  An analytical treatment of a simple opinion model with contrarian behavior is
presented. The focus is on the stationary dynamics of the model and in
particular on the effect of inhomogeneities in the interaction topology on the
stationary behavior. We start from a micro-level Markov chain description of
the model. Markov chain aggregation is then used to derive a macro chain for
the complete graph as well as a meso-level description for the two-community
graph composed of two (weakly) coupled sub-communities. In both cases, a
detailed understanding of the model behavior is possible using Markov chain
tools. More importantly, however, this setting provides an analytical scenario
to study the discrepancy between the homogeneous mixing case and the model on a
slightly more complex topology. We show that memory effects are introduced at
the macro level when we aggregate over agent attributes without sensitivity to
the microscopic details and quantify these effects using concepts from
information theory. In this way, the method facilitates the analysis of the
relation between microscopic processes and a their aggregation to a macroscopic
level of description and informs about the complexity of a system introduced by
heterogeneous interaction relations.
