  We propose the PageRank model of opinion formation and investigate its rich
properties on real directed networks of Universities of Cambridge and Oxford,
LiveJournal and Twitter. In this model the opinion formation of linked electors
is weighted with their PageRank probability. We find that the society elite,
corresponding to the top PageRank nodes, can impose its opinion to a
significant fraction of the society. However, for a homogeneous distribution of
two opinions there exists a bistability range of opinions which depends on a
conformist parameter characterizing the opinion formation. We find that
LiveJournal and Twitter networks have a stronger tendency to a totalitar
opinion formation. We also analyze the Sznajd model generalized for scale-free
networks with the weighted PageRank vote of electors.
