Prospect Theory, proposed by Daniel Kahneman and Amos Tversky in 1979, is arguably the most influential descriptive theory of decision making under risk. It replaced Expected Utility Theory as the dominant model of risky choice by incorporating three key empirical regularities: reference dependence, loss aversion, and probability weighting.
The Value Function
Unlike utility theory, which defines outcomes in terms of final wealth, Prospect Theory evaluates outcomes as gains or losses relative to a reference point. The value function v(x) is concave for gains (diminishing sensitivity to increasing gains) and convex for losses (diminishing sensitivity to increasing losses), and steeper for losses than for gains (loss aversion, with λ ≈ 2.25).
v(x) = −λ(−x)ᵝ for x < 0
where α = β ≈ 0.88, λ ≈ 2.25
Probability Weighting
The probability weighting function π(p) transforms objective probabilities into decision weights. It overweights small probabilities (explaining lottery ticket purchases and insurance buying) and underweights moderate-to-large probabilities. The weighting function is characterized by its inverse-S shape and is parameterized differently for gains (γ ≈ 0.61) and losses (δ ≈ 0.69).
Cumulative Prospect Theory
The 1992 refinement, Cumulative Prospect Theory (CPT), applies probability weighting to cumulative rather than individual probabilities, satisfying stochastic dominance. CPT uses a rank-dependent transformation: the decision weight for each outcome depends not on its probability alone but on its rank among other outcomes. This version is the standard formulation used in modern applications.