Humans rely on our social networks to make more accurate inferences about the world. Yet it remains unclear how those inferences are shaped by the medium through which information is exchanged and beliefs are shared. In this paper, we report two experiments where participants (N=645) were asked to make inferences about an unknown probability distribution based on limited private observations. They exchanged messages with neighbors in a small social network and were asked to update their beliefs over repeated rounds. We compared three conditions: a unidirectional message medium, a constrained slider medium, and an interactive chat. All groups were able to converge toward more accurate inferences, but their convergence rates varied across conditions in ways not well-captured by common models. We argue that computational models of collective behavior must move beyond the assumption of direct belief transmission to capture the complexities of sharing information through natural language.