  Assume two different communities each of which maintain their respective
opinions mainly because of the weak interaction between the two communities. In
such a case, it is an interesting problem to find the necessary strength of
inter-community interaction in order for the two communities to reach a
consensus. In this paper, the Information Accumulation System (IAS) model is
applied to investigate the problem. With the application of the IAS model, the
opinion dynamics of the two-community problem is found to belong to a wider
class of two-species problems appearing in population dynamics or in
competition of two languages, for all of which the governing equations can be
described in terms of coupled logistic maps. Tipping diffusivity is defined as
the maximal inter-community interaction that the two communities can stay in
different opinions. For a problem with simple community structure and
homogeneous individuals, the tipping diffusivity is calculated theoretically.
As a conclusion of the paper, the convergence of the two communities to the
same value is less possible the more overall interaction, intra-community and
inter-community, takes place. This implies, for example, that the increase in
the interaction between individuals caused by the development of modern
communication tools, such as facebook and twitter, does not necessarily improve
the tendency towards global convergence between different communities. If the
number of internal links increases by a factor, the number of inter-community
links must be increased by an even higher factor, in order for consensus to be
the only stable attractor.
