Now, researchers at Northwestern University have used statistical physics to confirm the theory behind this famous axiom.
The study will be published on May 3 in the journal. Scientific advances.
In the 1940s, Austrian psychologist Fritz Heider introduced the theory of social equilibrium, which explains how humans innately strive to find harmony in their social circles. According to the theory, four rules (an enemy of an enemy is a friend, a friend of a friend is a friend, a friend of an enemy is an enemy and, finally, an enemy of a friend is an enemy) lead to balanced relationships. .
Although countless studies have attempted to confirm this theory using network science and mathematics, their efforts have failed, as networks deviate from perfectly balanced relationships. Therefore, the real question is whether social networks are more balanced than expected according to a proper network model. Most network models were oversimplified to fully capture the complexities within human relationships that affect social equilibrium, yielding inconsistent results about whether observed deviations from network model expectations are in line with theory. social balance.
However, the Northwestern team successfully integrated the two key pieces that make Heider’s social framework work. In real life, not everyone knows each other and some people are more positive than others. Researchers have long known that each factor influences social bonds, but existing models could only account for one factor at a time. By simultaneously incorporating both constraints, the researchers’ resulting network model finally confirmed the famous theory some 80 years after Heider first proposed it.
The useful new framework could help researchers better understand social dynamics, including political polarization and international relations, as well as any system that comprises a mixture of positive and negative interactions, such as neural networks or drug combinations.
“We’ve always thought that this social intuition works, but we didn’t know why it worked,” said István Kovács, lead author of the Northwestern study. “All we needed was to solve the mathematics. If you look at the literature, there are many studies on the theory, but there is no agreement between them. For decades, we kept misunderstanding it. The reason is that real life is complicated. We realized that we needed to take into account both limitations simultaneously: who knows who and that some people are friendlier than others.
“We can finally conclude that social media aligns with expectations that were formed 80 years ago,” added Bingjie Hao, the study’s first author. “Our findings also have broad applications for future use. Our mathematics allows us to incorporate constraints on the connections and preference of different entities in the system. That will be useful for modeling other systems beyond social networks.”
Kovács is an assistant professor of Physics and Astronomy at Northwestern’s Weinberg College of Arts and Sciences. Hao is a postdoctoral researcher in his laboratory.
What is the theory of social equilibrium?
Using groups of three, Heider’s social equilibrium theory maintains the assumption that humans strive to maintain comfortable and harmonious relationships. In balanced relationships, all people like each other. Or, if a person doesn’t like two people, those two are friends. Imbalanced relationships exist when three people don’t like each other, or one person likes two people who don’t like each other, causing anxiety and tension. The study of such frustrated systems led to the 2021 Nobel Prize in Physics for Italian theoretical physicist Giorgio Parisi, who shared the prize with climate modelers Syukuro Manabe and Klaus Hasselmann.
“It seems very aligned with social intuition,” Kovács said. “You can see how this would lead to extreme polarization, which we see today in terms of political polarization. If everyone you like also dislikes all the people you don’t like, then that results in two parties that hate each other.” .
However, it has been a challenge to collect large-scale data that lists not only friends but also enemies. With the emergence of Big Data in the early 2000s, researchers attempted to see if such signed social media data could confirm Heider’s theory. When generating networks to test Heider’s rules, individual people serve as nodes. The edges connecting the nodes represent the relationships between individuals.
If the nodes are not friendly, then the edge between them is assigned a negative (or hostile) value. If the nodes are friends, then the edge is marked with a positive (or friendly) value. In previous models, edges were assigned positive or negative values at random, without respecting both restrictions. None of those studies accurately captured the reality of social media.
Finding success in limitations
To explore the problem, Kovács and Hao turned to four large-scale, publicly available, signed network data sets previously curated by social scientists, including data from (1) user-rated comments on the social news site Slashdot; (2) exchanges between members of Congress in the House; (3) interactions between Bitcoin traders; and (4) product reviews from consumer review site Epinions.
In their network model, Kovács and Hao did not assign truly random positive or negative values to edges. For each interaction to be random, each node should have an equal chance of encountering each other. However, in real life not everyone knows others within a social network. For example, a person may never meet his friend’s friend who lives on the other side of the world.
To make their model more realistic, Kovács and Hao distributed positive or negative values based on a statistical model that describes the probability of assigning positive or negative signs to existing interactions. That kept the values random, but random within the limits given by the limitations of the network topology. In addition to who knows who, the team took into account that some people in life are friendlier than others. Friendly people are more likely to have more positive and less hostile interactions.
By introducing these two constraints, the resulting model showed that large-scale social networks consistently align with Heider’s social equilibrium theory. The model also highlighted patterns beyond three nodes. It shows that social equilibrium theory applies to larger graphites, involving four and possibly even more nodes.
“Now we know that these two limitations have to be taken into account,” Kovács said. “Without them, you can’t find the right mechanisms. It sounds complicated, but it’s actually pretty simple math.”
Perspectives on polarization and beyond
Kovács and Hao are currently exploring several future directions for this work. In one possible direction, the new model could be used to explore interventions aimed at reducing political polarization. But researchers say the model could help better understand systems beyond social groups and connections between friends.
“We could look at excitatory and inhibitory connections between neurons in the brain or interactions that represent different combinations of drugs to treat diseases,” Kovács said. “The study of social networks was an ideal playground to explore, but our main interest is to go beyond investigating interactions between friends and looking at other complex networks.”
The code and data behind the article, “Proper network randomization is key to assessing social equilibrium,” are available on Github: https://github.com/hbj153/signed_null