Societal Polarization
The Impact of Social Network Density, Agent Openness, and Cross-Issue Influence
On January 6th, 2021 we saw the nation’s capital become ground zero for many to reject an election they perceived as illegitimate. Throughout 2021, instead of citizens coming together to fight an apolitical, existential enemy (covid-19), many instead turned on each other. And now, in November of 2021 a jury has found Kyle Rittenhouse, not guilty.
Three very divisive events that are seemingly unconnected, yet it could be predicted with significant accuracy, one’s opinions on several issues, knowing only how one feels about a single event.
This is in part, due to what is generally known as Polarization. What is polarization? Is it when views become too extreme? Is it when people refuse to change their minds or talk with one another?
I had the privilege to work with some amazing and talented people (Justin Mittereder, Brandon Frulla and Dr. Stephen Davies) to take a closer look at the phenomenon. The full research paper can be accessed here.
Nailing down a definition for “polarization” was actually one of the more interesting challenges that came up during our research. After some digging, we concluded that polarization could mean different things to different people. While “polarization” is fine for everyday use, we found we had to explore a bit further to really get at the heart of the issue, deciding to create proxies for the term “polarization.”
Polarization Proxy #1: Assortativity Coefficient
The first proxy is assortativity. Assortativity measures the tendency of agents to associate with other like-minded agents.
One can visualize this by imagining a high school cafeteria. Students will tend to sit at tables with other like-minded students. In this way, the assortativity is high. Now imagine the same cafeteria, however, this time students are assigned random seating. The assortativity would be low. Assortativity is an important concept to keep in mind, as we move to the model.
The Model
We created the model using Mesa, a powerful agent based modeling framework, written in python.
Characteristics
The following are the main characteristics of the model, with a short explanation underneath.
N heterogenous agents who encounter each other on a social network.
We start with a random amount of agents, connected in a network graph.
Edge Probability of a random Erdos-Renyi graph which controls network density
Agents have a chance to connect with other agents, via an edge.
Agents have opinions on multiple issues, each of which is on a continuum
Agents have a certain value for an array of opinions. This value can range from 0 to 1.
Openness Threshold and Disgust Threshold that control the degree of agent opinion influence
Agents can be pulled or pushed away from a certain opinion, based on another agent.
One of the major building blocks in our model is Bounded Confidence. There’s a degree to which an agent is influenced, which is determined by its openness threshold. The figure below demonstrates this, with two agents and a single opinion.
In the first example, the blue agent will not be “pulled” (influenced) towards the grey agent on a particular issue, since the grey agent is not within the blue agent’s range of openness. In the second example, the blue agent is “pulled” towards the grey agent on a particular issue, since the grey agent is within the blue agent’s threshold of openness.
There can also be cases of the inverse, where an agent is “disgusted” or “pushed away” by another agent.
With this concept in mind, we can move on to our second polarization proxy.
Polarization Proxy #2: Issue Alignment
We defined Issue Alignment (IA) as the tendency for people who agree on one issue to also agree on other (unrelated) issues. Some examples we may encounter these days are:
Minimum wage
Pro-choice
taxes
gun laws
immigration
If people generally adhere to an entire suite of opinions, we term that society “Issue Aligned” and claim this is an indication of polarization.
Why does Issue Alignment occur?
Possible explanations of issue alignment can be hard to pin down. A possible explanation is that there is some deep, underlying principle to people’s value systems that connects seemingly unconnected issues. Another could be the rise of popular media outlets that each articulate a set of opinions on various issues. However, the model we created demonstrates that it is not necessary for ideological coherence or media influence to be present for issue alignment to develop. Cross-issue influence is sufficient.
Cross-issue Influence
We define Cross-Issue Influence as the effect that an agent can have on one of its neighbor’s opinions, based on their agreement or disagreement on a different issue.
This could have wide-reaching implications on how we interpret the causes of polarization and what societal changes might be necessary to reduce it.
In the following example, the opinion of the blue agent on issue Y can be influenced by the grey agent’s opinion on issue X.
Likewise, the agent can be negatively influenced if the opinion on an issue is within the “disgust threshold.”
Quantifying Issue Alignment
To measure the degree of Issue Alignment in a virtual society, we measure the number of distinct opinion buckets that exist. A “bucket” is a specific set of numerical opinions on the various issues. All agents in the same bucket agree on all the issues, within a certain threshold of ε (.05).
For example, the above agents are highlighted by bucket. Since agents α and δ have similar opinions on issues 1, 2 and 3, they are within the same bucket. Where as agent β and agent γ are in entirely different buckets, due to the difference in opinions on all issues.
We interpret fewer buckets to mean more Issue Alignment (polarization).
Some other potentially interesting additions are the following:
Clones, a pair of agents that agree on every issue.
Anti-Clones, a pair of agents that disagree on every issue.
Running the simulations, produces the following graph.
The above graph shows that the number of clones increases as time goes on and the number of buckets drops down to just 2.
Some of the main takeaways from the research are the following:
Lower network density leads to higher polarization.
If people are “too open” and easily believe what they hear, this can lead to echo chambers forming more readily.
Issue alignment endogenously appears with Cross-issue influence.
This would encourage the idea that giving oneself the freedom to agree with others on a certain issue and disagree on other issues, would lead to a less polarized society. With the advent of social media and the idea of getting clicks above all else, achieving this freedom may seem a monumental task. Yet this freedom may be the first steps needed to reverse our current course and restore a much needed sense of comradery.