Within the framework of expected utility theory with rank-dependent probabilities, the authors present a hypothesis concerning the shape of the probability transformation function. This hypothesis is consistent with the "preference reversals" phenomenon. In particular, it is consistent with the finding (1) that the frequency of reversals is higher when the P-bet is preferred to the corresponding $-bet than when the $-bet is preferred over the corresponding P-bet and (2) that the $-bet is chosen more frequently than the corresponding P-bet. It is also consistent with aversion to fair, symmetric risk and with the simultaneous participation in actuarially unfair lotteries and insurance. Copyright 1990 by Royal Economic Society.
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