete this paper. Since our model is based on an axiomatized preference relation and has a good descriptive ability, it can either serve as a normative or a descriptive decision model under risk.