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A simulation model is presented that represents belief change, based on Thagard’s theory of explanatory coherence, within a population of agents who are connected by a social network. In this model there are a fixed number of represented beliefs, each of which are either held or not by each agent. These beliefs are to different extents coherent with each other – this is modelled using a coherence function from possible sets of core beliefs to [-1,1]. The social influence is achieved through gaining of a belief from another agent across a social link. Beliefs can be lost by being dropped from an agent’s store. Both of these processes happen with a probability related to the change in coherence that would result in an agent’s belief store. A resulting measured “opinion” can be retrieved in a number of ways, here as a weighted sum of a pattern of the core beliefs – opinion is thus an outcome and not directly processed by agents. Results suggest that a reasonable rate of copy and drop processes and a well connected network are required to achieve consensus, but given that, the approach is effective at producing consensuses for many compatibility functions. However, there are some belief structures where this is difficult.