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Can any prominent theory of decision under risk rationalize both small-stakes risk aversion and largestakes risk aversion? Do some prominent theories fail to rationalize patterns of same-stakes risk aversion? How do reference payoffs enter in the answer to these questions? What would be the characteristics of a theory of decision under risk that would be immune to calibration critique? We offer a theoretical duality analysis that addresses these questions. We report dual propositions and corollaries that calibrate the implications of nonlinear transformation of probabilities or payoffs (or both). We also report several experiments that provide data on the empirical relevance of the two types of calibration patterns.


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