Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct nonparametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank‐dependent, or that the weighting function is nearly linear. Nonparametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well‐known certainty effect.