  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 Barab\'asi-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.
