Models of minority opinion spreading

Maxi San Miguel (Physics of Complex Systems, University of Balearic Islands) has won the Medal of the Royal Society of Physics in Spain. Congratulations for this excellent researcher. His studies linking Physics to Social Dynamics are very interesting. And so, Wio, Toral, Tessone, Amengual, San Miguel (2004), have exposed several neighborhood models of minority opinion spreading the idea which we analyze in this article. According to the authors, the neighborhood models are locally defined neighborhood cells systems with complete connectedness. Neighborhood cells change shape and size during evolution. The question is How an initially minority opinion can become majority? Obviously, there are several theoretic models like Galam Model. Galam (2002) says that social inertia is a conservative response to the risk of a change maintaining social status quo. Let be a binary opinion and initially there is a minority against social reform. Cells are defined only by their size. A tie in the voting is a "No" for social reform. When all the agents in the cell adopt an opinion, agents join a meeting cell randomly selected. Decision rule is applied in all the cells. Agents randomly redistributed in the meeting cells carry their adopted opinion. Applying a mean-field analysis, there is a threshold value of initial minority supporters such that the minority opinion finally becomes majority. There is an asymmetric unstable fixed point or "faith point". Time to reach consensus is fast and system-size independent. In this model, individuals are fixed at the sites of a regular lattice and meeting cells are locally defined by a tessellation of the lattice. Consensus is always reached in finite systems in a finite number of steps. In an infinite system the initial minority opinion wins regardless the amount of initial supporters. Why? Because a critical size for an initial local domain of minority supporters exists: a domain of overcritical size always exists in a large enough population. Neighborhood models describe a more efficient spreading of minority opinion, but spreading takes a much longer time.