A longstanding problem in the social, biological, and computational sciences is to determine how groups of distributed individuals can form intelligent collective judgments. Since Galton's discovery of the "wisdom of crowds" [Galton F (1907 social networks | collective intelligence | social learning | wisdom of crowds | experimental social science S ince Galton's discovery of the "wisdom of crowds" over 100 years ago (1), results on crowdsourcing (1, 2), prediction markets (3), and financial forecasting (4, 5) have shown that the aggregated judgment of many individuals can be more accurate than the judgments of individual experts (2, 4, 6-8). Statistical explanations for this phenomenon argue that group accuracy relies on estimates taken from groups where individuals' errors are either uncorrelated or negatively correlated, thereby preserving the diversity of opinions in a population (9). Thus, although individuals may have estimates both far above and far below the true value, in aggregate these errors cancel out, leaving an accurate group judgment (2, 9, 10).Recent experimental evidence has suggested that the wisdom of crowds may be undermined by processes of social influence, in which people exchange information about their estimates and revise their judgments to align with one another (11-13). When social influence leads to correlated errors, both independence and diversity are reduced, which has been argued to compromise the reliability of the group judgment (9,(11)(12)(13)(14)(15)(16)(17)(18). In direct contrast with these results, however, theoretical models of social learning (19-21) have suggested that the effects of social influence on collective decisions vary based on the structure of the interaction network, predicting that, under the right conditions, social learning can lead a group's median judgment to improve (20)(21)(22)(23)(24).This prediction derives from the assumption that, when people learn about the beliefs of others, they revise their own beliefs to become more similar to their social referents (11, 12, 25, 26). Following the DeGroot model of social learning, this theory suggests that each individual's revisions are based on a weighted average of their own belief and the beliefs of their social referents (19). Thus, an individual's revision is determined in part by the amount of weight they place on their own belief relative to social information. When this "self-weight" is independently and identically distributed (i.i.d.) throughout a population, and the population is embedded in a decentralized social network (i.e., one in which everyone is equally connected), this model predicts that belief distributions will converge on the statistical mean of the initial, independent beliefs (SI Appendix). Thus, if the initial group mean is accurate, exposure to social influence will lead individuals in the group to become more accurate, improving the accuracy of the group's median, even as the group mean remains fixed (SI Appendix).We build on the DeGroot model to generate theoretical predictions ...