It has long been observed that humans in interaction tend to adapt their behavior to become more similar to their interlocutors. Yet the reasons why such entrainment arises in some conversations and not others remain poorly understood. Early work suggests an influence of different personality traits on the degree of entrainment speakers engage in. However, some of these results have never been replicated to test their generalizability. Moreover, a recent finding draws into question whether these and other effects are strong enough to create differences between speakers that persist across multiple conversations. We investigate a variety of personality traits for their influence on a local form of acoustic-prosodic entrainment in two kinds of spontaneous conversation. To our knowledge, this is the first attempt to detect such effects across several interactions per subject and the first attempt to replicate some influential early work in a more natural context. We find virtually no impact of personality, suggesting that prior results might not generalize to a more natural context or entrainment on other linguistic variables.