The axelrod model for the dissemination of culture revisited

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of F cultural features, each of which can assume q states. Pairs of adjacent vertices interact at a rate proportional to the number of features they share, which results in the interacting pair having one more cultural feature in common. The Axelrod model has been extensively studied during the past ten years, based on numerical simulations and simple mean-field treatments, while there is a total lack of analytical results for the spatial model itself. Simulation results for the one-dimensional system led physicists to formulate the following conjectures. When the number of features F and the number of states q both equal two, or when the number of features exceeds the number of states, the system converges to a monocultural equilibrium in the sense that the number of cultural domains rescaled by the population size converges to zero as the population goes to infinity. In contrast, when the number of states exceeds the number of features, the system freezes in a highly fragmented configuration in which the ultimate number of cultural domains scales like the population size. In this article, we prove analytically for the one-dimensional system convergence to a monocultural equilibrium in terms of clustering when F = q = 2, as well as fixation to a highly fragmented configuration when the number of states is sufficiently larger than the number of features. Our first result also implies clustering of the one-dimensional constrained voter model.

Original languageEnglish (US)
Pages (from-to)860-880
Number of pages21
JournalAnnals of Applied Probability
Volume22
Issue number2
DOIs
StatePublished - Apr 2012

Fingerprint

Voter Model
Model
One-dimensional System
Population Size
Exceed
Culture
Dissemination
Clustering
Social Influence
Converge
Configuration
Spatial Model
Fixation
Vote
Mean Field
Stochastic Processes
Adjacent
Directly proportional
Infinity
Imply

Keywords

  • Axelrod model
  • Constrained voter model
  • Cultural dynamics
  • Homophily
  • Interacting particle systems
  • Ppinion dynamics
  • Social influence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

The axelrod model for the dissemination of culture revisited. / Lanchier, Nicolas.

In: Annals of Applied Probability, Vol. 22, No. 2, 04.2012, p. 860-880.

Research output: Contribution to journalArticle

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