To Bayes or not to Bayes? A comparison of two classes of models of information aggregation

We model the aggregation process used by individual decision makers (DMs) who obtain probabilistic information from multiple, possibly nonindependent, sources. We distinguish between two qualitatively different aggregation approaches: compromising, by averaging the advisors' opinions, and combining the forecasts according to a naive implementation of Bayes rule that assumes conditional independence between advisors. The DMs in our studies received forecasts from two or three advisors who had access to multiple diagnostic cues, and made a large number of decisions. Our data are unusually rich in many respects since the studies involve natural sampling of cues with various levels of dependence and various patterns of information overlap. This provides an excellent opportunity to compare the quality of these models. Overall, the DMs' judgments were closest to the averaging model but, clearly, they did not rely exclusively on this model. The DMs' aggregates were more in line with the naive Bayes rule when the advisors provided extreme forecasts were highly consistent with each other, and induced high levels of confidence. On the other hand, when the advisors disagreed with each other, the DMs were less confident and their aggregates were predicted well by a simple averaging rule.