This paper presents an experimental investigation of persuasion bias, a form of bounded rationality whereby agents communicating through a social network are unable to account for possible repetitions in the information they receive. The results indicate that network structure plays a significant role in determining social influence. However, the most influential agents are not those with more outgoing links, as predicted by the persuasion bias hypothesis, but those with more incoming links. We show that a boundedly rational updating rule that takes into account not only agents' outdegree, but also their indegree, provides a better explanation of the experimental data. In this framework, consensus beliefs tend to be swayed towards the opini...