Coherence and Consistency of Investors' Probability Judgments

Abstract

This study investigates the quality of direct probability judgments and quantile estimates with a focus on calibration and consistency. The two response modes use different measures of miscalibration, so it is difficult to directly compare their relative (in)accuracy. We employed a more refined within-subject design in which decision makers (DMs) used both response modes to make judgments about a random sample of stocks accompanied by identical information to facilitate comparison between the two judgment methods. DMs judged the probabilities that the stocks will reach a certain threshold, provided lower and upper bounds of these forecasts, and estimated median, 50%, 70%, and 90% confidence intervals of their future prices. We found that the judgments were internally consistent and coherent, but in most cases they were slightly miscalibrated. We used several new methods of analysis that allow for more precise and reliable comparison between the two response modes. We inferred point probability estimates for the target events from the confidence intervals and analyzed them by the same methods applied to binary judgments. Interestingly, when we quantified miscalibration in identical fashion for both methods we did not find evidence of differential levels of miscalibration for the probability judgments and the confidence intervals. We discuss the theoretical and practical implications of these results.