The Tweedledum and Tweedledee of dynamic decisions: Discriminating between diffusion decision and accumulator models

Abstract

Theories of dynamic decision-making are typically built on evidence accumulation, which is modeled using racing accumulators or diffusion models that track a shifting balance of support over time. However, these two types of models are only two special cases of a more general evidence accumulation process where options correspond to directions in an accumulation space. Using this generalized evidence accumulation approach as a starting point, we identify four ways to discriminate between accumulator and diffusion models. First, an experimenter can look at the information that decision makers considered to identify whether there is a filtering of near-zero evidence samples, which is characteristic of a relative-evidence decision rule (i.e, diffusion model). Second, an experimenter can disentangle different components of drift rates by manipulating the discriminability of the two response options relative to the stimulus to delineate the balance of evidence from the total amount of evidence. Third, a modeler can use machine learning to classify a set of data according to its generative model. Finally, machine learning can also be used to directly estimate the geometric relationships between choice options. We illustrate these different approaches by applying them to data from an orientation-discrimination task, showing converging conclusions across all four methods in favor of accumulator-based representations of evidence during choice. These tools can clearly delineate accumulator and diffusion models, and should be useful for comparing many other types of decision theories.