KNOWLEDGE, CALIBRATION, AND RESOLUTION - A LINEAR-MODEL

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. © 1992.