The protest on 18 December 2010 in Sidi Bouzid set in motion a revolutionary wave that swept across Tunisia, Algeria, Egypt and the Middle East and significantly changed the political landscape of the MENA region. Almost precisely ten years later, the killing of George Floyd by Minneapolis policemen triggered protests across the United States and led to worldwide demonstrations against police brutality and institutional racism. In fundamental terms, both social processes exhibit parallels. We observe two critical social systems in which a single incident leads to a cascade of struggle and protests. Within this context, On Revolutionary Waves and the Dynamics of Landslides develops a theoretical model that describes the dynamics of social contention. In essence, the model is an extension of the sandslide model developed by Bak et al. (1987) that replicates how grains of sand slide off the edge of a pile and in so doing create cascades that can lead to large-scale avalanches. Such type of self-organised criticality is what we also observe in social movements and at a larger scale, in revolutionary waves. The extended sandpile model in the paper takes account of the social nature of contention but retains the general dynamics. Instead of going further into details about the model in this blog, I would like to use the opportunity to discuss three broader implications that the extended sandpile model and similar models raise for modelling social dynamics.
The Power of Analogies
It is obvious that the underlying sandpile is only a stylised representation of how sand behaves in reality. Social movements are significantly more complex and the extended sandpile model is an even more abstract description of social contention and movements. The model ignores individual characteristics of actors, their idiosyncratic beliefs and motivations. Yet, empirically and at a fundamental level, we observe similarities between a singular grain of sand sliding down the edge of pile and taking along an ever-growing number of other grains of sand and a singular incident that sets in motion a spreading protest. In both cases, the systems, one of matter, the other social, demonstrate criticality – the former because the slopes of the pile of sand have become too steep, the latter because growing discontent with established practices cannot longer be curbed and the last straw breaks the camel’s back.
Indeed, the use of simple mechanic models that illustrate analogous behaviour to explain regularities of social systems is nothing new but evolved in the early 19th century under what had been termed physique (or mécanique) sociale. While such simplification entails the benefit of a better tractability that helps us understand the central dynamic motivators, it comes at the cost of lacking a detailed micro-foundation that acknowledges not only individual peculiarities but also motivations. I have shown that introducing further sophistication to the model in the form a heterogeneous characterisation of agents does not affect aggregate dynamics. Adolphe Quetelet (1835) has postulated the homme moyen – the average man that is representative of the mean value of a distribution. In fact, similar to James Clerk Maxwell’s study of molecules in gases, mean field approximations have been used to model crowd behaviour, macroeconomic models frequently rely on representative agents and similarly, replicator dynamics model population dynamics and institutions based on average traits and fitness. In view of the pervasiveness of the average man (or agent), one may be tempted to conclude that studies of social systems can dispense with micro-foundations and model social systems exclusively based on the averages of aggregates. Yet, the extended sandpile model shows that such a conclusion is misleading since it ignore fundamental elements of social dynamics, which brings me to my second point.
Complexity and the Need to Study Structure
Although individual actors are devoid of an extensive repertoire of actions and sophisticated beliefs, nor do they interact in a strategic manner that is based on expectations of the choices of others and the future consequences or their actions, the model exhibits highly complex dynamics. These dynamics are created by the interplay of two factors that we ordinarily observe in social systems – locality and externality. Locality implies that each social actor only engages with a strict subset of other actors, i.e. only their neighbours or peers. Since local conditions can vary significantly across larger populations, an actor facing a distinctly segregated neighbourhood may then face a situation that is entirely different from the population average. The second motivator – externality – implies that an individual action has (often unanticipated) consequence on the well-being, expectations or beliefs and thus choices of other actors. While in economics, positive and negative externalities refer to the provision of goods (such as the establishment of a public park) or bads (driving a noisy and polluting car), the externality in the extended sandpile model is caused by the discontent that an individual passes on to their neighbours. We have seen that once the system enters into a critical state, these local externalities create knock-on effects that can lead to large-scale discontent.
A mean field approximation of the resulting dynamics similar to Maxwell’s kinetic theory of gases, however, requires that these knock-on effects demonstrate certain regularities. Yet, as we have seen, social behaviour does not exhibit monotonic dynamics – onsets of social contention do not grow gradually over time. On the contrary, instead of a regularity of the average, we observe abrupt changes between periods of calm and sudden widespread discontent at seemingly random scale. Likewise, in the model, the sizes and durations of the social movements are not distributed according to the well-behaved Gaussian distribution we normally expect. Instead of the familiar bell-shaped normal distribution with a well-defined average, size and duration follow a power-law distribution.
The extended sandpile model then provides an interesting answer as to whether micro-foundation is necessary to study aggregate social dynamics. While individual characteristics might be of lesser importance for the system’s aggregate behaviour, it does not imply that we can ignore the role of the individual and substitute them by a representative or aggregate agent. Only a micro-founded study recognises the interaction structure created by individual social relations that is vital for the complex social dynamics we observe. Such structure and the arising feedback effects create emergent behaviour that is chaotic in nature and cannot be deduced from averages. Yet, we might then conclude that social dynamics are generally too chaotic to model, which brings me to my third point.
Order in Chaos
While the social dynamics follow a random chaotic process when studied at the micro-level, we still observe regularities at the aggregate level. The scale and duration of social contentions follow a power law distribution. While changes to the characteristics of agents alter the system’s local dynamics at the micro-scale, a more sophisticated representation of the individual does not affect these attributes of social movements. In addition, the power law distribution is scale-invariant which indicates that the properties that hold for smaller populations over a relatively short period hold (proportionally) for larger populations and longer periods.
This makes for some interesting food for thought and implications that may hold for a wider number of studies of social dynamics. While social systems may exhibit dynamics that are chaotic at the micro-level, patterns become consistent at the aggregate level. These patterns may then be robust across a diverse number of social systems. Indeed, power law distributions and particularly Zipf’s law have been found to hold in various social contexts. In addition, these patterns are unaffected by idiosyncratic actions of individuals and do not require a detailed understanding and modelling of individual motivations. Yet, the abstraction from individual motivation and the independent evolution of aggregate regularities do by no means imply that the model suggests a lack of individual agency. Similar to rates of birth, marriage, suicide and employment, the regularities of these rates do not preclude individual motivations and decisions that affect these rates. It merely suggests that variations in the individual characteristics disappear at the larger aggregate. To the contrary, the model demonstrates that an account of the individual remains critical for the study of social system since particular dynamics that lead to these consistent patterns emerge from the network in which social actors interact. An understanding of the interaction structure and the feedback effects between individual choices is therefore critical to comprehend the driving forces behind social movements which cannot be adequately modelled on the basis of aggregates and averages.
This commentary first appeared in the academic blog of Studies in Ethnicity and Nationalism: link