In this paper we present a model of sequential decision-makings of heterogeneous agents to explain self-controlled behaviors found in the empirical study. Each agent faces in sequence a binary decision and she makes her decision by reflecting her preference over two alternatives as well as social influence. The choices made by heterogeneous agents reflect both their own evaluations and the social influence received from other agents.  

There are basically two opposite cases, social cues influence to agents positively or negatively. And it is interesting question when information processing by individual agents is consistent with either conformity-like behavior (positive social influence) or nonconformity-like behavior (negative social influence). In the former case, agents will tend to follows the trend, but in the later case, agents behave against to the majority does and may offset the current trend by choosing a differing one. As a consequence nonconformist-like behavior does a softening of the current social trend.

We show the collective dynamics lead to outcomes that appear to be deterministic in spite of being governed by a stochastic decision models at the agent levels. We investigate the level of cascade size and find relationship between agents’ preference strength and the level of social influence on the cascade size. When the social influence is strong, the collective decision process settles down to a fraction of agents that is not predetermined by agents’ preferences. In this case, we observe a polarized collective decision. In this case, a decision tends to reinforce previous decisions and thus become more extreme that reflects trend following by the population and a large cascade occurs. However, when the social influence is relatively weak, the collective decision is determined by the agents’ preferences.

The role of nonconformist-like behavior is crucial to control cascade. Non-conformists who make decisions against social cues can offset the current trend and by choosing a differing one from the majority choice. Although the impact decreases with the number of agents involved, the existence of a small number of nonconformist-like behavior is enough for self-controlling cascade by a softening cascade.

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1. Collective Behavior under Coordination Games with Ternary Choice