m = measure of predictive success;

r = hit rate, the relative frequency of correct predictions;

a = the area, the relative size of the predicted subset compared with the set of all possible outcomes.

The search for better area theories guided by a measure of predictive success aims at the maximization of this measure. Therefore it is of interest to ask the question which sets of outcomes maximize the expectation of the measure of predictive success for a given probability distribution. The answer reveals the implied structure of a theory which is unimprovable with respect to the measure. In section 2 this problem will be discussed. Three measures of predictive success will be examined,

In section 3 axioms will be introduced which impose plausible requirements on the functional form of a measure of predictive success which depends only on the hit rate r and the area a. In section 4 a theorem will be proved which shows that a subset of these axioms characterizes

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21.10.1999, Webmaster