Last time I have admitted that I have misread one well-known generalization of the Sznajd model. This time I would like to present you the original interpretation proposed by Stauffer in . Though I would like to note that I was still unable to reproduce Stauffer's original result.
As we have already written last time this generalization of the Sznajd model introduces two intermediate opinions into the model. Namely, in order to switch opinion between the extremes agent must first go through the intermediate opinions. In this sense this model is similar to the AB model. Yet these two models produce different results: in AB model extreme opinions "win", while here one of the intermediate opinions should prevail .
What I have misread/misinterpreted last time was that in fact empty cells are usefull as this generalization also introduces movement of the agents. This adds additional "diffusion" step into the original algorithm of the Sznajd model.
So we have implemented the following algorithm. First select a random agent and move it to a random neighboring empty cell (if it is possible). Next select a new random agent and a random neighboring cell. If that cell contains an agent of the same opinion, then these two agents, as usual, convince their neighbors (if opinions are not too different).
This numerical algorithm is likely different from the one used in . Many technical details, which could have noteable impact, remain unclear. Thus it is likely why we fail to replicate the reported result ("third" place wining).
Feel free to explore the dynamics of Stauffer's four state Sznajd model. In this app you have only "one" parameter - proportion of empty cells and agents with different opinions. Try maybe you will capture the moment when the third wins?
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.
- D. Stauffer. Better being third than second in search for a majority opinion. Advances in Complex Systems 5: 97-100 (2002). doi: 10.1142/S0219525902000511.