# Models of risky choice: A signed difference analysis

Signed difference analysis is a methodology that is used to derive a set of ordinal predictions from a mathematical model (Dunn & James, 2003; Dunn & Kalish, 2018). It generalizes state-trace analysis to models with more than one latent variable (Dunn & Kalish, 2018) where each of two or more dependent variables is an arbitrary monotonic function of a specified function of the latent variables. This is a property of many models of risky choice in which the probability of choosing option A over option B is an unknown monotonic function of a model-specific function of the subjective utilities of the two options (and potentially additional parameters). We consider two models of risky choice – the fixed utility model (e.g., cumulative prospect theory) and the random subjective expected utility (RSEU) model proposed by Busemeyer and Townsend (1993). The main difference between the two models is that the predictions of the fixed utility model depend only on the difference between the utilities of the two options while those of the RSEU model also the utilities are modified by a term representing their subjective variance. We derive critical predictions from each of these models and test them against data from two experiments.

*Psychological Review*,

*100*(3), 432--459.

*Journal of Mathematical Psychology*,

*85*(3), 36--54.

*Journal of Mathematical Psychology*,

*47*(4), 389--416.

*State-trace analysis*. Springer.