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In particular, this decision maker violates transitivity, because, considering again the three gambles, A, C, D, we see that he prefers A to C, C to D, but D to A. From that vantage point, we may want to place stronger constraints on the binary choice probabilities, so that we do not end up overfitting data by accommodating models that really are poor approximations of the cognitive process of interest.
In a supermajority specification, we specify a lower bound on the rate, i.the minimum probability with which a decision maker must choose consistently with their preference, for each gamble pair. For example, in the data analysis of Section 7 we will consider a supermajority level of 0.