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.
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