Random expected utility and certainty equivalents: mimicry of probability weighting functions

For simple prospects routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank-dependent preferences. That is, a subject with random expected utility preferences can have expected certainty equivalents exactly like those predicted by rank-dependent probability weighting functions of the inverse-s shape discussed by Quiggin (J Econ Behav Organ 3:323–343, 1982) and advocated by Tversky and Kahneman (J Risk Uncertainty 5:297–323, 1992), Prelec (Econometrica 66:497–527, 1998) and other scholars. Certainty equivalents may not nonparametrically identify preferences: Their conditional expectation (and critically, their interpretation) depends on assumptions concerning the source of their variability.