Social and political systems can be characterized as being linear or nonlinear in their structure and behavior. Nonlinear systems are something other than the sum of their parts due to the synergies between those parts. These synergies make the whole greater or less than the sum of the parts and thus create emergent patterns that are in a dynamic state of nonequilibrium.1 This nonequilibrium state is often seen as a basic condition for dynamic change and systems evolution.2 Such nonequilibrium emergent patterns defy interpretation through more traditional linear methods within political science that interpret macro level patterns as statistical averages over micro-level individuals which in turn leads to equilibrium outcomes.3

### Nonlinearity

In looking at the underlying dynamics to many of the greatest governance issues of today one can identify that they are inherently nonlinear. For example, today’s environmental challenges are often modeled in terms of the social dilemma and tragedy of the commons, where certain types of interactions on the micro-level lead to very different emergent outcomes on the macro-level. Another such example of nonlinear dynamics is cascading failures, such as seen in financial crises, which are driven by feedback loops. Coupled to this are issues surrounding the butterfly effect where small actors or even individuals can have an increasingly disproportionate effect, terrorism, and cyber warfare being examples. Suffice to say, as the world becomes more interconnected and interdependent it also becomes more nonlinear. In such a case one needs to think in terms of nonlinearity in order to effectively interpret events and develop the appropriate institutional structures.4

The process of governance can be understood as a social function or institution that is designed to manage, make decisions and guide the development of a community of people. In so doing the institutions of governance have to in some way aggregate the opinions or intelligence of their members towards making decisions. Societies are invariably complex in that they consist of many parts – nations today consist of millions, even hundreds of millions of people, yet their primary decision-making institutions may consist of only a few thousand people, yet these governing institutions are expected to be in some way representative of the will or interests of the underlying much larger social systems. A central question of interest then is how do we go from the micro-level of the millions of individuals and distributed interactions to the macro-level of the formal political institutions.

In important question is how do we go from the vast complex system of the populace at large to the concentrated institutions of governance in a way that is representative of the larger populace. Here we can recognize the current political challenges that we are having with populism, and likewise, global governance can be understood as one surrounding emergence. As populism is driven by a disconnect between the populace at large and the smaller set of political institutions, the politicians, and the ruling elite.5 And this ties in with a broader unresolved major question of our time, global governance; how could we develop political institutions that go all the way from the local level to the global level in a coherent fashion that is inclusive enough and representative enough to be robust against populism? The study of nonlinearity in politics and emergent nonequilibrium processes can help us better understand such issues.

### Equilibrium

In linear models the macro-level is nothing more than the sum of the micro-level, the whole is a simple aggregation or statistical aggregation of the micro-level.6 That is to say, if we want to talk about the system as a whole we use a process of generalizing, where we take the average and define the whole in terms of this statistical average. For example, if most Chinese people speak Mandarin as their primary language, then we simply equate the Chinese language with Mandarin. More formally this process is called renormalization or coarse graining. Coarse-graining is a term from physics which essentially means that we compress the information down into a reduced form.7 Like compressing an image on our computer, the computer uses an algorithm to reduce the small detailed variation down into a compact form. Coarse graining merges specific states of the world that have similar properties so as to reduce the underlying complexity.

For example, we often coarse grain the voting system by taking an electoral area and instead of looking at all the details we define it by the average, what the majority vote for. In such a way we have coarse-grained the unit abstracted away from the detail and reduced the complexity.7 Because we have thrown out this information it is now much easier to deal with the whole system but also we do not actually know what is happening down below the level that we renormalized to – we have thrown out a large section of the complexity. In simple systems, this underlying information does not matter much, however, in complex systems it turns out that this is important information.8

Various algorithms can be used to perform this process of coarse graining, but what happens when we renormalize or coarse grain through the statistical average is that we tend towards equilibrium. We take a complex distribution and search for the mean or average, then instead of dealing with all the details, we deal with just a representative of the whole; the average comes to represent the whole. Of course, the result of this is that everything becomes based on this average person. Part of the problem of throwing out the variety in this way is that you also throughout the particularities of the individual. The individual no longer matters it is all about the mass average person. This is the essence of mass media politics, it is about appealing to the average of the mass.8 And this should be something that we can identify with, as politics within developed economies has evolved into media politics and left behind to a large extent is ideological roots, there has also been a tendency towards the center, because in such a system if you are the average then you will win, if you are on the fringes you will lose.10

This dynamic creates strong incentives to be the average, both for members of the population at large and also for politicians, because if you can appeal to the average then you will win. Variety is not accounted for and it is dumbed down; one person one vote irrespective of any other variation among the members. That one vote gets bundled up into a huge mass and averaged out. The end result is that if you are on the fringes you will virtually always lose. Over time this places a force on the agents to move back towards the center. The results of this are macro level equilibrium outcomes; on the micro-level, the system is configured to push the members towards the average and the result of this on the macro-level is an equilibrium outcome.

Equilibrium analysis has been a central tool of modern science. It has been a powerful tool that has given us much insight and traction on phenomena that were otherwise beyond our grasp. Equilibrium analysis is helpful in many ways particularly in simpler systems and stable environments when a system is in a stable basin of attraction. However, it will not tell us about major processes of change that inherently engender non-equilibrium dynamics; thus it will not tell us about a lot of things that we are really interested in. The unfortunate thing about equilibrium analysis is that it is really a shortcut, a shortcut that bypasses complexity and in so doing it gives us some insight into systems that are complex, but it does this by ignoring the complexity. This is not a major issue until you actually start to take an interest in complexity itself, in which case a tool that purposefully bypasses it is not going to be of much use to us. One then needs to shift to nonlinear models that allow for non-equilibrium outcomes which are characteristic of many social phenomena and particularly major processes of change.

### Nonequilibrium

Nonlinearity is fundamentally a product of the interdependence between elements within a system or over time. When we turn up the interconnectivity, interdependencies come to form and the system goes from linear behavior to nonlinear behavior.11 Correspondingly, we get nonequilibrium outcomes on the macro-level because of synergies and emergence and also nonequilibrium processes of change over time, driven by feedback dynamics. The statistical output of nonlinear systems moves away from a normal distribution – which is dominated by the average – and tends to follow a power law distribution, where there are a very few very large events and a very many very small events. Outputs do not tend towards an equilibrium average; indeed they tend to diverge the larger the sample taken.12

Normal Gaussian and power law distributions differ radically. The main feature of the Gaussian distribution can be entirely characterized by its mean and variance while a power law distribution does not show a well-behaved mean or variance. A power law, therefore, has no average that can be assumed to represent the typical features of the distribution and no finite standard deviations. A review of the different kinds of power law phenomena shows that underlying each is a collapse of the independence assumption. Once independence among data points collapses, and interdependence or interaction occurs, then the seeds of power law formations are planted and this changes the overall dynamics of the system in fundamental ways.12

Unlike in linear systems, where the average value tells us a lot about the underlying variables, with power law distributions the average does not tell us much about the particularities of the variables underneath it. Thus we can not use the average as being representative of the whole system and coarse-graining through statistical averages stops working. For example, if we had a population with a wealth distribution that was a normal Gaussian distribution, most people would have the average income of say thirty thousand dollars, while few would have very high or very low incomes, thus we could craft a political policy or an economic policy directed at that average and effect the whole system.

However, with a power law distribution, there will be a hand full of people that are extraordinarily wealthy while the mass will be relatively poor. The Power law distribution is also called a Pareto distribution or more popularly known as the “80/20” rule. It was named after the Italian economist Vilfredo Pareto, who observed that 80% of income in Italy was received by 20% of the Italian population. We can also note that today the net worth of Americans is in fact distributed according to a power law and this corresponds to what has been identified as the hollowing-out of the American middle class. In a world of power law distributions, extreme events become much more prominent. Extreme events can take many forms, such as extremely wealthy individuals, or sudden and severe disturbances like a class 9 earthquake or a financial meltdown. Extreme events, which in a Gaussian world could be safely ignored, are not only more common than expected but also of vastly larger magnitude and far more consequential.13

### Long Tail

These extreme events have an interesting property they emerge first in the long tail – which is the portion of the distribution having a large number of occurrences far from the “head” or central part of the distribution – but then driven by positive feedback can gather momentum until they eventually break into the mainstream and change the game for the mass of the people. The challenge for public representatives is to sort out the signal from the noise in the long tail and spot early on the emergent extreme events that could reshape the landscape. The Gaussian focus on averages obscures these events, treating them as meaningless “outliers” where they get lost in the process of statistical coarse-graining. In such circumstances, new events only become noticed when they hit the mainstream at which time they have already grown high momentum and it is no longer possible to alter them.13

Because of this, in complex systems, people sometimes say that it is “the tail that wags the dog.” This means that because of heightened connectivity and interdependencies there is a much greater possibility for positive feedback to take hold.14 Small events on the fringes can get amplified into large changes. Change starts on the fringes – where there is diversity and space to experiment – then through feedback moves into the center. Because of heightened connectivity and compounding feedback, the move into the center can happen very quickly, if you focus just on the mass, average in the center, you will continuously be shocked and surprised becoming vulnerable and reactionary.15 What happens is that when we coarse grain we through out the detail; because the diversity lies at the edges of the distribution by basing the abstraction on the mean average we also throughout the diversity within the system and in complex systems this has a consequence. The diversity and variation of the actors comes to be a critical element, which can not be ignored. This is increasingly an issue we face, as the world becomes more nonlinear and complex while models and institutional structures remain linear, we are continuously presented with surprises and shocks with the result being a reactionary mode setting in.15

In a paper on the subject by McKelvey and Boisot they described the “Gaussian perspective of the world” as one built on atomism, privileging “stability over instability, structure over process, objects over fields, and being over becoming.”16 There is a natural and very human tendency to generalize so as to simplify; to seek out the typical or the average and to search for more predictability. In linear systems, it is mainly the equilibrium that matters, in nonlinear systems though it is both the little parts that matter and also the overall emergent pattern. You can not just affect the average in order to effect the whole system, you need to dig into the complexity of all the parts and understand the variation to identify the specificities of the system.17 You have to know the details of the individuals and how they are connected. Previously this was not possible within large societies but with advancements in computation, the wealth of new data sources coming from all directions and new computational models this is increasingly possible. Dealing with nonlinearity invariably means using computational methods. Because one has to deal with all the little parts and their diverse characteristics this requires a massive amount of information and computation.

### Nonlinear Political Institutions

This is not simply an academic exercise though, as information technology plays the same central role in the practical design of political institutions that are appropriate to managing complex social systems. When the complexity of the larger social system goes above a certain level the system can not be effectively coarse-grained into a linear model of representation. In order to harness the complexity and diversity in the broader social system, political institutions need to be direct, peer-to-peer and information technology now makes this a possibility. The linear political institutional model of the Industrial Age, based on a representational political system and mass public opinion, was constructed around the constraints of the available technology of mass media one-way communications and the need to manage the newly formed mass population of the nation state.

However, as the influential author Clay Shirky notes, what is special about this current wave of information and communications technology is that it enables not just one to one telecommunication, as was the case with the phone and telegram, neither just one to many communication as with mass media like the radio or television, but for the first time in history many to many telecommunications and this is a game changer that is currently reshaping virtually all social institutions from business and commerce to media and entertainment.18 These collaborative platforms are reshaping organizations in enabling unmediated and automated interaction and collaboration between many people through which they can make collective decisions and coordinate towards implementing and enforcing them. Political institutions may well be the last to experience this transformation but it would appear unlikely that they can somehow avoid it and remain relevant in a network society.

The rewards for achieving a better understanding of how to operate in a nonlinear world of power law distributions are enormous and the results of staying within a linear model are diminishing with every new connection. As can be seen in viral videos on social media, small moves, smartly made, can lead to exponential improvements provided they leverage the deep structures that define nonlinear dynamics. In contrast to the scaling strategies that work in a linear world, different and even more powerful scaling strategies become feasible in a nonlinear world of the internet and globalization, the only question is who will manage to leverage these, will it be the makers of ISIS or the makers of Wikipedia.19

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