This paper presents a new theory, called Preference Cloud Theory, of decision-making under uncertainty. This new theory provides an explanation for empirically-observed Preference reversals. Central to the theory is the incorporation of preference imprecision which arises because of individuals’ vague understanding of numerical probabilities. We combine this concept with the use of the Alpha model (which builds on Hurwicz’s criterion) and construct a simple model which helps us to understand various anomalies discovered in the experimental economics literature that standard models cannot explain.