Often, public discussions of questions of great social import exhibit two important properties: (1) they admit only equivocal answers, (2) and they are influenced by conformity bias. We study how social networks can influence the flow and reliability of information in matters of public opinion. In our model, heterogeneous agents express public opinions where those expressions are driven by the competing priorities of accuracy and of conformity to one’s peers. Agents learn, via Bayesian conditionalization, from private signal from nature, and the public declarations of other agents. We show that, in the presence of equivocal evidence and a modicum of conformity bias, communities of rational agents can fail to learn the truth, even in the long run.