Collective Threshold Model Based on Utility and Psychological Theories

Collective Threshold Model Based on Utility and Psychological Theories

Zhenpeng Li (Dali University, Dali, China) and Xijin Tang (CAS Academy of Mathematics and Systems Science, Beijing, China)
Copyright: © 2013 |Pages: 9
DOI: 10.4018/ijkss.2013100105
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Abstract

In this paper the authors investigate critical phase transition characteristic of collective action by considering the mechanisms of both rational utility and psychological threshold based on the Granovetter (1978)'s threshold model. Numeric simulation is used to observe the collective dynamics with consideration of both spatial factor and social network friendship density. The authors observe that activation threshold model with both utility and psychological thresholds included shows more stable in phase transition than that in the classic model. The authors also find that spatial factor and friendship network density have trivial impact on final equilibrium of collective behavior.
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2. Granovetter’S Threshold Model

Granovetter (1978)’s threshold model is one of the classic models which are used to describe collective action, such as riots and strikes. The model assumes that the possibility of each actor would join the collective action depends on the proportion of actors who have been participated in the action. In one social group, each member has his/her specific activation threshold for one specific action, and the group threshold belongs to certain probability distribution. The threshold for the instigator is zero, the radical has lower threshold and the conservative has higher threshold. The strict mathematic form of threshold model is as following:

(1) where is the probability mass distribution of group threshold, and F(x) is the corresponding cumulative distribution function and stands for the proportion of actors whose threshold is equal or less than x. We assume at the certain discrete time step t the ratio of actors who have been entered into collective action is r(t), then at step t + 1 the proportion of actors who join in the action is r(t + 1) = F(r(t)):

  • Proposition: When r (t + 1) = r (t), the equilibrium state of one collective action is reached. The final equilibrium number of actors joining the collective action is denoted by .

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