An Algorithm for Coherent Conditional Probability Assessments

Conditional probability assessments are the most general and proper tools to represent the uncertainty on a nite domain of events without structure. In fact in ractical problems the available information is not so rich to be representable by an algebraic structure. Moreover the numerical assessments are best expressed in connection with the hypothetical occurrence of particular events (like possible observations, symptoms, etc.). These assessments can not be arbitrarily given, but they must satisfy a coherence principle. Coherent conditional probabilities are fully characterized in literature (Coletti (1994) and Coletti & Scozzafava (1996)), but these characterizations involve a partition of the sure event, whose cardinality could make the problem computationally intractable. In this paper we detect some cases where the checking of coherence can be decomposed into subproblems decreasing the global complexity. We also propose a relevant algorithm.