A Note on Probability Forecasts and “Hedging”

The consideration of a maxim and a statement, both of which are concerned with “hedging” on the part of meteorologists who prepare probability forecasts, leads to the identification of a property which all proper scoring systems for such forecasts should possess. A scoring system, to be proper, should encourage the meteorologist to make his probabilities correspond to his true beliefs. The conditions which a proper scoring system must satisfy are formulated in mathematical terms. Several existing scoring systems are examined to ascertain whether or not the systems are proper.