The Psychometric Properties of Probability and Quantile Forecasts

Forecasting tournaments are a well established method for assessing human forecasting skills. Most forecasting tournaments are based on a format where participants estimate the probabilities of discrete events. For predictions of continuous values, the possible range of outcome values is divided into mutually exclusive bins covering the entire outcome distribution so that probabilities for each bin can be elicited. An alternative approach involves directly eliciting forecasts about quantiles of the continuous quantity. Using both simulated data and data from 1,147 participants who completed five surveys focused on forecasting tasks in a longitudinal study, we compared the psychometric properties of quantile and probability elicitation methods. In the simulation, we demonstrated that items in the quantile format recovered parameters that defined forecasters’ latent forecasting skill in fewer items than the probability format, and identified several idiosyncrasies in accuracy scores for the probability format that drive these differences. In the empirical analyses, we elicited forecasts about a set of 36 forecasting questions in both formats: quantile forecasts at five fixed probability values (5%, 25%, 50%, 75%, 95%) and probability forecasts for five pre-determined item-specific bins. Consistent with the simulated results, our findings revealed that forecasts in the quantile format showed considerably stronger internal consistency, achieving a suitable reliability level with fewer items. When cross-validating how well individual forecasters’ accuracy on in-sample questions predicted their performance in out-of-sample questions, the variability in the accuracy of quantile forecasts was more statistically explainable. Despite its desirable properties, errors and signs of comprehension difficulties were more frequently observed in the quantile format. Further research is needed to refine elicitations that optimize the effectiveness of quantile-based forecasting judgments.