Nonlinear perception of risk is integrated into models of decision under ambiguity, thereby providing a theoretical basis for behavioral analyses that involve both risk and ambiguity. The main model replaces the risk front of maxmin expected utility by rank-dependent utility, and it is derived from simple, observable axioms that are not restricted to expected utility under risk. The model highlights the interaction between risk attitude and ambiguity attitude, and it is compatible with the paradoxical choices hypothesized by Machina. Following the same idea, nonlinear perception of risk can also be integrated into variational and multiplier preferences. When applied to comparative ambiguity attitudes, the idea enables more comparisons by allowing for both heterogeneous taste and perception of risk.
