On the Shape of the Probability Weighting Function

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.…”

Why environmental and resource economists should care about non-expected utility models

“…It can be done using a variety of approaches, with the recent literature favoring the trade-off approach (Wakker and Deneffe, 1996). 4 Empirical work has elicited PWFs for mostly monetary, such as Gonzalez and Wu (1999), and much less frequently lifeduration, gambles, with a mixture of outcomes (see Bleichrodt and Pinto, 2000;or Wakker and Deneffe, 1996). For example, the PWF in the monetary-gamble domain is concave for low probabilities and convex for high probabilities with the weight equivalent to the actual probability ranging between 0.3 and 0.5 (Prelec, 1999).…”

“…(4) varies: there is not one weighting function that best approximates relationships for everyone in the sample. Gonzalez and Wu (1999) suggest a two-parameter specification for the probability weighting function, and also suggest a non-parametric approach, making no assumptions about the form. The latter would allow each individual to exhibit their own weighting function.…”

The internal consistency of the standard gamble: tests after adjusting for prospect theory

“…Transformed probabilities equal one when p = 1 and zero when p = 0, and are non-decreasing with probability. The common empirical finding is that individuals transform probabilities in an inverse S-shaped pattern (e.g., Abdellaoui, 2000;Bleichrodt and Pinto, 2000;Bleichrodt et al, 1999;Camerer and Ho, 1994;Gonzalez and Wu, 1999;Kahneman and Tversky, 1979;Lattimore et al, 1992;Tversky and Fox, 1995;Tversky and Kahneman, 1992;Wu and Gonzalez, 1996;, such that people appear to overweight small probabilities, underweight large probabilities, and perceive w(p) as equal to p at approximately 0.4. This general pattern is observed in the domains of both gains and losses (e.g., see Bleichrodt, 2001;Tversky and Kahneman, 1992).…”