Value Certainty in Diffusion Decision Models

The drift-diffusion model (DDM) is widely used and broadly accepted for its ability to account for binary choices (in both the perceptual and preferential domains) and response times (RT), as a function of the stimulus or the choice alternative (or option) values. The DDM is built on an evidence accumulation-to-bound concept, where, in the value domain, a decision maker repeatedly samples the mental representations of the values of the available options until satisfied that there is enough evidence (or support) in favor of one option over the other. As the signals that drive the evidence are derived from value estimates that are not known with certainty, repeated sequential samples are necessary to average out noise. The classic DDM does not allow for different options to have different levels of precision in their value representations. However, recent studies have shown that decision makers often report levels of certainty regarding value estimates that vary across choice options. There is therefore a need to extend the DDM to include an option-specific value certainty component. We present several such DDM extensions and validate them against empirical data from four previous studies. The data support best a DDM version in which the drift of the accumulation is based on a sort of signal-to-noise ratio of value for each option (rather than a mere accumulation of samples from the corresponding value distributions). This DDM variant accounts for the impact of value certainty on both choice consistency and response time present in the empirical data.