Expected utility theory with imprecise probability perception: explaining preference reversals

ABSTRACT

This article presents a new model for decision-making under risk, which provides an explanation for empirically-observed preference reversals. Central to the theory is the incorporation of probability perception imprecision, which arises because of individuals’ vague understanding of numerical probabilities. We combine this concept with the use of the Alpha EU model and construct a simple model which helps us to understand anomalies, such as preference reversals and valuation gaps, discovered in the experimental economics literature, that standard models cannot explain.

KEYWORDS:

• Alpha EU model
• anomalies in expected utility theory
• decision under risk
• imprecise probability perceptions
• preference reversals valuation gaps

JEL CLASSIFICATION:

• D81

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ To clarify any possible confusion, we would like to note that in Hurwicz model, α represents the optimism of the decision maker, whereas in the decision-making under ambiguity literature, in particular Alpha EU, it represents the pessimism. Here, we follow the ambiguity literature’s convention rather than Hurwicz’s convention, and ascribe a negative meaning to the α parameter.

² We will briefly mention Willingness-to-Pay in the conclusions.

³ These lotteries are examples given in Schmidt, Starmer, and Sugden (2008). For the imprecision level, we assume that β = ψp(1−p); There is no particular reason for choosing this, except that is simple and satisfies the assumptions of the theory. See the supplementary file for the details about the calculations and the production of the graphs in the article.