Cumulative Prospect Theory (CPT), the leading behavioral account of decision making under uncertainty, assumes that the probability weight applied to a given outcome depends on its ranking. This assumption is needed to avoid the violations of dominance implied by Prospect Theory (PT). We devise a simple and direct non-parametric 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. The estimated changes in relative weights range from +3% to -3%, and in no case can we reject the hypothesis of rank-independence. Our estimates rule out changes in relative probability weights larger than a few percent as ranks change with 95% confidence. In contrast, conventional calibrations of CPT preferences for the same subjects imply that probability weights should change by 20% to 40%. Models with reference distributions (notably Koszegi and Rabin, 2006) have similar implications, and hence we falsify them as well. 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.
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