The Voter Model with Homogeneous Mixing

Abstract

This chapter is devoted to the analysis of a simple opinion model in order to illustrate the ideas developed in the previous chapter. The projection from micro to macro emphasizes the particular role played by homogeneous mixing as a requirement for the Markovianity of the projected model. We present a Markov chain analysis of the binary voter model (VM) with a particular focus on its transient dynamics and show that the general VM can be reduced to the binary case by further projection. Finally, the question of interaction constraints in form of bounded confidence is addressed. Homogeneous interaction probabilities (homogeneous mixing) are assumed in all the analyses presented in this chapter. Interaction heterogeneities are left for the next chapters.