Nowak, Szamrej, & Latane (1990) Dynamic Theory of Social Impact

Nowak, A., Szamrej, J., & Latané (1990). From private attitude to public opinion: A dynamics theory of social impact. Psychological Review, 97, 362-376. 

This paper extends work on social impact theory (Latané 1981), which looks at how individuals' attitudes are influenced by others.

• "Social impact theory concerns the magnitude of impact that one or more people or groups (sources) have on an individual." (p. 364)
• Under this theory, the impact is a multiplicative function of three factors: the strength of the sources (e.g., their authority or power of persuasion), the immediacy of the sources (e.g., their closeness in space and time), and the number of sources. 
• Some math was done to get at some aspects of this relation. For example, the strength of influence was proportional to the square root of the number of sources. However, it was a static theory, and does not account for the fact that influences occur with feedback and cascades. 

The model
They built a computational model of agents on a 2-D square grid.
Each agent has four attributes:

1. Attitude: a binary trait denoting the agent hold one of two attributes. 
2. Persuasiveness: the degree to which an individual can persuade someone with the opposite attitude to change. This was drawn from a random distribution (0-100), and changed randomly every time the agent changed its attitude. 
3. Supportiveness: the degree to which an individual can convince someone with the same attitude to retain it. Like persuasion, this was drawn from a random distribution (0-100), and changed randomly every time the agent changed its attitude. 
4. Immediacy: Relates to the agent's position on the grid. This is an attribute of pairs of agents. 

Model dynamics

• The strength of an agent's influence on another was inversely related to the square of the (Euclidean) distance between them.  
• The total persuasive impact
• i_p = n^.5 * [\sum [p_i/d_i^2]/n]
• where i_p is the persuasive impact, n is the number of individuals with an opposing view, p_i is the persuasiveness of source i, and d_i is the distance between the source and the recipient. 
• The total impact of social support is the same, except that p_i is replaced with s_i (supportiveness) and n denotes the number of individuals with the same view. 
• Change rule: an individual's attitude changes if the impact of the individual from those with a different opinion is greater than the impact of those with the same opinion. 
• Updating is synchronous for all agents at each time step. 

Results

This model led to clustering of opinions, so that there is a landscape of spatial clusters. 

A neat trick -- this leads to group polarization.