Rank-dependent utility
Also known as: Rank-dependent expected utility
Probabilities are weighted by an outcome's rank, not one at a time, so dominance is preserved.
What it means
Rank-dependent utility is a theory of choice under risk in which probabilities are transformed through a weighting function applied to the cumulative distribution of outcomes ordered by rank, rather than to each outcome's probability in isolation. This rank-ordering device lets the model accommodate the overweighting of extreme outcomes and the certainty effect while, unlike the original prospect theory, never violating first-order stochastic dominance. It supplied the mathematical machinery that Tversky and Kahneman adopted for cumulative prospect theory, where the same cumulative weighting is applied separately to gains and to losses. The approach generalizes expected utility — which it recovers when the weighting function is the identity — and underlies much modern decision theory. Its key insight is that how a probability is weighted depends on how good or bad its outcome is relative to the others.
Examples
The best possible outcome in a gamble can be overweighted precisely because it sits at the top of the rank order, capturing the allure of a jackpot.
Insurance sells because the worst outcome sits at the bottom of the rank order and gets extra weight: a one-in-ten-thousand house fire feels heavy enough to pay a premium against every year.
Add a pound to every prize in a raffle and rank-dependent utility still prefers it — unlike original prospect theory, cumulative weighting can never rate the dominated raffle higher.
First described in John Quiggin (1982).