AGENT BASED MODELS AND OPINION DYNAMICS AS MARKOV CHAINS
Sven BANISCH, Ricardo LIMA AND Tanya ARAUJO
Abstract. This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM
dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it
possible to establish the cases where the macro model is still Markov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in
applications. For such a purpose a crucial role is played by the type of probability distribution used to implement the stochastic part of the model which deﬁnes the updating rule and governs the
dynamics. In addition, we show how restrictions in communication leading to the co–existence of diﬀerent opinions follow from the emergence of new absorbing states. We describe our analysis in
detail with some speciﬁc models of opinion dynamics. Generalizations concerning diﬀerent opinion representations as well as opinion models with other interaction mechanisms are also discussed. We
ﬁnd that our method may be an attractive alternative to mean–ﬁeld approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics, and more generally of
Keywords: Agent Based Models, Opinion Dynamics, Markov chains, Micro Macro, Lumpability , Transient Dynamics .
MSC: 37L60, 37N25, 05C69.