A Quantitative Measure of Relevance Based on Kelly Gambling Theory

This paper proposes a quantitative measure relevance which can quantify the difference between useful and useless facts. This measure evaluates sources of information according to how they affect the expected logarithmic utility of an agent. A number of reasons are given why this is often preferable to a naive value-of-information approach, and some properties and interpretations of the concept are presented, including a result about the relation between relevant information and Shannon information. Lastly, a number of illustrative examples of relevance measurements are discussed, including random number generation and job market signaling.