With vast amounts of high-quality information at our fingertips, how is it possible that many people believe that the Earth is flat and vaccination harmful? Motivated by this question, we quantify the implications of an opinion formation mechanism whereby an uninformed observer gradually forms opinions about a world composed of subjects interrelated by a signed network of mutual trust and distrust. We show numerically and analytically that the observers resulting opinions are highly inconsistent (they tend to be independent of the observers initial opinions) and unstable (they exhibit wide stochastic variations). Opinion inconsistency and instability increase with the world complexity represented by the number of subjects, which can be prevented by suitably expanding the observers initial amount of information. Our findings imply that even an individual who initially trusts credible information sources may end up trusting the deceptive ones if at least a small number of trust relations exist between the credible and deceptive sources.
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