Before revision:  If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992).
After revision:  If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon's theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992).