Intemperate fourth-order lottery choices under rank-dependent utility

In the experimental literature, Cumulative Prospect Theory (CPT), evaluated from the status quo reference point, and Rank Dependent Utility (RDU) are often assumed to imply the same fourth-order lottery choices. In this note, we show that this equivalence need not hold. The RDU model, calibrated with the standard probability weighting and power value functions, and representative parameter values from Tversky and Kahneman (1992) and Bernheim and Sprenger (2020), chooses the intemperate lottery, whereas the CPT DM, evaluated from the status quo reference point with the same parameter values chooses the temperate lottery. The divergence arises because RDU and CPT assign cumulative probability weights differently in this lottery setting. The result suggests that RDU may help explain the relatively high proportion of intemperate choices reported in experimental studies.