2011/07/22 by Nicolas Lanchier, Lanchier, Nicolas, Jason Schweinsberg +1
Mathematics · Physics and Astronomy · Social Sciences · #60K35 #Complex Network Analysis Techniques #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Opinion Dynamics and Social Influence #Probability (math.PR) #math.PR #msc:60K35
paper · pdf · doi:10.48550/arxiv.1107.4413
arxiv created 2011/07/22 · openalex publication_date 2011/07/22 · arxiv updated 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Axelrod model is a spatial stochastic model for the dynamics of cultures which, similarly to the voter model, includes social influence, but differs from the latter by also accounting for another social factor called homophily, the tendency to interact more frequently with individuals who are more similar. Each individual is characterized by its opinions about a finite number of cultural features, each of which can assume the same finite number of states. Pairs of adjacent individuals interact at a rate equal to the fraction of features they have in common, thus modeling homophily, which results in the interacting pair having one more cultural feature in common, thus modeling social influence. It has been conjectured based on numerical simulations that the one-dimensional Axelrod model clusters when the number of features exceeds the number of states per feature. In this article, we prove this conjecture for the two-state model with an arbitrary number of features.