Is There a Plausible Theory for Decision under Risk?

Theories of decision under risk that model risk averse behavior with decreasing marginal utility of money have been critiqued with concavity calibration arguments. This paper introduces a convexity calibration that applies to decision theories that represent risk aversion with nonlinear transformation of probabilities. We explain the duality of calibrations that imply implausible large stakes risk aversion for theories that represent risk averse preferences with nonlinear transformations of (a) payoffs or (b) probabilities. The dual calibrations make clear why plausibility problems with theories of decision under risk are fundamental. Heretofore, calibration critiques have been based on thought experiments. This paper reports real experiments that provide data on the empirical relevance of the critiques.