Non-expected utility theories: Weighted expected, rank dependent, and, cumulative prospect theory utility

Abstract

Expected utility theory serves as the standard model for decision-making under uncertainty, yet empirical evidence reveals systematic violations of its core axioms. The independence axiom, in particular, fails to account for the Allais paradox, wherein agents demonstrate non-linear weighting of probabilities. Furthermore, the one-dimensional characterization of risk aversion in the von Neumann-Morgenstern framework leads to logically inconsistent predictions when scaling from small to large stakes. Alternative frameworks—weighted expected utility, rank dependent utility, and cumulative prospect theory—mitigate these deficiencies by relaxing the independence axiom and allowing for more sophisticated risk characterizations. Weighted expected utility introduces a weighting function that permits indifference curves to fan out, reconciling choice behavior with experimental observations. Rank dependent utility utilizes cumulative probability transformations to preserve monotonicity while accounting for the relative ranking of outcomes. Cumulative prospect theory extends these concepts by measuring payoffs relative to a status quo reference point and incorporating diminishing sensitivity and loss aversion. Collectively, these non-expected utility theories provide a more robust descriptive account of human behavior by acknowledging that risk preferences are influenced by both the magnitude of outcomes and the subjective transformation of their associated probabilities. – AI-generated abstract.