Conditions

Social-influence models make various predictions about the structural conditions under which consensus, opinion fragmentation, and opinion polarization can emerge. The term "structural" indicates that we focus here on aspects that are external to the individual. These aspects change the environment in which agents influence each other and may inform the development of intervention strategies.

Note that different models of how agents exert influence on each other (see the Models page) often make opposite predictions about whether certain conditions foster or hamper the emergence of opinion convergence, fragmentation, and polarization. Here, we summarize central insights.

Homophily

Homophily is a strong force in human interaction. In many contexts, humans tends to select interaction partnes with similar opinions. This is not always a consequence of a preference for similar interaction partners. It can also result from so-called "social foci" and characteristics of the social environment.

In tandem with positive social-influence, homophily creates a self-reinforcing feedback loop that can contribute to fragmentation of opinions. If network contacts happen to agree, they will interact and grow more similar. This, in turn, intensifies similarity and makes subsequent interaction more likely. This loop can generate clusters when opinions converge locally but differences between clusters persist. Reinforcement models even generate opinion polarization (cluster grow more dissimilar) when homophily is sufficiently strong. In constrast, models assuming negative influence generate less polarization under strong homophily, as homophily leads to fewer communication between agents that influence each other negatively.

Recently, homophily has received a lot of attention, as personalization algorithms installed on online social networks increase homophily.

Multiple influence dimensions and multilayered networks

Most studies assume that agents influence each other on a single dimension. It has been shown that increasing the number of dimensions increases the chances that consensus emerges. The reason is simple. When agents initially hold random opinions on a large number of dimensions, then the chance that two agents disagree on most dimension is very low. Thus, when there are many opinon dimensions, agents tend to agree (on average), which fosters social influence (homophily) and makes negative influence less likely.

This conclusion depends on two assumptions, however. First, when the different opinions are correlated, then agents who disagree on one dimensions will also tend to disagree on other dimensions. This makes reaching a consensus less likely. This correlation is sometimes refered to as "congruency". Second, Battiston et al. (2018) added the assumption that agents discuss certain issues only with a subset of their contacts. For instance, agents may not discuss religious issues with their colleagues. As a consequence, they are not exerting influence on their colleagues' religious views. This assumption can contribute to preserving diversity.

When opinions are measured on a nominal scale, not only the number of issues but also the number of possible traits per issue matters. Strikingly, the number of traits has the opposite effect than the number of influence dimensions, as Axelrod demonstrated. Higher numbers of traits decrease the chance that two connected agents with random opinions happen to agree. As a consequence, influence is less likely (homophily) and diversity is preserved.

One-to-one, many-to-one, and one-to-many communication

In many models, interaction is modeled dyadically. Two agents are selected and then one exerts influence on the other. This is one-to-one communication. Other models implemented that influence can be "social" in that first an agent is selected for opinion update. Next, the influences of multiple network contacts on the agent is aggregated. This is many-to-one communication. In the most classical models, for instance, it is assumed that agents move towards the average of their contacts' opinions. In some models, this can make a big difference. For instance, Axelrod modeled one-to-one communication, assuming that an agent adopts a nominial trait from a contact. In a many-to-one version of this model, one could assume that the selected agent adopts the most frequent trait in her neighborhood. Flache and Macy showed that this fosters diversity and makes polarization more robust to noise. A third communication form is called one-to-many communication. It has been argued that this form best represents communication in online social networks (such as Twitter and Facebook) where users share content with all their contacts at the same time. Keijzer et al. (2018) demonstarted that this can increase fragmentation and polarization, in particular in highly clustered networks. The reason is that when an agent A happens to not be influenced by a neighbor B, then A does not only grow more similar to B. In addition, A grows dissimilar to their common friends who have been influenced.

Demographic diversity and faultline strength

In some models, agents are not only described by opinions. In addition, they hold fixed attributes representing demographic attributes such as gender, and ethnicity. Demographic attributes are, in addition, assumed to affect the selection of communication partners. Implementing homophily (see above), it is assumed that agents tend to communicate with demographically similar others. When agents hold only a single demographic attribute, reinforcement models and negative-influence models generate more opinion polarization.

The effects of demograpghic diversity are more complex when agents hold multiple demographic attributes. In line with the faultline hypothesis from the management literature and classical sociological theories, models predict that polarization is more likely when multiple demographic attributes are correlated. With uncorrelated demographic attributes, in contrast, agents tend to share attributes with most interaction partner, which fosters consensus formation.

Timing of contacts

In his famous "Contact theory" Allport proposed that contact between members of different groups has the potential to improve intergroup relations. Some social-influence models, however, add that it matters who is when brought into contact with whom.

Models of negative influence, for instance, imply that opinion polarization can be prevented when first agents with similar demographic attributes interact. Demographic similarity leads to positive social influence and opinion convergence. If then agents interact with members of the other demographic subgroup, opinion similarity will lead to positive relationships between the groups and foster opinion convergence. The opposite interaction schedule will lead to opinion polarization, as demographic differences and opinion disagreement will trigger negative influence.

The opposite prediction follows from reinforcement models. When agents with similar demographic subgroups interact in the first phase, opinions will be reinforced and subgroups will likely develop opposite opinions. These differences will prevent opinion convergence in the second phase.

Spatial segregation

• Feliciani, T., Flache, A., & Tolsma, J. (2017). How, When and Where Can Spatial Segregation Induce Opinion Polarization? Two Competing Models. Journal of Artificial Societies and Social Simulation, 20(2)

• Flache, A. 2019. Social integration in a diverse society: Social complexity models of the link between segregation and opinion polarization. Pp. 213-228 in: F. Abergel, B.K. Chakrabarti, A. Chakraborti, N. Deo and K. Sharma (Eds.). New Perspectives and Challenges in Econophysics and Sociophysics, Springer New Economic Windows. https://doi.org/10.1007/978-3-030-11364-3_15

Network clustering (transitivity)

• • Keijzer, M. A., Mäs, M., & Flache, A. (2018). Communication in online social networks fosters cultural isolation. Complexity, 1–20

  • FORTUNATO, S. (2005). On The Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann. International Journal of Modern Physics C 16(2): 259–70.

  • STAUFFER, D. and Meyer-Ortmanns, H. (2004). Simulation of Consensus Model of Deffuant et Al. on a Barabási- Albert Network. International Journal of Modern Physics C 15(2): 241–46.

  • see https://arxiv.org/pdf/0710.3256.pdf, page 20

Population size

Initial opinion distribution