When reasoning about a claim, it makes sense to be more persuaded if lots of other people agree. But, there are many factors that make weighing the evidence behind a consensus complicated. For example, a consensus might be more or less informative depending on the type of claim, or whether each consensus member formed their opinions independently. These factors might also influence people differently depending on their own assumptions or preferences. In this study we used a mock social media paradigm to assess how persuaded people were by two factors: the presence of consensus (no consensus vs. consensus), and source independence (a consensus based on independent information sources vs. a consensus formed off shared, dependent sources). We varied these factors at both the group and individual level. At the group level, we assessed a third factor: whether people were influenced by the type of claim being reasoned about (we assessed 60 different claims divided into 4 categories). Almost everyone was more persuaded by consensus trials compared to no consensus trials. However, the strength of this effect was credibly stronger if the claim was likely to have a ground truth. We found that around one third of participants were sensitive to source independence. Of these, three quarters were more persuaded by a consensus based on independent sources, but the quarter who were more persuaded by dependent sources were persuaded just as strongly.