  We reformulate the agent-based opinion dynamics models of Weisbuch-Deffuant
and Hegselmann-Krause as interactive Markov chains. So we switch the scope from
a finite number of n agents to a finite number of n opinion classes. Thus, we
will look at an infinite population distributed to opinion classes instead of
agents with real number opinions. The interactive Markov chains show similar
dynamical behavior as the agent-based models: stabilization and clustering. Our
framework leads to a discrete bifurcation diagram for each model which gives a
good view on the driving forces and the attractive states of the system. The
analysis shows that the emergence of minor clusters in the Weisbuch-Deffuant
model and of meta-stable states with very slow convergence to consensus in the
Hegselmann Krause model are intrinsic to the dynamical behavior.
