Models of risky choice: A state-trace and signed difference analysis

Models of risky choice fall into two broad classes; fixed utility models that satisfy the condition of simple scalability and everything else. While it is known that choice behavior can be observed that is inconsistent with all models, this has largely been based on the construction of special cases. We use state-trace analysis and signed difference analysis to test a set of models on a set of ecologically representative risky choices. An advantage of this approach is that there is no requirement to posit a particular form for the error function that links the difference in the utilities of two gambles, A and B, with the probability of choosing A over B. We presented groups of participants with 30 variable gambles (A), each paired with one of four fixed gambles (B). We use state-trace analysis to test the prediction of all fixed utility models that the probability of choosing each A has the same order for all B. The results show that this prediction is not confirmed and a more complex model is required. We then use signed difference analysis to test two more complex models — the random subjective expected utility model based on Decision Field Theory and a fixed utility mixture model. We derive a key prediction from the random subjective expected utility model and show that it is confirmed by the data. In contrast, the data are shown to be inconsistent with the fixed utility mixture model