Risky decisions which violate transitivity and double cancellation

Abstract Two experiments are described which test predictions of the subjectively expected utility model (SEU) for simple gambles. Tversky's (1969) paradigm is used to test transitivity and double cancellation. However, the mode of presentation of the gamble was changed from Tversky's to eliminate explanations of violations of the conditions based on indiscriminability or attentional factors. Another change from Tversky is that statements about how subjects had chosen were systematically recorded. In each experiment some subjects stated that they had switched from choosing the better payoff to choosing the better probability in a manner consistent with the lexicographic semiorder (LS) decision rule. These subjects were defined as the LS group. As predicted, the consequences of the SEU model were violated more often by this group and, also, the choice patterns of these subjects corresponded closer to the LS decision rule pattern. It is concluded that (1) the violations of transitivity and double cancellation observed in the LS groups were due to preferences rather than indiscriminability or attentional factors; (2) the results are not too damaging to the SEU model when it is compared to alternative measurement models. Ultimately, however, the only way to accomodate such results is through information-processing models, which can take account of both the choice patterns observed and people's statements about them.