SFB 303 Discussion Paper No. B - 130

Author: Selten, Reinhard
Title: Properties of a Measure of Predictive Success
Abstract: The measure of predictive success investigated in this paper has been introduced as an instrument for the comparison of area theories for characteristic function experiments (Selten and Krischker 1983). An area - theory is a theory which predicts a subset of all possible outcomes.The measure of predictive success developed by Selten and Krischker (1983) can be described as follows:
m = r - a , where
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, r - a and two other ones, namely r/a and (r-a)/(1-a), which also has been used in the literature (Forman and Laing 1983).
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 m = r - a up to increasing monotonic transformations. Another subset characterizes m = r - a up to positive linear transformations. This is shown in section 5.
Creation-Date: October 1989 
Unfortunately this paper is not available online. Please contact us to order a hardcopy.

SFB 303 Homepage

21.10.1999, Webmaster