Vacillating voter model

Vacillating voter model is a generalization of the voter model, which shows that contrarian behavior can emerge from imitative interactions [1]. This result is kind of interesting and counter-intuitive as usually, in other models of opinion dynamics, contrarian behavior is being explicitly built in.

The model

The model is strongly reminiscent of the voter model, yet with a small caveat. If a randomly selected voter has the same opinion as its (first) randomly picked neighbor, he picks another (second) neighbor and adopts its opinion.

This simple change has a profound effect. In case of the original voter model on a square lattice the flip probability is \( \frac{k}{4} \) (where \( k \) is a number of disagreeing neighbors). In this model on a square lattice flip probability is larger: \( 0 \) (for \( k=0 \)), \( \frac{1}{2} \) (for \( k=1 \)), \( \frac{5}{6} \) (for \( k=2 \)) and \( 1 \) (for \( k \geq 3 \)). These vacillating agents more easily succumb to the peer pressure, even if only one neighbor disagrees.

HTML 5 app

This app does not have any parameters besides the probability used during model initialization. Yet feel free to explore consensus times of this simple model.

Acknowledgment. This post was written while reviewing literature relevant to the planned activities in postdoctoral fellowship ''Physical modeling of order-book and opinion dynamics'' (09.3.3-LMT-K-712-02-0026) project. The fellowship is funded by the European Social Fund under the No 09.3.3-LMT-K-712 ''Development of Competences of Scientists, other Researchers and Students through Practical Research Activities'' measure.

References

• R. Lambiotte, S. Redner. Dynamics of vacillating voters. Journal of Statistical Mechanics 2007: L10001 (2007). doi: 10.1088/1742-5468/2007/10/L10001. arXiv:0710.0914 [physics.soc-ph].