The problem of the aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. The difficulty lies in the fact that a seemingly reasonable aggregation procedure, such as propositionwise majority voting, cannot ensure an equally consistent collective outcome. The literature on judgment aggregation refers to such dilemmas as the doctrinal paradox. Three procedures have been proposed in order to overcome the paradox: the premise-based and conclusion-based procedures on the one hand, and the fusion approach on the other hand. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question is how good the fusion approach is in tracking the truth, and how it compares with the premise-based and conclusion-based procedures. We address these questions in a probabilistic framework and show that belief fusion does especially well for individuals with a middling competence of hitting the truth of a proposition.