Mats Björkman

Realism of confidence in sensory discrimination: The underconfidence phenomenon

This paper documents a very pervasive underconfidence bias in the area of sensory discrimination. In order to account for this phenomenon, a subjective distance theory of confidence in sensory discrimination is proposed. This theory, based on the law of comparative judgment and the assumption of confidence as an increasing function of the perceived distance between stimuli, predicts underconfidence—that is, that people should perform better than they express in their confidence assessments. Due to the fixed sensitivity of the sensory system, this underconfidence bias is practically impossible to avoid. The results of Experiment 1 confirmed the prediction of underconfidence with the help of present-day calibration methods and indkated-a-good quantitative fit of the theory. The results of Experiment 2 showed that prolonged experience of outcome feedback (160 trials) had no effect on underconfidence. It is concluded that the subjective distance theory provides a better explanation of the underconfidence phenomenon than-do previous accounts in terms of subconscious processes.

Stimulus—event learning and event learning as concurrent processes

Abstract A modified version of Brunswiks lens model is applied to the analysis of event learning and stimulus—event learning as concurrent processes in the nonmetric case. It is demonstrated that functional validity, defined as a matrix containing the joint occurrence of responses and events, is the product of the ecological matrix and the utilization matrix. The special case of a two-choice situation is examined in detail and achievement for various types of performance is studied. A method for quantitative separation of the two processes is presented.

Knowledge, calibration, and resolution: A linear model

Abstract Calibration expresses the correspondence between subjective and objective probability, i.e., relative frequency. A subject is perfectly calibrated if for all propositions assigned the probability x x, x x of them are true. When proportion correct is plotted against categorized assessments of subjective probability one gets a calibration curve. Resolution expresses the degree to which the subject can sort correct and incorrect items into different categories. A model which approximates the calibration curve by a linear function c(xt) = a + bxt is suggested, where c(xt) is the predicted proportion correct when the probability assessment is xt. Perfect calibration means that a = 0, b = 1. When c(xt) is combined with the distribution of assessments a linear relation •c = a + b x is obtained; •c is the predicted mean proportion correct and x is the mean of the probability assessments. The model was tested on (1) individual data from an experiment with 250 general knowledge items and (2) group data from a study by Lichtenstein and Fischhoff (1977, Organizational Behavior and Human Decision Processes, 20, 159–183). The fit between predicted (•c) and observed proportion correct ( c ) was satisfactory for 31 of 33 subjects in the individual study and for all 19 conditions in the group study. The two studies were compared in some detail with respect to relationships between knowledge on the one hand and calibration and resolution on the other.

Relations between learning curve parameters and amount of material to be learned

SUMMARYThis paper is concerned with the problem of relating learning parameters to the length of material to be learned. Parameters of a learning curve equation—previously used in two experimental studies—were determined for varying length of materials. The learning curve is, where R is a scaled learning measure, b a parameter indicating the asymptotic level, β a parameter showing the curvature and the mean reaction threshold. According to the data model, on which the measurement method is based, the parameters b and β should be inter-individually invariant. The inter-individual differences in learning ability are accounted for by the parameter , the reaction threshold (the value to which R must reach for a correct reaction to occur).The main results of the investigation may be summarized as follows: a) The investigation supports the hypothesis that β, the curvature of the learning curve, is invariant for lists of varying length. At least it can be said that β is highly resistant to this kind of experimen...

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.

Single cue probability learning: Do subjects give priority to small errors or task-regularity?

Abstract In traditional studies of single cue probability learning the subjects errors and the covariation he/she establishes between the judgments and the cue (cue dependency) are confounded. Learning results in increased cue dependency which is necessarily accompanied by decreasing errors. This paper presents a method for disentangling errors from cue dependency. This is done by (1) making the criterion contingent upon the judgments instead of the cue, and (2) giving standard instructions, implying that the cue is informative about the criterion. In this way errors are controlled independently of any covariation that the subject may create between the cue and the judgments, and indirectly between the cue and the criterion (task regularity). The paper examines whether subjects aim at small errors or task-regularity when the task does not allow them to do both. It was found that error reduction does occur only when task-regularity can be maintained. Conclusion: task regularity, and thus cue-dependency, has priority to error reduction under the standard conditions used in single cue probability learning experiments. The study may be viewed as an example of conditions under which a cue illusion (false beliefs in the validity of a cue) arises.