The Deuant model on Z with higher-dimensional opinion spaces

Abstract. When it comes to the mathematical modelling of social interaction pat-terns, a number of dierent models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph structure and share their opinions. A prominent example of the so-called bounded con dence models is the one introduced by Deuant et al.: Two neighboring in-dividuals will only interact if their opinions do not dier by more than a given threshold . We consider this model on the line graph Z and extend the results that have been achieved for the model with real-valued opinions by considering vector-valued opinions and general metrics measuring the distance between two opinion values. As in the univariate case there turns out to exist a critical value c for at which a phase transition in the long-term behavior takes place, but c depends on the initial distribution in a more intricate way than in the univariate case. 1