It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from linear probability weighting, consistent with prospect theory. 20% of the subjects weight probabilities near linearly and behave essentially as expected value maximizers. Moreover, individuals are cleanly assigned to one type with probabilities close to unity. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling.

A large body of evidence has documented that risk preferences depend nonlinearly on outcome probabilities. We discuss the foundations and economic consequences of probability-dependent risk preferences and offer a practitioner's guide to understanding and modeling probability dependence. We argue that probability dependence provides a unifying framework for explaining many real-world phenomena, such as the equity premium puzzle, the long-shot bias in betting markets, and households' underdiversification and their willingness to buy small-scale insurance at exorbitant prices. Recent findings indicate that probability dependence is not just a feature of laboratory data, but is indeed manifest in financial, insurance, and betting markets. The neglect of probability dependence may prevent researchers from understanding and predicting important phenomena.

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that the increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. Contrary to gains, no coherent change in relative risk aversion is observed for losses. These results not only challenge expected utility theory, but also prospect theory.

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people's proneness to probability distortions.