Probability weighting function
Also known as: Weighting function shape
The inverse-S curve describing exactly how stated odds get distorted into decision weights.
What it means
The probability weighting function is the specific mathematical curve that maps objective probabilities onto the decision weights used in prospect theory. Its characteristic inverse-S shape is concave for small probabilities (overweighting) and convex for moderate-to-large ones (underweighting), crossing the identity line around the 0.3 to 0.4 region, with steep changes near the endpoints of zero and one. Two psychological parameters are often distinguished: curvature, which captures sensitivity to probability changes, and elevation, which captures overall optimism or attractiveness of gambling. Empirical estimates from cumulative prospect theory pin down typical parameter values, and the function differs for gains versus losses and across individuals and domains. It is the formal object that generates the certainty effect, the possibility effect, and the fourfold pattern.
Examples
Plotted out, the curve shows a 1% chance treated as if it were nearer 5%, while a 90% chance is treated as if it were closer to 80%.
A 5% chance of rain sends people out with umbrellas, while the difference between a 60% and a 70% forecast changes almost nothing — steep at the ends, flat in the middle.
Fitted to the same person, the curve sits higher for losses than gains: a 2% chance of a house fire buys insurance, while a 2% shot at a bonus barely registers.
First described in Tversky & Kahneman (1992); Gonzalez & Wu (1999).