Clusters of like-minded individuals can impede consensus in group decision-making. We implemented an online color coordination task to investigate whether control over communication links creates clusters impeding group consensus. In 244 6-member networks, individuals were incentivized to reach a consensus by agreeing on a color, but had conflicting incentives for which color to choose. We varied (1) if communication links were static, changed randomly over time, or were player-controlled; (2) whether links determined who was observed or addressed; and (3) whether a majority existed or equally many individuals preferred each color. We found that individuals preferentially selected links to previously unobserved and disagreeing others, avoiding links with agreeing others. This prevented cluster formation, sped up consensus formation rather than impeding it, and increased the probability that the group agreed on the majority incentive. Overall, participants with a consensus goal avoided clusters by applying strategies that resolved uncertainty about others.