This paper builds on our previous work suggesting a functional form for how people distort probability in the context of prospect theory. Our earlier work tested simple conditions of curvature (i.e., concavity and convexity) using specially designed choice ladders. The approach in this paper is different. We use a choice-based cash equivalence procedure and then compute a global model fit. We develop a nonparametric algorithm to estimate the general shape of the distortion’s functional form. The shape is well modelled using a linear in log odds functional form.

Gonzalez, R. & Wu, G. (1999). On the shape of probability weighting function. Cognitive Psychology, 38, 129-166. 10.1006/cogp.1998.0710 PMid:10090801

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Abstract

Empirical studies have shown that decision makers do not usually treat probabilities linearly. Instead, people tend to overweight small probabilities and underweight large probabilities. One way to model such distortions in decision making under risk is through a probability weighting function. We present a nonparametric estimation procedure for assessing the probability weighting function and value function at the level of the individual subject. The evidence in the domain of gains supports a two-parameter weighting function, where each parameter is given a psychological interpretation: one parameter measures how the decision maker discriminates probabilities, and the other parameter measures how attractive the decision maker views gambling. These findings are consistent with a growing body of empirical and theoretical work attempting to establish a psychological rationale for the probability weighting function