Magnitude-sensitive sequential sampling models of confidence
Magnitude-sensitivity refers to the effect that decisions between two alternatives tend to be faster when the intensities of both alternatives (e.g., luminance, size, or preference) are increased even if their difference is kept constant. Previous studies proposed several computational models to describe decision and response time distributions in experimental paradigms with changes of stimulus magnitude. However, with only responses and response times as dependent variables, there was a high degree of model mimicry. We suggest to include confidence judgments as an additional dependent variable in experiments and models. We present three experiments, two brightness discrimination tasks and a motion discrimination task, in which the intensities of both alternatives were varied and confidence judgments were recorded. Under some stimulus manipulations, confidence increased with stimulus magnitude while accuracy remained constant. We generalized several previously proposed dynamical models of confidence and response time to account for magnitude-sensitivity by adding intensity-dependent noise parameters. We fitted each model to the data and compared models quantitatively. The intensity-dependent dynamical weighted evidence, visibility and time model (iddWEVT) was best in fitting the joint distribution of response times, choice and confidence judgments for the different experimental manipulations. Previous studies explained increasing confidence but constant accuracy with stimulus magnitude by a positive evidence bias, i.e. for the computation of confidence, people might rely only on the evidence supporting their decision and ignore evidence for the alternative. However, sequential sampling models offer an alternative explanation for these effects by considering the dynamics of a decision and by taking response times into account in the computation of confidence. We suggest that identification of computational models of decision making but also models of confidence can be improved by considering decisions, reaction times, and confidence at the same time.