Probability weighting and L-moments

• Novel cubic probability weighting function for rank-dependent utility theories.
• Cubic probability weighting function as a linear trade-off between three L-moments.
• Connection between economic decision theory and optimal portfolio theory in finance.
• Inverse S-shaped function = aversion to dispersion + attraction to positive skewness.
• Common ratio effect can co-exist with a reverse common ratio effect.

Several popular generalizations of expected utility theory—cumulative prospect theory, rank-dependent utility and Yaari's dual model—allow for non-linear transformation of (de-)cumulative probabilities. This paper shows an unexpected connection between probability weighting and the statistical theory of L-moments. Specifically, cubic probability weighting results in a linear tradeoff between the expected value (the first L-moment), Gini (1912) mean difference statistic (the second L-moment, also known as L-scale) and the third L-moment (measuring skewness). Inverse S-shaped probability weighting function crossing the 45° line at a probability ≤0.5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions.