A multi-opinion evolving voter model with infinitely many phase transitions

Abstract

We consider an idealized model in which individuals' changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge. Specifically, an interaction between $x$ and one of its neighbors $y$ leads to $x$ imitating $y$ with probability $(1-\alpha )$ and otherwise (i.e., with probability $\alpha$) $x$ cutting its tie to $y$ in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion situation, finding that the model has infinitely many phase transitions. Moreover, the formulas describing the end states of these processes are remarkably simple when expressed as a function of $\beta =\alpha /(1-\alpha )$.

15 pages, 6 figures

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Cited by in corpus (10)

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• Collective dynamics of belief evolution under cognitive coherence and social conformity
• Noise in Coevolving Networks
• Transitivity reinforcement in the coevolving voter model
• Adaptive network models of collective decision making in swarming systems
• Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models
• Spontaneous symmetry breaking of active phase in coevolving nonlinear voter model
• Local Symmetry and Global Structure in Adaptive Voter Models
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• Aging in coevolving voter models