Before revision:  Substantial effort in previous research on these questions has focused on investigating the role of social influence in promoting the wisdom of the crowd or, conversely, leading the crowd astray . Specifically, many previous studies have sought to infer the importance of social influence network attributes (such as influence centralization) to explain the accuracy of collective estimates. In this paper, we argue that this approach is limited and can lead to inconsistent conclusions. Based on our theoretical analysis, numerical simulation, and reanalysis of four previously published experiments (which included a total of 4,002 human URLanized in 131 independent groups ), we demonstrate that the wisdom of crowds in estimation tasks depends on the interaction between the following two factors:
After revision:  Substantial effort in previous research on these questions has focused on investigating the role of social influence in promoting the wisdom of the crowd or, conversely, leading the crowd astray , resulting in conflicting conclusions about how the social network structure determines the impact of social influence. Here, we demonstrate that it is not enough to consider the network structure in isolation. Using theoretical analysis, numerical simulation, and reanalysis of four previously published experiments (which included a total of 4,002 human URLanized in 131 independent groups ), we demonstrate that the wisdom of crowds in estimation tasks depends on the interaction between the following two factors: