This paper discusses the reliability of group judgment in the context of indirect voting systems and the Condorcet jury theorem. To describe such systems, composite majority functions are introduced and their properties studied. Associated Banzhaf numbers appear as a natural measure of decisional power. The paper examines how collective judgmental competence depends on structural properties of the decision making system. Formulas are developed to measure the loss (or gain) in judgmental competence due to simple changes in system structure, such as overlapping membership.