  Possibility of reaching a consensus in social systems with strong initial
fragmentation is one of the most interesting issues in sociopysics. It is also
intriguing what the dynamics of such processes is. To address those problems,
we performed computer simulations using well-established models of social
opinion formation, namely the voter, Sznajd, and Latan\'e models. We
investigated opinion dynamics in cases where the initial number of opinions is
very large, equal to the number of actors (the voter and Latan\'e models) or
when every second actor has their own opinion (Sznajd model), with some
variations on the update schemes, lattice topologies, effective ranges of
interaction, and information noise levels. For all considered models, the
number of opinions assumed by the actors is finally almost always reduced to
only one. However, while the voter and Latan\'e models exhibit a power-law time
decrease in the number of opinions, the Sznajd model follows a complex
three-stage behavior. We also demonstrated that the mean/median time of
reaching the consensus scales with system size according to a power law for
voter and Sznajd models, while for the Latan\'e model this increase is even
faster. Our results show that in the studied models the consensus is possible,
provided that a long enough and model-dependent time to reach this state is
available.
