Combining and Extremizing Real-Valued Forecasts

Understand

The weighted average is by far the most popular approach to combining multiple forecasts of some future outcome.

• This paper shows that both for probability or real-valued forecasts, a non-trivial weighted average of different forecasts is always sub-optimal.
• More specifically, it is not consistent with any set of information about the future outcome even if the individual forecasts are.
• Furthermore, weighted averaging does not behave as if it collects information from the forecasters and hence needs to be extremized, that is, systematically transformed away from the marginal mean.