An Operational View of Coherent Conditional Previsions

In this paper we propose a characterization theorem for coherent conditional previsions assessed on finite conditional random variables. The main feature is the direct applicability of the results to model practical problems. In fact the check of coherence and the inferential steps are reduced to the solvability of linear systems and of linear pro- gramming problems, respectively. The guideline of the procedure has been the already stated results for coherent conditional probabilities, so that now we have a unified theory for uncertainty represented by belief or synthesized by prevision. The procedure turns out to be helpful when the size of the relevant quantities strongly depend on the different scenarios in which they are considered. A simple example shows the potentiality of the entire machinery on a decision-aid problem.