TY - JOUR

T1 - Indistinguishability of small probabilities, subproportionality, and the common ratio effect

AU - Dierkes, Maik

AU - Sejdiu, Vulnet

N1 - Funding information: Financial support by the Dr. Werner Jackstädt Foundation, Germany is gratefully acknowledged.

PY - 2019/12

Y1 - 2019/12

N2 - We 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.

AB - We 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.

KW - Common ratio effect

KW - Indistinguishability of small probabilities

KW - Probability weighting

KW - Subproportionality

UR - http://www.scopus.com/inward/record.url?scp=85074330009&partnerID=8YFLogxK

U2 - 10.1016/j.jmp.2019.102283

DO - 10.1016/j.jmp.2019.102283

M3 - Article

AN - SCOPUS:85074330009

VL - 93

JO - Journal of mathematical psychology

JF - Journal of mathematical psychology

SN - 0022-2496

M1 - 102283

ER -