Estimating true beliefs in opinion dynamics with social pressure

Social networks often exert social pressure, causing individuals to adapt their expressed opinions to conform to their peers. An agent in such systems can be modeled as having an (true and unchanging) inherent belief while broadcasting a declared opinion at each time step based on his/her inherent belief and the past declared opinions of his/her neighbors. An important question in this setting is parameter estimation: how to disentangle the effects of social pressure to estimate inherent beliefs from declared opinions. This is useful for forecasting when agents' declared opinions are influenced by social pressure while real-world behavior only depends on their inherent beliefs. To address this, Jadbabaie et al. (2023) formulated the interacting Pólya urn model of opinion dynamics under social pressure and studied it on complete-graph social networks using an aggregate estimator, and found that their estimator converges to the inherent beliefs unless majority pressure pushes the network to consensus. In this work, we study this model on arbitrary networks, providing an estimator that converges to the inherent beliefs even in consensus situations. Finally, we bound the convergence rate of our estimator in both consensus and nonconsensus scenarios; to get the bound for consensus scenarios (which converge slower than nonconsensus), we additionally found how quickly the system converges to consensus.