S. Galam's referendum model
Eleven years ago I have written a post about many particle interactions in the kinetic exchange models. Few days ago I have stumbled upon that post and noticed that it features a model that has little in common with kinetic exchange models. Under these circumstances the only natural thing is to write a dedicated post highlighting the said model.
So, consider how we make decisions. Not all of us are skilled and informed enough to make decisions on our own in all possible everyday scenarios. I may be a physicist, but I do not understand some branches of physics well enough. I am not speaking about the questions outside my work or hobby expertise. In such cases, we must rely on our social contacts (acquaintances, co-workers, family members, etc.) to help us decide.
Referendum model
In Galam's referendum model [1] people meet in their discussion groups of varied sizes. For simplicity sake, let us assume that group sizes and composition are random. In other words, during each round of discussion (time tick) the people will form new groups of a random size. Thus, the most important parameter in this model is the group size distribution (the app allows groups up to \( 6 \) people to be formed).
To keep the discussion as simple as possible, let us assume that afterwards, everyone in the group will have same opinion as the initial majority in the group. Let us also assume that the question is binary, i.e., it may be answered with "yes" or "no". If an odd number of people form a group, there will be a clear initial majority. On the other hand, if there is an even number of people in the group, then there will be a certain probability to end up no clear initial majority (both "yes" and "no" options receiving the same "support"). In this case, S. Galam notes that people have a conservative tendency, and thus, in case of a tie, the members of such discussion group will choose the more conservative option (lets say that it is the "no" option). Interestingly enough, this simple and very realistic assumption may cause society to shift from a positive (\(\xi(t)>0\)) attitude towards the negative (\(\xi(t)<0\)) attitude.
We want to draw your attention to the fact that \( \xi \) here represents the mean opinion. If you prefer a raw fraction of individuals choosing the "yes" option, then you may obtain it this way:
\begin{equation} x_{+} = \frac{1 + \xi}{2} . \end{equation}
Interactive app
We invite you to explore the interactive app below. You may adjust initial condition, \(\xi(0)\), and the probabilities to have specific group sizes, \(p[N]\). Observe what happens when the probability to have even-sized group grows small, \(p[2] + p[4] + p[6] \ll p[3]+p[5]\), i.e., when the tie-breaker mechanism applies rarely.
References
- S. Galam. Sociophysics: A review of Galam models. International Journal of Modern Physics C 19: 409-440 (2008). doi: 10.1142/S0129183108012297. arXiv:0803.1800 [physics.soc-ph].
