Are there natural followers in human communication, speakers who consistently converge more than others? Similarly, are there natural leaders, speakers with whom others converge more? Are such tendencies consistent across different linguistic characteristics? We use the Switchboard Corpus, a large collection of telephone conversations, to perform a large-scale study of convergence of speakers in multiple conversations with different interlocutors, across six linguistic characteristics. Having data from each speaker in several conversations makes it possible to investigate whether there are individual differences in likelihood to converge, among speakers (more or less likely to converge), and among interlocutors (more or less likely to elicit convergence). We only find evidence for individual differences by interlocutor, not by speaker; this shows that there are natural leaders, who elicit greater degrees of convergence than others, across different characteristics and different conversations. The absence of a similar finding for natural followers, speakers who converge more than others, suggests that the role of social aspects in mediating convergence is stronger than that of putative individual differences in propensity to converge, or that such propensities are characteristic-specific.