On the Nature of the Nonexistence of Ordinal Relationships between Measures of the Accuracy and Value of Probability Forecasts : An Example

Abstract

t has been shown previously that ordinal relationships between measures of the accuracy and value ofprobability forecasts do not exist, in general, in N-state (N > 2) situations. Some implications of this resultare illustrated by comparing the accuracy and value of such forecasts in a realistic decision-making situation-a three-action, three-state situation involving the protection of a fruit orchard against frosts and freezes.Geometrical interpretations of the forecasts and measures are described and then used to investigate the existence of ordinal relationships in this so-called fruit-frost situation. The results indicate, as expected, thatan increase in forecast accuracy can lead to a decrease in forecast value. Some generalizations and speculations related to the existence and nonexistence of such ordinal relationships are presented.