Separating curvature and elevation: A parametric probability weighting function

This paper presents a preference foundation for a two-parameter family of probability weighting functions. We provide a theoretical link between the well-established notions of probabilistic risk attitudes (i.e., optimism and pessimism) used in economics and the important independent measures for individual behavior used in the psychology literature (i.e., curvature and elevation). One of the parameters in our model measures curvature and represents the diminishing effect of optimism and pessimism when moving away from extreme probabilities 0 and 1. The other parameter measures elevation and represents the relative strength of optimism vs. pessimism. Our empirical analysis indicates that the new weighting function fits elicited probability weights well, and that it can explain differences in the treatment of probabilities for gains compared to that for probabilities of losses.