Implicit Degree of Support for Finite Lower-Upper Conditional Probabilities Extensions

With this paper we propose an im- plicit degree of support on coherent extensions for probabilistic models based on partial conditional lower- upper assessments. Such degree of support is induced by the di®erent extension bounds that operationally appear during a nowadays consoli- dated automatic procedure. These di®erent bounds are those induced by the \extreme" distributions com- patible with the initial assessment, i.e. those that strictly attain at least one of the constraints imposed by the modeler. The minimum and the maximum of these extension bounds determine the so called \least com- mitment" coherent extension inter- val, while the intermediate values can be used to grade the support of the initial assessment for tighter in- tervals. The appropriateness of the degree of support pass through the proof of coherence of particular sub- intervals of the wider \least com- mitment" coherent extension range. The proposed degree of support can be helpful in the process of ¯nding appropriate extension bounds when- ever the general way produce a too vague conclusion.