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Top1. Introduction
Although individual behavior is too complex to fully explain, collective behavior satisfies certain laws. According to Thomas C. Schelling, the 2005 Nobel Prize Winner in Economics, “sometimes the results are surprising, sometimes they are not easily guessed, sometimes the analysis is difficult” (Schelling, 2006). This point was emphasized by scientist Philip Ball in his book entitled Critical Mass: How One Thing Leads to Another, “collective behaviors are not necessary equal to the linear sum of behaviors of all persons, …, it can be transferred sharply to the totally inverse aspect even if few individuals change their behaviors slightly” (Ball, 2004) . This phase transition phenomenon is called percolation. Percolation makes the system flourish or collapse suddenly if it is at the intermediate state between order and disorder (Bakir, Tarrasy, et.al., 2016). For example, it is difficult to transition from few accepting a new technology to its widespread public acceptance (Friedkin et.al., 2016; Chen, J. et.al., 2021; Chen, S. et.al., 2021). The technology is suddenly accepted by the wider public if, and only if, the corresponding acceptance probability reaches a certain threshold (Wu, L.F. et.al., 2019). The collapse of China’s stock market in 2015 is another example. A-shares suffered a crash during the 52 trading days between June 15 and August 26. Only 102 of the total A-shares rose and as many as 2,498 dropped, of which 1,541 dropped by more than 50 percent (the data coming from https://xueqiu.com/4292490144/50196986). Considering these examples and circumstances, we would note that there seems to be a special attractor that attracts the system running toward this “percolation” point. It is also seen that percolation exists pervasively, such that the system always evolves around the critical point. This seems to be an attractor that attracts the system to move toward a certain criticality. In this paper, we ask: To achieve system percolation, how many individuals need to change their behaviors, and who are the individuals whose behaviors need to change?
According to scholars, the complexity of a system’s criticality of percolation relies on the properties of the system. In turn, the system’s properties are deterministic under certain interactive rules between agents and between agents and their environment. In this sense, four categories of system, according to agent behavior and system structure, are defined in Figure 1.
Figure 1. Interactivity between agents in a system