Allais Paradoxes Can be Reversed by Presenting Choices in Canonical Split Form

This paper tests Birnbaum’s (2004) theory that the constant consequence paradoxes of Allais are due to violations of coalescing, the assumption that when two branches lead to the same consequence, they can be combined by adding their probabilities. Rank dependent utility and cumulative prospect theory imply that the Allais paradoxes are due to violations of restricted branch independence, a weaker form of Savage’s sure thing axiom. This paper will analyze separately whether erroneous random response variation might be responsible for these two effects. When errors are factored out, violations of restricted branch independence also remain significant and opposite from the direction of Allais paradoxes, suggesting that models such as CPT that attribute Allais paradoxes to violations of restricted branch independence should be rejected.