Predict the size of human groups with physics

Only by knowing the average number of friends each person has could scientists at the Complexity Science Hub (CSH) predict the size of groups of people in a video game. For this, they modeled the formation of social groups on an example taken from physics, namely the self-organization of particles with spin.

Sociologists have focused on how social groups are forming and the underlying mechanism for a long time. The urge to avoid stress, as well as homophily – the tendency of people to join groups with others who share similar characteristics, traits or opinions – have been observed in many different contexts.

“Although several models have been studied, little is known about how homophily and stress avoidance affect the formation of human groups, and in particular the breakdown by size of them – if there are a lot of them small groups or a few big ones, for example,” says Jan Korbel of CSH and first author of the study. By using two contemporary areas of physics, called self-assembly and spin glasses, scientists are now shedding new light on the formation of social groups.

Cognitive challenges of people in groups

A defining characteristic of humans is that they organize themselves (often for specific purposes) into groups. “The difficulty here is that it requires coordination, which requires a lot of effort,” says Stefan Thurner from CSH. “As groups grow and internal conflicts arise, coordination can quickly reach and exceed the cognitive limits of humans.”

“So there must be specific mechanisms that allow humans to organize themselves effectively into groups. And these should be explainable with some very general human behavioral characteristics, such as homophily and the tendency to avoid stress at within groups,” continues Thurner.

People behave like particles with spin

Social groups usually emerge when people with similar opinions begin to interact with each other. “In previous studies, we investigated the self-assembly nanoparticles in small thermodynamic systems, where they spontaneously form high-order structures without any external intervention. Then we realized: it’s similar to what people do,” Korbel recalls.

People interact with each other and groups emerge very similar to particles that form colloids or polymers. Motivated by this, the research group developed a simple model for homophilic humans that is based on the self-organizing mechanisms of particles with spin.

Little information, big result

This model was able to predict the group size distribution in the multiplayer online game Pardus. “Normally you would need to know the structure of the network and how it is designed,” says Korbel.

“Here we only need to know how many friends a player has on average.” With this relatively small amount of information, the researchers were able to predict how many groups of a certain size would appear.

Key Quantities in Social Systems

“Of course, people are more complicated than particles, but certain types of interactions between them are similar, in particular the number of possibilities that a set of people can form groups. This number is called entropy, and that’s our starting point for math modeling,” says Thurner.

There were phases where people tended to form large groups, but others where that didn’t happen because opinions were too different. “Becoming part of a large group would have been too much of a social stress for them in that situation,” says Korbel. Besides entropy, this social constraint is the other key quantity here, a key quantity comparable to energy in physics. The more alike the people in the group are, the less social stress they can experience.

From magnets to opinions

From a physical point of view, this can be compared to spins: whereas in magnets all spins point in the same direction, in spin glasses, which are alloys of metals and non-metals, they are disordered . Because of that complex structure, the pirouettes are in “stress”, because they have to line up with several other pirouettes, and they cannot do it at the same time. “It looks like a group with different opinions. You can’t align with all of them and you’re probably frustrated,” Korbel established.

“Intriguingly, very different systems can have the same expression for entropy. In our case, social individuals appear to have similar entropy to structure-forming systems, such as certain spin glasses,” says Thurner.

“Our new model can help predict phenomena in sociology in relation to social networks and mass media that lead to social frustration and polarization,” concludes Korbel. It also shows the potential of interdisciplinary research approaches, particularly appreciated at the Complexity Science Hub.

“The vision is to finally get more quantitative models that are testable on real data of how Homo sapiens organize themselves into groups, perhaps the thing we do best as a species,” adds Thurner. .

The research is published in Physical examination letters.