Granovetter (1978) provides an outstanding example of threshold models of collective behavior. The author defines an individual’s threshold as the situation in which the net benefits of joining a case begin to surpass its costs and employs this concept to clarify devotion to a riot. In this model, the price to a person of associating with a riot is a decreasing function of the number of individuals already uprising, since the probability of being caught decreases as the size of the riot grows. Each person has a threshold shown as the number of rioters he wants to observe before he is willing to start participating in the process him- or herself.
The model aims to forecast, given the initial distribution of individuals’ thresholds, the final quantity of rioters. In this way, the model illustrates that individuals’ characters cannot be assumed from aggregate outcomes, and vice versa, since agents’ decisions are co-dependent.
Granovetter’s model also illustrates how a person’s decision does not depend on his preferences alone but is influenced by what others desire. Thus, the author states that, although necessary, knowledge of preferences, motives, and beliefs of the people involved is not adequate in explaining outcomes. On the contrary, it is necessary to explain how persons’ preferences interact to explain collective outcomes, and neglecting such interactions may misguide one into assuming non-existing relationships between aggregate outcomes and personal preferences. If the distributions of thresholds differ even slightly from group to group, very different outcomes may appear. The model can elucidate high variances across diverse groups.
The major drawback to this type of model is that the final possible outcomes they depict are ultimately determined by the selection of the initial distribution of personal thresholds. That is, the agent is required to make ad hoc hypotheses about the attribute of the initial population. Such an obligation implies knowledge and information that are not likely to be easily obtainable.
There is, nevertheless, another way to initiate threshold levels in models of collective behavior.
Indeed, it is feasible to model thresholds not as an individual to each agent, but as significant levels in the distribution of potential outcomes for the entire community. The latter technique implies the advantage of not needing arbitrary assumptions about agents’ dispersals and, for any period, employs realized proportions of the considered event as a proxy for initial settings.
Within the context of the research on collective behavior, Granovetter recognizes the existence of critical levels of social characteristics that enable the observer to deduce the direction toward which a community will move after the critical level is attained. In addition to the introduction of his revolutionary model, Granovetter contributes by spotting non-linearity in the expansion of social phenomena. Indeed, he illustrates that patterns of group interaction are non-linear and that a person’s decision to adopt a specific behavior grows at an increasing rate as that behavior becomes more prevalent within his group. We believe that threshold models are essential in explaining social behavior and this paper is an attempt to depict such a model initially introduced by Granovetter.
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