A Subjectivist View of Calibration (Report No. 82-6)

Abstract

Calibration concerns the relationship between subjective probabilities and the long-run frequencies of events. Theorems from the statistical and probability literature are reviewed to discover the conditions under which a coherent Bayesian expects to be calibrated. If the probability assessor knows the outcomes of all previous events when making each assessment, calibration is always expected. However, when such outcome feedback is lacking, the assessor expects to be well calibrated on an exchangeable set of events if and only if all the events in question are viewed as independent. Although this strong condition has not been tested in previous research, we speculate the past findings of pervasive overconfidence are not invalid. Although experimental studies of calibration hold promise for the development of cognitive theories of confidence, their value for the practice of probability assessment seems more limited. Efforts to train probability assessors to be calibrated may be misplaced.