Bayesian Updating; Central Tendency; Judgmental Forecasts; Information Aggregation; Model Averaging;
Decision-makers often collect and aggregate experts’ point predictions about continuous outcomes, such as stock returns or product sales. In this article, the authors model experts as Bayesian agents and show that means, including the (weighted) arithmetic mean, trimmed means, median, geometric mean, and essentially all other measures of central tendency, do not use all information in the predictions. Intuitively, they assume idiosyncratic differences to arise from error instead of private information and hence do not update the prior with all available information.Updating means in terms of unused information improves their expected accuracy but depends on the experts’ prior and information structure that cannot be estimated based on a single prediction per expert. In many applications, however, experts consider multiple stocks, products, or other related items at the same time.For such contexts, the authors introduce ANOVA updating - an unsupervised technique that updates means based on experts’ predictions of multiple outcomes from a common population. The technique is illustrated on several real-world datasets.