Predicting Sizes of Human Groups with Physics

The scientists at the Complexity Science Hub (CSH) utilized their knowledge of the average number of friends each person has to successfully predict group sizes in a computer game. To achieve this, they employed a physics example of self-organization of particles with spin to model the formation of social groups.

Sociologists have focused on how social groups develop and the mechanism behind them for a long time. The urge to avoid stress, in addition to homophily– the tendency of individuals to join groups with others with similar features, traits, or opinions– has been observed in several contexts.

Jan Korbel, the first author of the study from CSH, explained that despite the numerous models that have been explored, there is still limited knowledge about how homophily and stress avoidance impact the development of human groups, including the distribution of group sizes, such as whether there are many small groups or a few larger ones. The research sheds new light on the establishment of social groups by utilizing two contemporary fields from physics, namely self-assembly and spin glasses.

Cognitive challenges of individuals in groups

One defining feature of humans is that they arrange themselves (commonly for specific purposes) in groups.

According to Stefan Thurner from CSH, the challenge here is that this requires coordination, which calls for a great effort. When groups grow in size and internal disputes arise, coordination can quickly reach and go beyond the cognitive limits of human beings.

Thurner adds that specific mechanisms must allow human beings to arrange in groups successfully. Moreover, these should be explainable with a few quite general human behavioral features, such as homophily and the tendency to prevent stress within groups.

Individuals acting like particles with spin

Social groups normally arise when people with identical viewpoints start interacting with each other. Korbel recalls that in previous studies, they examined the self-assembly of nanoparticles in small thermodynamic systems, where they spontaneously form high-order structures with no external interventions. Then we realized: that this resembles what individuals do.

People interact with each other, and groups emerge extremely identical to particles that develop colloids or polymers. Encouraged by this, the research group established a simple model for homophilic human beings that is based upon the mechanisms of self-organization of particles with spin.

Small information, big outcome

This model managed to predict 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,” Korbel explains the results.

“Here, we only have to know the number of friends a player has on average.” With this fairly small amount of information, the researchers could predict how many groups of a certain size would show up.

Key quantities in social systems

According to Thurner, despite people being far more complex than particles, certain interactions between them are identical, particularly the number of possibilities that a set of individuals can make groups. This number is called entropy, and this is our starting point for mathematical modeling.

There were phases where individuals tended to create large groups. However, others when this did not take place because opinions were too different. Korbel states that becoming a part of a large group would have been too much social stress for them in this scenario. Entropy, this social stress, is the other crucial quantity here– a crucial quantity comparable to energy in physics. The more identical individuals in the group, the less social stress they could experience.

From magnets to opinions

In terms of physics, this is comparable to spins, where in magnets, spins align in the same direction, while in spin glasses, which are alloys of metals and non-metals, spins are disordered.

This complex structure places stress on the spins as they need to align with several other spins, which they can’t do simultaneously. Korbel uses this analogy to describe a group with differing viewpoints, where it’s impossible to align with everyone, and frustration can occur.

Thurner notes that various systems can have identical expressions for entropy, including social individuals and structure-forming systems like certain spin glasses. Korbel suggests that their new model can aid in predicting phenomena related to social networks and mass media that cause social frustration and polarization in sociology. This highlights the potential of interdisciplinary research approaches that are highly valued at the Complexity Science Hub.

Thurner adds, “The vision is to obtain more quantitative models that are testable on real data of how Homo sapiens organizes itself in groups, perhaps the thing we do best as a species.”

Read the original article on PHYS.

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