Towards the full information chain theory: answer depth and source models

Abstract: A problem of optimal information acquisition for its use in general decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter. A companion article developed the notion of a question difficulty functional for questions concerning input data for a decision making problem. Here, answers which an information source may provide in response to such questions are considered. In particular, a real valued answer depth functional measuring the degree of accuracy of such answers is introduced and its overall form is derived under the assumption of isotropic knowledge structure of the information source. Additionally, information source models that relate answer depth to question difficulty are discussed. It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.