Updating Beliefs Under Risk and Uncertainty

It is possible to represent decision makers’ beliefs on the algebra R×R, rather than R alone. Doing so allows us to represent decision makers’ perceptions of risk on one part of the algebra, and their perceptions of uncertainty on the other. This paper shows that such beliefs can be updated in a ‘Bayesian’ manner and that the resulting representation of beliefs is reasonable relative to some other approaches. The model of belief formation and decision making is then used to explain some instances of anomalous economic behaviour.