An axiomatic theory of conjoint, expected risk

This paper presents an axiomatization of subjective risk judgments that leads to a representation of risk in terms of seven free parameters. This is shown to have considerable predictive ability for risk judgments made by 10 subjects. The risk function retains many of the features of the expectation models-e.g., a constant number of parameters independent of the number of outcomes-but it also allows for asymmetric effects of transformations on positive and negative outcomes. This arises by axiomatizing independently the behavior with respect to gambles having entirely positive outcomes and those with entirely negative outcomes. Complex gambles are decomposed into these, and zero outcomes, using the expected risk property. The resulting risk function compares favorable with other functions previously suggested. It is also demonstrated that preference judgments are distinct from risk judgments, and that the theory does not apply as well to the former.