A signal-detection analysis of fast-and-frugal trees

Models of decision making are distinguished by those that aim for an optimal solution in a world that is precisely specified by a set of assumptions (a so-called "small world") and those that aim for a simple but satisfactory solution in an uncertain world where the assumptions of optimization models may not be met (a so-called "large world"). Few connections have been drawn between these 2 families of models. In this study, the authors show how psychological concepts originating in the classic signal-detection theory (SDT), a small-world approach to decision making, can be used to understand the workings of a class of simple models known as fast-and-frugal trees (FFTs). Results indicate that (a) the setting of the subjective decision criterion in SDT corresponds directly to the choice of exit structure in an FFT; (b) the sensitivity of an FFT (measured in d') is reflected by the order of cues searched and the properties of cues in an FFT, including the mean and variance of cues' individual d's, the intercue correlation, and the number of cues; and (c) compared with the ideal and the optimal sequential sampling models in SDT and a majority model with an information search component, FFTs are extremely frugal (i.e., do not search for much cue information), highly robust, and well adapted to the payoff structure of a task. These findings demonstrate the potential of theory integration in understanding the common underlying psychological structures of apparently disparate theories of cognition.