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

@article{Shi2013AME,
  title={A multi-opinion evolving voter model with infinitely many phase transitions},
  author={Feng Shi and Peter J. Mucha and Richard Durrett},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 6},
  pages={
          062818
        }
}
  • F. ShiP. MuchaR. Durrett
  • Published 29 March 2013
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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-α) and otherwise (i.e., with probability α) x cutting its tie to y in order to instead connect to a randomly chosen individual… 

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References

SHOWING 1-10 OF 43 REFERENCES

Graph fission in an evolving voter model

Using simulations and approximate calculations, it is explained why these two nearly identical models of a social network in which individuals have one of two opinions and their opinions and the network connections coevolve have such dramatically different phase transitions.

Nonequilibrium phase transition in the coevolution of networks and opinions.

  • P. HolmeM. Newman
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
A simple model of the convergence of opinion in social systems, with a single parameter controlling the balance of the two processes, that undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.

Opinion and community formation in coevolving networks.

This model includes the opinion-dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation and shows the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.

Cooperation, social networks, and the emergence of leadership in a prisoner's dilemma with adaptive local interactions.

It is shown how the network adaptation dynamics favors the emergence of cooperators with the highest payoff, and these "leaders" are shown to sustain the global cooperative steady state.

Evolutionary games in self-organizing populations

It is shown how the individual capacity of forming new links or severing inconvenient ones can change the nature of the game, and if the linking rules are local, numerical simulations show that the resulting networks capture some of the features characteristic of real-world social networks.

Multi-Stage Complex Contagions

It is demonstrated that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, which cannot occur in single-stage contagion models.

Coevolution of strategy and structure in complex networks with dynamical linking.

This work provides analytic results for the limiting cases where linking dynamics is much faster than evolutionary dynamics and vice versa, and shows how the individual capacity of forming new links or severing inconvenient ones maps into the problem of strategy evolution in a well-mixed population under a different game.

Consensus formation on adaptive networks.

  • B. KozmaA. Barrat
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
The investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion, although it also promotes the division of these clusters.