Theories of decision under risk that model risk averse behavior with decreasing marginal utility of money have previously been critiqued with calibration analyses. This paper introduces a dual calibration critique that applies to decision theories that represent risk aversion with nonlinear transformation of probabilities or nonlinear transformation of payoffs or both types of transformations. The dual calibration critique makes clear how plausibility problems with theories of decision under risk are fundamental. Testable calibration propositions are derived that apply to dual theory of expected utility, cumulative prospect theory, rank dependent utility theory, and expected utility theory. Heretofore, calibration critiques have been based on thought experiments. This paper reports real experiments that provide data on the empirical relevance of the calibration critique to evaluating the plausibility of theories of decision under risk.
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