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An individual's opinions about media bias derive from their own independentassessment of media outputs combined with peer pressure from networkedpolitical allies and opponents. Here we generalize previous idealized,probabilistic models of the perception formation process, based on a network ofBayesian learners inferring the bias of a coin, by introducing obdurate agents(partisans), whose opinions stay fixed. It is found that even one partisandestabilizes an allies-only network, stopping it from achieving asymptoticlearning and forcing persuadable agents to vacillate indefinitely (turbulentnonconvergence) between the true coin bias $\theta_0$ and the partisan's belief$\theta_{\rm p}$. The dwell time $t_{\rm d}$ at the partisan's beliefincreases, as the partisan fraction $f$ increases, and decreases, when multiplepartisans disagree amongst themselves. In opponents-only networks, asymptoticlearning occurs, whether or not partisans are present. However, thecounterintuitive tendency to reach wrong conclusions first, identified inprevious work with zero partisans, does not persist in general for $\theta_0\neq \theta_{\rm p}$ in complete networks; it is a property of sparselyconnected systems (e.g.\ Barab\'{a}si-Albert networks with attachment parameter$\lesssim 10$). In mixed networks containing allies and opponents, partisansdrive counterintuitive outcomes, which depend sensitively, on where theyreside. A strongly balanced triad exhibits intermittency with a partisan(sudden transitions between long intervals of static beliefs and turbulentnonconvergence) and asymptotic learning without a partisan.

Discerning media bias within a network of political allies and opponents: Disruption by partisans