Interpreting point predictions: Some logical issues

Forecasters regularly make point predictions of future events. Recipients of the predictions may use them to inform their own assessments and decisions. This paper integrates and extends my past analyses of several simple but inadequately appreciated logical issues that affect interpretation of point predictions. I explain the algebraic basis for a pervasive empirical finding that the cross-sectional mean or median of a set of point predictions is more accurate than the individual predictions used to form the mean or median, a phenomenon sometimes called the "wisdom of crowds." I call attention to difficulties in interpretation of point predictions expressed by forecasters who are uncertain about the future. I consider the connection between predictions and reality. In toto, the analysis questions prevalent prediction practices that use a single combined prediction to summarize the beliefs of multiple forecasters.