In Prospect Theory, decision makers do not weight outcomes by their objective probabilities but by transformed decision weights. The probability weighting function w(p) has a characteristic inverse-S shape: it overweights small probabilities (making rare events seem more likely than they are) and underweights moderate to large probabilities. This single function explains several major anomalies in risky choice.
The Prelec Function
Prelec: w(p) = exp(−(−ln p)ᵅ)
Gains: γ ≈ 0.61
Losses: δ ≈ 0.69
Crossover point ≈ 1/3
The Fourfold Pattern
Probability weighting, combined with the value function, produces the fourfold pattern of risk attitudes: risk aversion for moderate-to-high probability gains (concavity of v dominates), risk seeking for low-probability gains (overweighting of small p dominates — lottery tickets), risk seeking for moderate-to-high probability losses (convexity of v dominates — gambling to avoid sure losses), and risk aversion for low-probability losses (overweighting of small p — insurance buying).
This fourfold pattern elegantly explains behaviors that expected utility theory cannot: why people simultaneously buy lottery tickets and insurance, why they take risks to avoid sure losses but avoid risks for sure gains, and why the same person can be both risk seeking and risk averse depending on the domain and probabilities involved.