Consensus formation in the Deffuant model

Licentiate thesis, 2014

This thesis deals with a mathematical model used in the context of social interaction in large groups, introduced by Deffuant et al. in 2000. Each individual holds an opinion and shares it with others in random pairwise encounters. If the difference in opinions of two interacting agents is less than a given threshold, the discussion will lead to an update of their opinions towards a compromise. If the difference is too large, however, they will ignore each other and separate with their opinions staying unchanged. Many results on long-time behavior of this opinion formation process – mainly dealing with whether a common consensus is reached or not – were established using computer simulations (for different underlying network topologies; interactions can only take place between neighboring individuals). In the two papers this thesis is based on, we study the model on integer lattices analytically, using geometric arguments and probabilistic tools as well as concepts from statistical physics. While the first paper focusses on univariate opinions but considers also higher-dimensional lattices as well as infinite percolation clusters as underlying network graphs, the second one sticks to the infinite line graph as topology and deals with multivariate opinions instead.