The Fourfold Pattern of Risk Attitudes

Definition

Risk attitude isn't a fixed trait — it flips depending on the sign of the outcome and the size of the probability. Kahneman and Tversky's cumulative prospect theory predicts and confirms "a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability." The pattern comes from combining two separate distortions: an S-shaped value function (concave for gains, convex for losses) and a probability-weighting function that underweights moderate-to-high probabilities but overweights small ones.

In the Book

Chapter 1 lays the mechanism out concretely: an 85% chance to lose $1,000 versus a sure loss of $800 is preferred by most people (risk-seeking in losses, despite the gamble's worse expected value), which mirrors ordinary risk aversion for an 85% chance to win $1,000 versus a sure $800 gain. Chapter 3 formalizes this with an experiment on 25 subjects (Table 3.4), showing the pattern holds for 22 of them individually, not just in aggregate — and stress-tests it against alternative explanations by looking at cross-subject correlations, which come out near zero, ruling out a simple "trait" of general risk aversion or risk seeking. The book also traces the low-probability half of the pattern to real markets: the same overweighting of small probabilities that makes people risk-seeking for a lottery ticket (a small chance of a large gain) makes them risk-averse enough to buy insurance (paying a certain small loss to avoid a small chance of a large loss).

Why It Matters

A single number — "risk tolerance" — cannot predict someone's choices across situations, because the same person is reliably risk-averse in one quadrant (likely gains, unlikely losses) and reliably risk-seeking in the other two. This explains otherwise-puzzling co-occurrences: the person who buys both lottery tickets and insurance isn't inconsistent, they're following the same probability-weighting curve into two different quadrants. Anywhere a decision-maker faces choices framed as probable versus improbable gains or losses — investing, litigation settlement, safety spending — knowing which quadrant you're in predicts the bias before you see the choice.