Inferring true voting outcomes in homophilic social networks

We investigate the problem of binary opinion aggregation in a social network regarding an objective outcome. Agents receive independent noisy signals relating to the outcome, but may converse with their neighbors in the network before opinions are aggregated, resulting in incorrect opinions gaining prominence in the network. Recent work has shown that, in the general case, there is no procedure for inferring the correct outcome that incorporates information from the connections between agents (i.e. the structure of the social network). We develop a new approach for inferring the true outcome that can benefit from the additional information provided by the social network, under the simple assumption that agents will more readily convert to the true opinion than to a false one, generating a homophilic effect for voters with the correct opinion. Our proposed approach is computationally efficient, and provides significantly more accurate inference in many domains, which we demonstrate via both simulated and real-world datasets. We also theoretically characterize the properties that are necessary for our approach to perform well. Finally, we extend our approach to directed social networks, and cases with many alternatives, and outline areas for future research.