Subjects Adjust Criterion on Errors in Perceptual Decision Tasks
The optimal strategy in detection theory is to partition the decision axis at a criterion C, labeling all events that score above C “Signal”, and all those that fall below “Noise.” The optimal position of C, C*, depends on signal probability and payoffs. If observers place their criterion at some place other than C*, they suffer a loss in the Expected Value (EV) of payoffs over the course of many decisions. We provide an explicit equation for the degree of loss, where it is shown that the falloff in value will be steep in contexts of good discrimination and will be a flatter gradient in contexts of poor discrimination. It is these gradients of loss in EV that, in theory, drive C toward C*, strongly when discrimination is good, weakly when discrimination is poor. When signal probabilities or distributions variances are unequal, the basins of attraction are asymmetric, so that dynamic adjustments in C will be asymmetric, and thus, as we show, will leave it biased. We address our analysis to acquisition speed, response variability, discrimination reversal and other aspects of discriminated performance. In the final section, we develop an error correction model that predicts empirically observed deviations from C* that are inconsistent with the standard model, but follow from the proposed model given knowledge of d′.