A large literature is concerned with analysis and empirical application of theories of decision making for environments with risky outcomes. Expected value theory has been known for centuries to be subject to critique by St. Petersburg paradox arguments. More recently, theories of risk aversion have been critiqued with calibration arguments applied to concave payoff transformations. This paper extends the calibration critique to decision theories that represent risk aversion solely with transformation of probabilities. Testable calibration propositions are derived that apply to four representative decision theories: expected utility theory, cumulative prospect theory, rank-dependent expected utility theory, and dual expected utility theory. Heretofore, calibration critiques of theories of risk aversion have been based solely on thought experiments. This paper reports real experiments that provide data on the relevance of the calibration critiques to evaluating the plausibility of theories of risk aversion. The paper also discusses implications of the data for (original) prospect theory with editing of reference payoffs and for the new dual-self model of impulse control. In addition, the paper reports an experiment with a truncated St. Petersburg bet that adds to data inconsistent with risk neutrality.
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