  Currently used models of opinion formation use random initial conditions. In
reality, most people in a social network, except for a small fraction of the
population, are initially either unaware of, or indifferent to, the disputed
issue. To explore the consequences of such specific initial conditions, we
study the polarization of social networks when conflicting ideas arise on two
different seed nodes and then spread according to a majority rule. Using the
configuration model and the stochastic block model as examples, we show that
this framework leads to substantially different outcomes than those which
employ random initial conditions. Moreover, the empirically observed splits in
the karate and the dolphins' networks naturally come out of this paradigm. Our
work thus suggests that the existing opinion dynamics models should be
reevaluated to incorporate the initial condition dependence.
