Noisy Deffuant's bounded confidence model

Let us briefly come back to the Deffuant's model and discuss the impact of noise on the dynamics of the model. There multiple ways to introduce the noise into the model, so here we will focus on the way proposed in [1].

The core of the model remains the same as proposed in the original paper [2]. The only difference is that after we select the first agent, it may change opinions independently with probability \( p_n \). If agent decides to change opinion independently, then its new opinion is resampled from uniform distribution (in the same manner as during the initialization of the model). Otherwise, the second agent is selected and their opinions are update as in the original model.

At first introduction of noise seems to do a trivial thing. Clusters are no longer as tight as without noise. They appear to be more spread out. But in certain cases a non-trivial effect can be seen. Namely, smaller and less stable cluster emerge. For some parameter sets these "side" clusters persist, but in some cases they appear and disappear, only to reappear at some later time.

Feel free to explore the new dynamics using the app below. Unlike earlier, here we report only logarithmic density of agents in certain opinion ranges (0.01 increments). The darker the color, the more agents share similar opinions. The ticks on the plot were placed in 0.1 increments.

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

• M. Pineda, R. Toral, E. Hernandez-Garcia. Noisy continuous-opinion dynamics. Journal of Statistical Mechanics 2009: P08001 (2009). arXiv: 0906.0441 [physics.soc-ph]. doi: 10.1088/1742-5468/2009/08/P08001.
• G. Deffuant, D. Neau, F. Amblard, G. Weisbuch. Mixing beliefs among interacting agents. Advances in Complex Systems 3: 87-98 (2000). doi: 10.1142/S0219525900000078.