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An individual's opinions about media bias derive from their own independent assessment of media outputs combined with peer pressure from networked political allies and opponents. Here we generalize previous idealized, probabilistic models of the perception formation process, based on a network of Bayesian learners inferring the bias of a coin, by introducing obdurate agents (partisans), whose opinions stay fixed. It is found that even one partisan destabilizes an allies-only network, stopping it from achieving asymptotic learning and forcing persuadable agents to vacillate indefinitely (turbulent nonconvergence) between the true coin bias θ 0 and the partisan's belief θ p. The dwell time t d at the partisan's belief increases, as the partisan fraction f increases, and decreases, when multiple partisans disagree amongst themselves. In opponents-only networks, asymptotic learning occurs, whether or not partisans are present. However, the counterintuitive tendency to reach wrong conclusions first, identified in previous work with zero partisans, does not persist in general for θ 0 ≠ θ p in complete networks; it is a property of sparsely connected systems (e.g. Barabási–Albert networks with attachment parameter ≲ 10). In mixed networks containing allies and opponents, partisans drive counterintuitive outcomes, which depend sensitively, on where they reside. A strongly balanced triad exhibits intermittency with a partisan (sudden transitions between long intervals of static beliefs and turbulent nonconvergence) and asymptotic learning without a partisan. Counterintuitively, in an unbalanced triad, one of the persuadable agents achieves asymptotic learning at θ 0 , when the partisan is located favorably, but is driven away from θ 0 , when there is no partisan. The above results are interpreted briefly in terms of the social science theory of structural balance. • Even one partisan destabilizes an allies-only network and drives vacillating beliefs. • Disagreeing partisans heighten network instability and shorten dwell times. • Opponents-only networks achieve asymptotic learning with or without partisans. • Wrong conclusions are reached first in sparsely connected opponents-only networks. • Various ally-opponent networks containing partisans exhibit intermittency. [ABSTRACT FROM AUTHOR]

Perceptions of political bias in the media are formed directly, through the independent consumption of the published outputs of a media organization, and indirectly, through observing the collective responses of political allies and opponents to the same published outputs. A network of Bayesian learners is constructed to model this system, in which the bias perceived by each agent obeys a probability density function, which is updated according to Bayes's theorem given data about the published outputs and the beliefs of the agent's political allies and opponents. The Bayesian framework allows for uncertain beliefs, multimodal probability distribution functions, and antagonistic interactions with opponents, not just cooperation with allies. Numerical simulations are performed to test the idealized example of inferring the bias of a coin. It is found that some agents converge on the wrong conclusion faster than others converge on the right conclusion under a surprisingly broad range of conditions, when antagonistic interactions are present which "lock out" some agents from the truth, e.g. in Barabási–Albert networks. It is also found that structurally unbalanced networks routinely experience turbulent nonconvergence, where some agents fail to achieve a steady-state belief, e.g. when they are allies of two agents who are opponents themselves. The subtle phenomenon of long-term intermittency is also explored. • Opponents-only networks encourage the wrong conclusion to be reached first. • Ally-opponent networks prevent a steady-state conclusion from being reached. • Some agents in ally-opponent networks vacillate between certainty and doubt. • Discernment of media bias by Bayesian learners fits structural balance theory. [ABSTRACT FROM AUTHOR]