  We develop a model of opinion dynamics where agents in a social network seek
to learn a ground truth among a set of competing hypotheses. Agents in the
network form private beliefs about such hypotheses by aggregating their
neighbors' publicly stated beliefs, in an iterative fashion. This process
allows us to keep track of scenarios where private and public beliefs align,
leading to population-wide consensus on the ground truth, as well as scenarios
where the two sets of beliefs fail to converge. The latter scenario - which is
reminiscent of the phenomenon of cognitive dissonance - is induced by injecting
'conspirators' in the network, i.e., agents who actively spread disinformation
by not communicating accurately their private beliefs. We show that the agents'
cognitive dissonance non-trivially reaches its peak when conspirators are a
relatively small minority of the population, and that such an effect can be
mitigated - although not erased - by the presence of 'debunker' agents in the
network.
