Indistinguishability of small probabilities, subproportionality, and the common ratio effect

Publication date: December 2019Source: Journal of Mathematical Psychology, Volume 93Author(s): Maik Dierkes, Vulnet SejdiuAbstractWe show that, in the framework of Cumulative Prospect Theory, subproportionality as a property of the probability weighting function alone does not automatically imply the common ratio effect. This issue is particularly relevant for equal-mean lotteries because both risk-averse and risk-seeking behavior have to be predicted there. As a solution, we propose three simple properties of the probability weighting function which are sufficient to accommodate the empirical evidence on the common ratio effect for equal-mean lotteries for any S-shaped value function. These are (1) subproportionality, (2) indistinguishability of small probabilities, and (3) an intersection point with the diagonal lower than 0.5. While subproportionality and a fixed point lower than 0.5 are common assumptions in the literature, the property indistinguishability of small probabilities is introduced for the first time. The ratio of decision weights for infinitesimally small probabilities characterizes indistinguishability and is also an informative measure for the curvature of the probability weighting function at zero. The intuition behind indistinguishability is that, even though the ratio of probabilities stays constant, individuals tend to neglect this relative difference when probabilities get smaller.

Source: Journal of Mathematical Psychology - November 7, 2019 Category: Psychiatry & Psychology Source Type: research