Explaining rank-dependent utility with regret and rejoicing

We fill a gap in the literature by formally defining the notion of aversion to risk of regret. An agent is sensitive to regret when her ex-post utility depends upon the forgone best payoff. An increase in the risk of regret occurs when the actual payoff and this best alternative become statistically less concordant. Accordingly, regret-risk aversion is characterized by the supermodularity of the bivariate utility function. We define a measure of regret-risk aversion in the small and in the large. We show that more regretrisk- averse agents are more willing to choose the risky act in a one-risky-one-safe menu, and that this bias is increasing in the skewness of the risky choice. This can explain the "possibility effect" that is well documented in decision theory. Symmetrically, we define the aversion to elation-risk that can prevail when the ex-post utility is alternatively sensitive to the forgone worst payoff. We show that elation-risk-seeking can explain the "certainty effect". We also show that a regret-risk-averse and elation-risk-seeking people behave as if they would have rank-dependent utility preferences with an inverse-S shaped probability weighting function that reproduces estimations existing in the literature.