Second-order decision analysis

The purpose of this work is to provide theoretical foundations of, as well as some computational aspects on, a theory for analysing decisions under ri sk, when the available information is vague and imprecise. Many approaches to model unprecise information, e.g., by using interval methods, have preva iled. However, such representation models are unnecessarily restrictive sin ce they do not admit discrimination between beliefs in different values, i. e., the epistemologically possible values have equal weights. In many situa tions, for instance, when the underlying information results from learning techniques based on variance analyses of statistical data, the expressibili ty must be extended for a more perceptive treatment of the decision situati on. Our contribution herein is an approach for enabling a refinement of the representation model, allowing for an elaborated discrimination of possibl e values by using belief distributions with weak restrictions. We show how to derive admissible classes of local distributions from sets of global dis tributions and introduce measures expressing into which extent explicit loc al distributions can be used for modelling decision situations. As will tur n out, this results in a theory that has very attractive features from a co mputational viewpoint.