Inside Prospect Theory: How the probability of outcomes changes attitudes towards risk

In Cumulative Prospect Theory, risk attitudes follow from the integration of the value function and of the probability distortions caused by the probability weighting function. However, textbooks and popular science books discuss the two functions separately, emphasize the role of the value function on risk attitudes, and exemplify the role of the probability distortions only for very low probabilities. In some instances, the predictions of this “teaching version” of the theory fall quite far from those of the actual theory. In this paper, we calculate the probability thresholds that determine risk attitude inversions – with respect to those expected from the value function alone – for different combination of the theory parameters, including the most used ones. Those thresholds were never reported explicitly in previous literature. We show that risk attitudes inversions can occur for simple prospects with quite high probabilities of the outcome (in some instances, up to 70%). A survey circulated to university teachers of prospect theory showed that risk attitudes inversions at such levels of probability are not commonly taken into consideration. Some untested empirical predictions of Cumulative Prospect Theory follow from the properties of the thresholds for risk attitude inversions.