Fig. 1: Illustration of the mechanisms underlying the link updating process in the dyadic1 and triadic2 models.
Nodes A, B, and C are individuals. Pluses and minuses within the nodes indicate the individuals’ binary opinions (positive or negative) about 3 issues. Blue lines indicate positive links and red lines indicate negative links between the individuals. The initial state (left panel) is a balanced triangle +--. What would happen if A changes the first of her opinions from \(+\) to \(-\)? Her similarity to B would decrease, justifying the already present negative link between them, but she would become more similar to person C on 2 of 3 issues, prompting her to change her link to C from \(-\) to \(+\). Because B and C have a positive link between them, this would create an imbalanced triangle ++-. However, according to the dyadic model (top right) A does not notice this imbalance because she does not consider the link between B and C, only her own dyadic relationships with B and C. Therefore, she is likely to change her belief and the link with C. Over time, with just one more change in her belief (e.g., switching the last of her three beliefs from \(-\) to \(+\)), prompting the change of the relationship with B from \(-\) to \(+\) as well, this triangle can become a balanced +++ triangle. In contrast, in the triadic model (bottom right panel) A notices that her opinion change would produce an imbalanced triangle and does not change her belief or her link with B. As a result, the triangle remains +--. For detailed description of the mechanisms assumed by each model, please see Eqs. (1)–(4) and the accompanying text in the Methods section.
