In many social systems, groups of individuals can find remarkably efficient solutions to complex cognitive problems, sometimes even outperforming a single expert. The success of the group, however, crucially depends on how the judgments of the group members are aggregated to produce the collective answer. A large variety of such aggregation methods have been described in the literature, such as averaging the independent judgments, relying on the majority or setting up a group discussion. In the present work, we introduce a novel approach for aggregating judgments - the transmission chain - which has not yet been consistently evaluated in the context of collective intelligence. In a transmission chain, all group members have access to a unique collective solution and can improve it sequentially. Over repeated improvements, the collective solution that emerges reflects the judgments of every group members. We address the question of whether such a transmission chain can foster collective intelligence for binary-choice problems. In a series of numerical simulations, we explore the impact of various factors on the performance of the transmission chain, such as the group size, the model parameters, and the structure of the population. The performance of this method is compared to those of the majority rule and the confidence-weighted majority. Finally, we rely on two existing datasets of individuals performing a series of binary decisions to evaluate the expected performances of the three methods empirically. We find that the parameter space where the transmission chain has the best performance rarely appears in real datasets. We conclude that the transmission chain is best suited for other types of problems, such as those that have cumulative properties.