Jumping to Conclusion? A Lévy Flight Model of Decision Making

Abstract

The diffusion model is one of the most prominent response time models in cognitive psychology. The model describes evidence accumulation as a stochastic process that runs between two boundaries until a threshold is hit, and a decision is made. The model assumes that information accumulation follows a Wiener diffusion process with normally distributed noise. However, the model's assumption of Gaussian noise might not be the optimal description of decision making. We argue that Levy flights, incorporating more heavy-tailed, non-Gaussian noise, might provide a more accurate description of actual decision processes. In contrast to diffusion processes, Levy flights are characterized by larger jumps in the decision process. To further examine this proposal, we compare the fit of the basic diffusion model and the full diffusion model (including inter-trial variability of starting-point, drift rate and non-decisional processes) to the fit of a simple and a complex version of a Levy flight model. In the latter model, the heavy-tailedness of noise distributions was estimated by an additional free stability parameter alpha. Participants completed 500 trials of a color discrimination task and 400 trials of a lexical decision task. Results indicate that a complex Levy flight model - including inter-trial variability parameters and alpha - shows the best fit in both tasks. Importantly, alpha-values correlated across tasks, indicating a trait-like nature of this parameter.