Cumulative Prospect Theory (CPT), published by Tversky and Kahneman in 1992, resolved a significant limitation of the original 1979 prospect theory: violations of first-order stochastic dominance. In the original theory, probability weighting was applied to individual outcome probabilities, which could lead to preferring dominated prospects. CPT applies weighting to cumulative probabilities instead, using a rank-dependent scheme.
Rank-Dependent Weighting
π₁⁺ = w⁺(p₁)
πᵢ⁺ = w⁺(p₁ + ... + pᵢ) − w⁺(p₁ + ... + pᵢ₋₁)
For losses (ranked similarly):
Decision weights use w⁻ applied to cumulative probabilities from below
The key innovation is that decision weights depend on the rank of each outcome, not just its probability. The best gain and worst loss receive disproportionate weight (because w overweights the tails of the cumulative distribution), while intermediate outcomes receive less weight. This captures the common observation that people focus on extreme outcomes.
Properties
CPT maintains all the psychologically important properties of original prospect theory — reference dependence, loss aversion, diminishing sensitivity — while satisfying stochastic dominance. It also allows separate probability weighting functions for gains (w⁺) and losses (w⁻), accommodating the empirical finding that the degree of probability distortion differs across domains. CPT is now the standard formulation used in behavioral economics, finance, and formal decision analysis.