Strictly weak consensus in the uniform compass model on Z

Nina Gantert, Markus Heydenreich, Timo Hirscher

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a realignment of opinions closer towards each other. This mechanism triggers formation of consensus among the individuals. Our main focus is on strong consensus (i.e., global agreement of all individuals) versus weak consensus (i.e., local agreement among neighbors). By extending a known model to a more general opinion space, which lacks a "central" opinion acting as a contraction point, we provide an example of an opinion formation process on the one-dimensional lattice Z with weak consensus but no strong consensus.

Original languageEnglish
Pages (from-to)1269-1293
Number of pages25
Issue number2
StatePublished - 2020


  • Consensus formation
  • Deffuant model
  • Interacting particle system
  • Invariant measures
  • Markov process
  • Opinion dynamics


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