Predicting peak of participants in collective action

•Extending existing models of human decisions on collective action.•Utilizing related attributions and factors of collective action.•Exploring how to predict peaks of participants in collective action.

In terms of the number of participants, almost each collective action has a life cycle where the number grows from zero to its peak where its maximum potential power or influence is acquired, then it decreases to zero eventually. Therefore, we concentrate on modeling, simulating, and predicting the peaks. The model is constructed based on previous models, and the data is collected from simulations. Preliminarily, it suggests that there exists a peak for collective action when its “jointness of supply” is less than one. Under complete homogeneity, the ideal peak is calculated and the ideal peaks function (IPF) is obtained. Then, heterogeneity is introduced into to the model, and the form of real peaks function (RPF) can be obtained based on simulations and statistical methods. For those who intend to organize a collective action and increase the peak of participants should take measures, such as ideology, leadership, and propagation, to enhance homogeneity or try to reduce heterogeneity.