  With social media, the flow of uncertified information is constantly
increasing, with the risk that more people will trust low-credible information
sources. To design effective strategies against this phenomenon, it is of
paramount importance to understand how people end up believing one source
rather than another. To this end, we propose a realistic and cognitively
affordable heuristic mechanism for opinion formation inspired by the well-known
belief propagation algorithm. In our model, an individual observing a network
of information sources must infer which of them are reliable and which are not.
We study how the individual's ability to identify credible sources, and hence
to form correct opinions, is affected by the noise in the system, intended as
the amount of disorder in the relationships between the information sources in
the network. We find numerically and analytically that there is a critical
noise level above which it is impossible for the individual to detect the
nature of the sources. Moreover, by comparing our opinion formation model with
existing ones in the literature, we show under what conditions people's
opinions can be reliable. Overall, our findings imply that the increasing
complexity of the information environment is a catalyst for misinformation
channels.
