Are there individual tendencies in convergence, such that some speakers 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 to perform a large-scale convergence study of speakers in multiple conversations with different interlocutors, across six linguistic characteristics. Because each speaker participated in several conversations, it is possible to look for individual differences in speakers' likelihood of converging and interlocutors' likelihood of eliciting convergence. We only find evidence for individual differences by interlocutor, not by speaker: There are natural leaders of convergence, who elicit more convergence than others across characteristics and across conversations. The lack of similar evidence for speakers who converge more than others suggests that social factors have a stronger effect in mediating convergence than putative individual tendencies in producing convergence, or that such tendencies are characteristic-specific.