Conditioning and Updating Under Cumulative Prospect Theory

Abstract

Under expected utility theory, unconditional expected utility can be decomposed into a weighted sum of conditional expected utilities where the weights are marginal probabilities. We derive necessary and sufficient conditions for a similar decomposition in the framework of Cumulative Prospect Theory (CPT). The conditions also ensure that a decision maker’s conditional preferences (given some event) remain within the CPT class. Our results are important for empirical analyses in which weighted marginal probabilities of events are used to explain a decision maker’s choices. The use of such marginal probabilities is a practical necessity in non-experimental settings.

Keywords: cumulative prospect theory, probability weighting function, conditioning, updating, dynamic consistency, consequentialism

JEL Classification: D80, D84