What Is Prospect Theory?
Prospect theory, developed by Daniel Kahneman and Amos Tversky in their landmark 1979 paper, is the most influential descriptive model of decision-making under risk. Unlike expected utility theory — which assumes people evaluate final wealth states using a concave utility function — prospect theory proposes that people evaluate changes relative to a reference point, are loss averse, exhibit diminishing sensitivity, and distort probabilities.
The S-Shaped Value Function
The left panel shows the value function v(x), which has three key features: (1) it is defined over gains and losses relative to a reference point, not over total wealth; (2) it is concave for gains and convex for losses — reflecting diminishing sensitivity to both gains and losses; (3) it is steeper for losses than for gains — capturing loss aversion. The parameter α controls curvature (diminishing sensitivity) and λ controls the steepness asymmetry (loss aversion).
Probability Weighting
The right panel shows the probability weighting function w(p). In expected utility theory, a 10% chance is weighted at exactly 0.10. In prospect theory, small probabilities are overweighted (w(0.05) > 0.05) and large probabilities are underweighted (w(0.95) < 0.95). The 45-degree line represents unbiased weighting. The parameter γ controls the curvature: lower γ means more distortion.
Why It Matters
Prospect theory explains a wide range of seemingly irrational behaviors: why people simultaneously buy lottery tickets (overweighting small probabilities of large gains) and insurance (overweighting small probabilities of large losses); why investors hold losing stocks too long (loss aversion plus risk-seeking in the loss domain) and sell winners too early (risk aversion in the gain domain); and why framing the same outcome as a gain or loss changes decisions (reference point dependence).