Partisan voter model on a two dimensional grid

While doing literature review for my postdoctoral project I have taken a look at [1]. I have even implemented related interactive apps, but I have forgotten about them and not written a post about the model on Physics of Risk.

In this post I am sharing an app which implements partisan voter model on a two dimensional grid. There is nothing special about this particular version of the model. Just the average consensus time for this topology ought to be a bit shorter.

Interactive app

Below you should see an app, which implements Masuda's partisan voter model on a two dimensional grid (every agent is able to interact with his four immediate neighbors).

Notice that for non-trivial values of \( \varepsilon \) the model appears to not be able to settle down close to the self-centered polarization state. Also note the peculiar shapes of the cluster of agents with similar external opinions. They are very much reminiscent of the clusters observed in the Ising model near the critical temperature.

Note that this app colors agents (cells) according to their external opinion, while in the equations from the earlier post they are referred to by their internal opinions.

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

• N. Masuda, N. Gibert, S. Redner. Heterogeneous voter models. Physical Review E 82: 010103(R) (2010). doi: 10.1103/PhysRevE.82.010103.