Expert consultant systems often perform computations on a directed graph of associated propositions. Each proposition is represented by a node. Edges connecting these nodes are associated with rules which organize the propositions into antecedent/consequent relationships. A node may be assigned a value through the edges that bind it to its antecedents. Various strategies are employed to determine assignment sequences that result in efficient computer consultation. One such strategy, the merit system, has been successfully implemented in Battle, an expert consultant system for the Marine Corps. The merit strategy enables Battle to focus the consultation process on the most appropriate questions. The merit system, originally defined for logical functions in the Multiple program, has been extended to the Mycin style of propagation and to the method of subjective Bayesian assignments used by Prospector. A procedure for merit calculations with any differentiable, real-valued assignment function is presented. Our experience has shown that merit values provide an efficient flow of control for expert consultation.