Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

Abstract

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.

Uncertainty Breeds Decreasing Impatience: The Role of Risk Preferences in Time Discounting

“…As Table III reveals, the value of the curvature parameter η of the utility function, 1.022, is not distinguishable from unity on average, with little variation across discounting types. The average subproportionality index α amounts to 0.499, indicating a pronounced departure from linear probability weighting in line with previous findings (Tversky and Kahneman, 1992;Gonzalez and Wu, 1999;Bruhin, Fehr-Duda, and Epper, 2007). 13 The overall picture revealed by our data is consistent with the typical empirical findings: On average, subjects systematically violate linear probability weighting and constant discounting.…”

“…This function is subproportional everywhere and, additionally, inverse S-shaped, which is in accordance with abundant empirical evidence (Tversky and Kahneman, 1992;Gonzalez and Wu, 1999;Abdellaoui, 2000;Bruhin, Fehr-Duda, and Epper, 2007). It conveniently captures the degree of departure from linearity by its single parameter α: A smaller value of α implies a more subproportional and more S-shaped probability weighting curve.…”

“…Intuitively speaking, scaling down the original probabilities makes them less distinguishable from each other and, therefore, the larger outcome tends to become more salient to the decision maker. That nonlinear probability weighting is the rule and not the exception has recently been shown by a finite mixture regression study which classifies individual decision makers according to their observed risk taking behavior: Bruhin, Fehr-Duda, and Epper (2008) find that, in three different data sets, 80% of the subjects exhibit substantial departures from linear probability weighting, whereas only 20% are not prone to such behavior.…”

From Uniform Expected Utility to Uniform Rank-Dependent Utility: An experimental study

“…The UEU criterion cannot account 515 for this choice pattern. However, if we assume that the subjects assign larger weights to the most attractive outcomes (k = 3), and that they use the simplest possible utility function u(x) = x, URDU with weight restriction (10) can predict the observed modal choice pattern. Using (11), we find that the weights for set A are w 2 1 = k/(1 + k) = 3/4 and w 2 2 = 1/(1 + k) = 1/4.…”

“…In the literature concerning RDU, there is a remarkable degree of convergence between studies regarding the functional form of the weighting function; the key ingredient for accurate predictions appears to be an inverted S-shaped 580 weighting function, where the lowest and (to a lesser degree) the highest outcomes are simultaneously overweighted at the expense of the middle ones [e.g., 2, 8,10,15,30]. In our study, however, we are able to explain the majority of the results with an overweighting of the most favorable outcomes (k > 1), which seems atypical if compared with the findings for risky decision making.…”