Stochastic choice and preference reversals

The preference reversal phenomenon is one of the most important, long-standing, and widespread anomalies contradicting economic models of decisions under risk. It describes the robust observation of frequent "standard reversals" where long-shot gambles are valued above moderate ones but then the latter are chosen, while the opposite "nonstandard reversals" happen rarely. This inconsistency casts severe doubts on commonly-used preference elicitation methods. Strikingly, alternative designs which should eliminate the phenomenon produce frequent nonstandard reversals instead, in a puzzling reversal of the phenomenon. We develop and test a model predicting when the phenomenon should occur, when its reversal should occur instead, and what determines the magnitude of the effects. The reversal of the phenomenon is predicted as a consequence of stochastic choice and risk aversion, without invoking any behavioral bias. The original phenomenon arises from stochastic choice and a systematic bias in monetary valuations, which is restricted to long-shot gambles. To validate the model, we conduct two experiments leading to the preference reversal phenomenon and its reversal, respectively. We employ a novel empirical approach allowing us to disentangle choice and valuation errors by relying on utilities estimated out of sample, and confirm that reversals are associated with errors in monetary valuations of long-shots, with the upward bias quantified at 293% in monetary terms. The data also confirms the model's novel predictions, showing that a larger bias strengthens the phenomenon and higher risk aversion strengthens its reversal. Surprisingly, our analysis implies that the magnitude of the original phenomenon has been underestimated so far.