  The puzzling idea that the combination of independent estimates of the
magnitude of a quantity results in a very accurate prediction, which is
superior to any or, at least, to most of the individual estimates is known as
the wisdom of crowds. Here we use the Federal Reserve Bank of Philadelphia's
Survey of Professional Forecasters database to confront the statistical and
psychophysical explanations of this phenomenon. Overall we find that the data
do not support any of the proposed explanations of the wisdom of crowds. In
particular, we find a positive correlation between the variance (or diversity)
of the estimates and the crowd error in disagreement with some interpretations
of the diversity prediction theorem. In addition, contra the predictions of the
psychophysical augmented quincunx model, we find that the skew of the estimates
offers no information about the crowd error. More importantly, we find that the
crowd beats all individuals in less than 2% of the forecasts and beats most
individuals in less than 70% of the forecasts, which means that there is a
sporting chance that an individual selected at random will perform better than
the crowd. These results contrast starkly with the performance of non-natural
crowds composed of unbiased forecasters which beat most individuals in
practically all forecasts. The moderate statistical advantage of a real-world
crowd over its members does not justify the ado about its wisdom, which is most
likely a product of the selective attention fallacy.
