Important perceptual judgments are often made by combining the opinions of several individuals to make a collective decision, such as when teams of physicians make diagnoses based on medical images. Although group-level decisions are generally superior to the decisions made by individuals, it remains unclear whether collective decision making is most effective when information is redundantly provided to all individuals within a group, or when each individual is responsible for only a portion of the total information. Here, we test this idea by having individuals and groups of different sizes make perceptual judgments about the presence of a weak visual signal. We found that groups viewing the entirety of information significantly outperformed groups that viewed limited portions of information, and that this difference in performance could be accounted for by a simple internal noise-averaging model. However, noise averaging alone was insufficient to account for improvements in individual and group-level performance as group size varied. These results indicate that sharing redundant information can enhance the quality of individual perceptual judgments and lead to better group decision making than dividing information across members of a group.