All posts by jhickey

How Societies Form and Change: A physics model of social hierarchy

Hierarchy appears to be an inescapable feature of animal, including human, societies. There are dominants and subordinates, bosses and employees, rulers and subjects, and an individual’s position in the social hierarchy to a large degree determines fundamental aspects of his or her life, including one’s health, access to resources, and influence in society. From the individual’s point of view, the hierarchy provides security, but also reduces one’s freedom. What determines how oppressive society is toward the individual? Would more freedom be better for society? How bad does societal inequality have to become before things start getting better? Are there any fundamental laws or rules that control how social hierarchy forms and evolves in a complex society of many interacting individuals and groups?

I am doing my PhD research in physics on these questions. Something I’m often asked is how can the study of social hierarchy be considered “physics”? The answer is “simple” – physicists try to construct simple models to reveal essential or underlying features of complex natural phenomena. Such a model has to be as simple as possible, yet it must be cleverly constructed so that, in its simplicity, the model captures essential features of reality. If this is achieved, the model can provide insights about underlying rules that may control or influence the real phenomenon.

I have constructed a simple physics model of the formation and evolution of social hierarchies, based on interactions between the individual members of the society. Computer simulations of the model produce societies that resemble real-world societies, and we can study how the simulated societies are formed and how they change in time. A scientific article presenting the model has been submitted to a journal and can be read online at ResearchGate [1]. In the following, I outline how the model works for a general (non-specialist) reader and briefly discuss what its results might mean in terms of understanding social hierarchy in the real world.

Violence and authoritarianism in fights for societal status

In the model, we imagine a society of individuals who each possess an amount of a single quantity that entirely determines the individual’s position in the society – this quantity is the individual’s societal status. The only thing that individuals in the model can do is exchange status with one another. This occurs through “fights” between pairs of individuals selected at random from among the population, where the loser of the fight loses a portion of his or her status to the winner. In each fight, two things must be determined: how much status is lost or gained, and who wins the fight. These two aspects of the fights are each controlled by a “parameter” of the model – a simple quantity whose value is set, by the researcher, at the beginning of the simulation.

When an individual loses a fight, he or she loses a fraction of his or her “before-fight” status (the status that the individual had going into the fight). The first parameter of the model, “delta” (δ), is this fraction. For example, if δ = 0.1, then 10% of the loser’s before-fight status gets transferred to the winner following the fight. A large value of δ means that the stakes are high: a victory can provide a large gain in status, but a loss carries a high cost in status. The parameter δ therefore represents the intensity or “violence” of societal interactions. This rule for determining the amount of status lost in a fight means that powerful (high status) individuals lose a lot of status when they lose, such that upset victories result in large rewards to the underdog or challenger, and that fights between high status rivals result in large separations in status, establishing the winner’s dominance over the loser. These are both realistic features.

In the model, the probability of winning the fight depends on the relative statuses of the two fighting individuals – the larger the difference in status between the two individuals, the greater the probability that the higher-status individual wins. The higher-status individual therefore has an advantage in the fight. But the size of this advantage is controlled in the model by a second parameter, “alpha” (α). When this parameter is large, the higher-status individual has a huge advantage in the fight, such that the higher-status individual is almost guaranteed to win, even if he or she only has a slightly higher status than the lower-status individual. On the other hand, when α is small, the higher-status individual must have a much larger status than his or her competitor in order to have a large advantage in the fight. In other words, the parameter α represents the degree to which having a higher status guarantees a victory. If higher status represents a higher level of “authority” in a hierarchical society, then the parameter α represents the degree of deference to authority, or “authoritarianism” in the society.

Simulated societies form and evolve

Based on these simple rules, we run a computer simulation that randomly selects pairs of individuals and makes them fight each other. Following many such fights, a distribution of status emerges. The particular shape of the status distribution represents the “structure” of the society. For small values of either parameter, δ or α, the shape of the status distribution is rather egalitarian – there are many individuals clustered around the average status, and few individuals with extremely low or extremely high statuses. For larger values of the parameters, the status distribution becomes more unequal, such that there are many individuals with low or very-low statuses and a few very-high status individuals. For certain parameter values, the status distributions closely resemble real-world household income distributions, which we use as a proxy for societal status in human societies [2].

The model also shows how the simulated societies change with time. For non-authoritarian and non-violent societal interactions (small δ and α), the distribution of status remains the same for long periods of time. Under these conditions, the societal structure is either stable on an infinite time-scale, or changes so slowly that it is essentially unchanged on a time-scale much longer than the time required to form it in the first place. Whatever structure the society has – more or less egalitarian, for example – it will be long-lived for small values of the parameters. As either parameter is increased, however, a transition eventually occurs where the distribution of status begins to change rapidly. Status becomes concentrated in the hands of a few individuals and the society runs away toward a “totalitarian” end-state in which a single individual controls all of the status of the society.

Viewing society through the lens of the model

The model thus suggests that the violence of societal interactions (δ) and the degree of authoritarianism (α) in the society must be kept in check in order for the society to retain its structure over long periods of time and not degrade into a totalitarian state. As either of these features of inter-individual interactions is increased the inequality of the society increases. When the level of inequality becomes large enough that the society nears the transition into runaway deterioration of its class structure, the society may be required to reduce one or both of the parameters in order to retain a viable structure. Analysts have suggested that several recent major political events, including Brexit and the election of Donald Trump, are best understood as backlashes against increasing societal inequality [3,4]. According to the model, for such backlashes to have a stabilizing effect on the social hierarchy, they must result in decreases in the violence of societal interactions, the degree of authoritarianism in the society, or both.

The model provides a conceptual framework or “pair of glasses” through which societal changes and their relationship to the long-term stability of the society can be examined. Of course, many questions arise, including just how small (or large) the parameters δ and α should be in order to optimize societal stability, and how do they increase or decrease due to the actions of individuals within the society (rather than being fixed at their initial values). And what happens when groups of individuals interact, and remember the histories of their past interactions? Using simple, realistic models we can try to get insight into these and other questions about how social hierarchies form and how they change in time.


[1] J. Hickey and J. Davidsen, “Self-organization and time-stability of social hierarchies”

[2] Ibid., section 4

[3] M. Blyth, “Global Trumpism”

[4] C. Phelps, “From Slump to Trump”