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If a theory permits a variety of preference patterns, we can build a probabilistic model by combining the various probabilistic models for all of the permitted patterns. For example, for Gambles A, C, D in Table 2, we can consider all six possible rankings (each from best to worst): ACD, ADC, CAD, CDA, DAC, DCA. In these models, the decision maker is allowed to rank order the gambles from best to worst according to any fixed ranking that is unknown to the researcher, then choose the preferred gamble in each gamble pair at least 50 (left hand side of Figure 7 ) or at least 90 (right hand side of Figure 7 ) of the time.
Open in a separate window Figure 7 Majority model (left) and 0.