Completing the information chain: On the theory of optimal information acquisition for quantitative decision making

Classical Information Theory solves the problem of maximizing the quantity of information that can be reliably transmitted over the given (imperfect) channel, without dealing with the questions of where the information comes from and what it’s going to be used for. If the information is to be used to make decisions, and the goal is to maximize the decision quality (e.g. by minimizing the properly defined loss) by making use of available information sources, then one needs to know what specific information is to be requested from a source so that, on one hand, the source would be able to fulfill the request accurately and, on the other hand, the information obtained would have a large impact on the decision quality for the specific problem at hand. It can be said that the developed methodology complements the classical Information Theory in that it deals–in the context of quantitative decision making at least–with the first and last link of the full “information chain”: extracting it from the source and using it to obtain the best possible decision. The classical Information Theory describes the middle link of that chain–in case a transmission of the information obtained from the source over some channel is involved. The middle link just happens to be largely independent of the end links and can be treated separately, while the end links are rather closely connected and therefore have to be treated together. It is curious to note that a similar state of affairs can often be observed in material supply chains: for example, if some raw material has to be extracted, transported and used to make a certain product, then the material to be extracted depends on the product that needs to be made and the given material can be extracted best from a certain source. The transportation task, however, has a more universal character and can usually be considered in abstraction from the nature of the particular material.;In classical Information Theory, the main question is two-fold: what is the maximum (theoretical) speed of accurate transmission for the given channel and how that speed can be (practically) achieved. The first part of the main question is addressed by calculating the channel capacity and the second part of the main question is addressed by designing appropriate codes for input symbols. The main question being addressed in the proposed approach is also two-fold: what is the maximum decision quality (for the given problem) that can be achieved by using the available information source(s) and what is the practical way of achieving that quality. The first part of this question is addressed by computing the pseudo-energy/loss efficient frontier for the given problem and (source specific) pseudo-temperature function, and the second part is addressed by designing appropriate questions (that lie on the efficient frontier) as means of extracting information from the source(s) optimally with respect to the decision making problem being solved.