Modelling Speed-Accuracy Tradeoffs in the Stopping Rule for Confidence Judgments

Making a decision and reporting confidence in the accuracy of that decision are thought to be driven by the same mechanism: the accumulation of evidence. Previous research has shown that choices and reaction times are well accounted for by a computational model assuming noisy accumulation of evidence until crossing a decision boundary (e.g., the drift diffusion model). Decision confidence can be derived from the amount of evidence following post-decision evidence accumulation. Currently, the stopping rule for post-decision evidence accumulation is underspecified. In the current work, we quantitatively and qualitatively compare the ability of four prominent models of confidence couched within evidence accumulation to account for this stopping rule. In two experiments, participants were instructed to make fast or accurate decisions, and to give fast or carefully considered confidence judgments. We then compared the different models in their ability to capture the speed-accuracy effects on confidence. Both qualitatively and quantitatively, the data were best accounted for by our newly proposed Flexible Collapsing Boundaries model, in which post-decision accumulation terminates once it reaches one of two opposing slowly collapsing confidence boundaries. Inspection of the parameters of this model revealed that instructing participants to make fast versus accurate decisions influenced the height of the decision boundaries, while instructing participants to make fast versus careful confidence judgments influenced height of the confidence boundaries. Our data show that the stopping rule for confidence judgments can be well described as an accumulation-to-bound process, and that the height of these confidence boundaries are under strategic control.