Consensus formation in the Deffuant model
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.