Reply to William R. Ferrell’s paper “A model for realism of confidence judgments: Implications for underconfidence in sensory discrimination”

Ferrell’s decision-variable partition model and our subjective distance model belong to the same family of Thurstonial models. The subjective distance model is limited to sensory discrimination with the method of constant stimuli and rooted in such notions as discriminal dispersion and sense distance. Ferrell’s model is intended to be wider in scope and to apply to both cognitive and sensory tasks. Both models need supplementary assumptions to predict calibration phenomena. The point of departure for us is the fact that the model predicts under-confidence under “guessing” and the empirical finding that people are about 100% correct when they report “absolutely certain.” Ferrell makes assumptions about cutoffs on the decision variable. The respondent is assumed to adjust or not adjust cutoffs according to “cues to difficulty.” We disagree with Ferrell’s claim that the hard-easy effect is explained by the respondent’s failure to adjust cutoffs sufficiently when there is a change in level of difficulty, and argue that this amounts to little more than a translation of the hard-easy effect into the lingua of Ferrell’s decision-variable partition model. Our argument is that the hard-easy effect is a consequence of the post hoc division of items according to solution probability. In addition, error variance may contribute to regression effects that enlarge the hard-easy effect. Finally, in contrast to Ferrell’s position, we regard inference (cognitive uncertainty) and discrimination (sensory uncertainty) as different psychological processes. An understanding of calibration in these two areas requires separate models.