Nonlinear Political Science

The use of nonlinear models in the social sciences makes it possible to identify how distributed nonlinear interactions can give rise to macro-level emergent patterns

Nonlinear political science is the application of nonlinear models to interpreting political systems.1 Since the advent of chaos theory in the 1970s nonlinear science has been growing and increasingly finding application in new domains of science. Some political analysts saw the importance of nonlinearity to political and administrative studies at this time but, more recently a growing number of scholars understand that the political world is increasingly characterized by nonlinearity and thus amenable to nonlinear dynamical techniques and models.1 Nonlinear models can greatly help to support the realism of political models in that there can be limited doubt that – like most other processes in the universe – social and political relationships are generally characterized by nonlinearity and complexity. Political systems often exhibit strong elements of sensitivity to small changes, unexpected consequences, non-equilibrium dynamics, the spontaneous emergence of patterns, and sudden changes in outcomes. A nonlinear approach implies the development and adoption of new theoretical models, but also new empirical methods to accompany these, such methods may include agent-based modeling and various forms of simulation, network analysis, neural network modeling, adaptive landscapes etc.2

Linear modeling within political science has its limitations in that it largely ignores networks of interactions between variables, synergies, and feedback dynamics and thus limits our capacity to identify and analyze the higher order patterns and processes of change that are manifest in the realm of complex social systems. Nonlinear methods can provide a rich and more extensive framework that would better allow researchers to model many topics of central interest within political science, such as regimes shifts, the dynamics of collective action and the emergence of political crisis.3

Linear & Nonlinear Systems

The term nonlinearity refers to a nonadditive relationship between the parts within a system, or between events over time. This means that when we put two or more things together the combined organization is greater or less than the sum of its parts. Likewise, nonlinearity may be present over time, meaning that a series of events is not a simple summation of each effect in isolation. This nonadditive nature to nonlinear systems is a product of the way that they interact. These nonadditive interactions are called synergies.4 Relations that add value to the combined organization beyond that of the individual parts are called positive synergies, those that subtract are called negative synergies.5 Likewise, nonlinear relationships over time derive from feedback loops between events, which work to compound or dampen down change as a system can grow or decay at an exponential rate.6

Although nonlinearity can be observed in relatively simple systems composing of only a few elements – such as the canonical example of a double pendulum with just two component parts – it is a key characteristic of complex systems where many different variables are interacting in a parallel or networked fashion to amplify or dampen down the results. Linear approaches take limited account of synergies and feedback dynamics; they search for a limited number of parameters that are seen to cause an event and that can be encoded into closed form equations. With linear models, we typically assume that the outcome is a product of either one or two or just a few direct variables. For example in asking why have we seen so much disruption in the political landscape this decade we might say that it is caused by the preceding financial crisis; thus identifying some direct cause and effect relationship between them. Another primary linear method used is to say that things are caused by many variables, but those variables are independent – like the atoms in a gas chamber. We can not say anything about any of the individual atoms but if we assume they are random we can use statistical methods which tell us something about the aggregate system.7

However in complex sociopolitical systems the results of some macro phenomenon are typically neither of these – neither the product of a small amount of direct cause and effect interactions or the product of a random distribution of a large number of independent variables – they are instead the product of some network of interactions between a number of variables that affect the outcome and it is the specific way that different things interact that generates the outcome.7

Nonlinear Political Systems

From the perspective of cybernetics, governments may be understood as a form of centralized regulatory system which regulates the social system through linear cause and effect methods such as criminal punishment or tax incentives

The distinction between linear and nonlinear works to define two different rule patterns within a system – or two different dimensions to the system. One which is linear and centralized and the other which is distributed and nonlinear. This distinction typically maps onto the divide within sociopolitical systems between the formal political institutions of the government and that of civil society. In the linear dimension to a system, there can be identified direct relations of cause and effect with limited mediation between them. In such direct cause and effect interactions without feedback, small changes can only cause small effects and big changes will cause big effects. This direct cause and effect relationship can be used to control and manage the organization via a centralized regulatory system that has at its disposal the means to induce the causes required to achieve the desired effects in the system. For example, governments typically have central banks the have the means to alter the rate at which they will provide loans this is then used as a mechanism to affect the general rate of interest in the economy. Thus the government is using an identified linear cause and effect relationship to control the behavior of the system.

The formal management apparatus of government as we know it, is a centralized hierarchical model that is expressive of a linear conception to management; it is a traditional linear control system.8 Like all linear control systems, it is designed to maintain homeostasis within the system that it is regulating through various linear cause and effect methods disposable to it. In the same way that a person driving a car has to use their visual sense to receive information, their brain to process it, and their arms and legs to maintain the car on the road, all linear control systems perform this same function and a centralized government is just one such example. Nonlinearity, in contrast, is uncontrollable through this traditional method of directly influencing the system. In nonlinear systems there are no direct linear and proportional relationships, you can try to affect the system in a certain way but you do not know what the outcome will be. The results of the same input effect may change over time depending on the context and specific arrangement in the system. Often such direct interventions into complex systems have many unintended consequences that create the opposite results from those that one may have predicted or desired.9 For example, the allied invasion of Iraq where the intent might have been to make the invading nations more secure would appear to have had the reverse effect, providing fuel to terrorism.

The nonlinear realm to political systems typically forms the vast majority of interactions and institutions within a society and which lie outside of the domain of direct influence by the government; what we might call civil society. Civil society is typically a very complex network of overlapping institutional structures.10 Civil society is composed of many peer networks, such as church groups, community groups, youth groups, labor unions, rotary clubs, interest groups, academic institutions, various charities, the media in various shapes and forms etc. Many of these are networked in their structure and do not exert any direct power over their members, being voluntary associations. The nonlinear dimension to a political system is then, the many overlapping networks throughout a society without centralized regulation by formal political institutions but still regulate public activities and opinions, and are sources of political power. In this context, we could, for example, identify totalitarianism as an expansion of the linear domain into the domain of the nonlinear civic space, as it tries to disintermediate the various civil networks within society and create a direct relationship between the state and the population while limiting the direct peer to peer interactions between people.11


Because political science typically uses linear models we often spend a lot of time focusing on the centralized and linear formal political institutions, simply because they fit into our models. The nonlinear dimension to the system of civil society is often then dealt with through statistical methods, we take a sample of public opinion and generalize that to the whole population. Political scientist and analysts spend a lot of time talking about either the interaction between government leaders or public opinion derive from statistical sampling of the mass of people. What goes unaccounted for in this method is the nonlinearly distributed set of connections, how people are connected, the different types of synergies that may exist within those connections and how that may lead to non-equilibrium outcomes that differ from pure statistical aggregations.

People taking pictures with smartphones. Information technology and social platforms are connecting people into ever larger distributed networks which will change the nature of politics in profound ways in the coming decades as individuals can communicate peer to peer

It can be noted here that as people become more interconnected such statistical methods that look at samples of masses assuming their independence will be limited in their result. It is only with reference to nonlinear models where we include distributed interactions between members and the potential for synergies between different networks of connections that we have the possibility to talk about emergence and non-equilibrium outcomes, which become key drivers in a system that exhibits heightened connectivity and interdependence. As long as we are using linear models all we will see is that only big events can cause big outcomes, in trying to simplify our models we will then remove small events that appear to not have significant outcomes, with such events being deemed as negligible and thus not relevant. The result of this though is that we will continuously come back to focusing on the centralized major actors in the system, without the potential to see how small events can create large outcomes through distributed nonlinear interactions within overlapping synergistic networks. Such an analysis is relevant in a political environment with low levels of complexity but will be rendered less functional given greater complexity.12 The more we turn up the interconnectivity within the system the greater the potential for nonlinear emergent outcomes and the more we will be surprised by the observed outcomes if we stay focusing on linear aggregations and centralized components.

Nonlinear distributed interactions give rise to emergent outcomes. Instead of statistical aggregations tending towards the mean or average the larger the sample we take, the opposite happens, we get power law distributions where statistical averages tell us little about what is going on in the system. A classical tool for modeling such nonlinear emergent outcomes would be agent-based modeling that is specifically designed to simulate the many distributed interactions between individuals and the emergent patterns that may arise from this.13 Whereas modeling complexity with linear models often involves adding an increasing amount of varying parameters making the model more complicated, the nonlinear approach recognizes that even with only a few variables complexity can arise out of their nonlinear interactions, through a process of emergence. Which is one of the basic ideas in complexity theory; that simple rules can create complex phenomena.14

Higher Order Change

Linear models are inherently static. They are always in relation to equilibrium. They model systems in terms of the different forces acting on the system to bring it back to equilibrium. Such models may tell us about normal periods of stable and incremental change. They tell us about the linear interaction between the components where one thing interacts to cause another and only big players can cause big effects. What it fails to tell us about are processes of higher order change.15 Nonlinearity implies higher order change, that is to say, the shift from one overall systems regime to another. For example, the move within Europe from the middle ages into the modern era, or the move from the Warring States Period in Chine to the formation of the first unified Chinese empire are both examples of a higher order macro level change where in all the political institutions become reconfigured in such a period of fundamental change. An analysis of the major parts and their interactions is limited, one needs to also look at the aggregate level. As is often the case with nonlinear systems, because of the emergence of patterns and processes on the macro level one can not just look at the parts one has to also look at the whole to understand what is going on. Without having some macro model to the overall process of change as a society goes from being premodern to modern, one could not derive such a phenomenon simply from how the parts interact.

With linear models when one wants to account for high order changes, such as the fall of regimes, we can only resort to stochastic models. Political history is littered with examples, where in some cases small persons or incidents have ignited massive armed conflicts or war and in other situations, similar events have resulted in no appreciable changes in status quo.15 An understanding of such processes of change requires, not simply an analysis of the major actors but instead, some indication of the distributed state of the system and an understanding of feedback processes involving cascading effects that occur when the decisions of citizens are interdependent over time. Each person’s payoff depends on the number of other people who do so at the same or later time. Cascades or herding effects in collective action are present when the adoption of a given behavior is dependent on interactions over time. In such a case the context within which people are making their choices to change or not is dependent not only on their personal propensities but also the context within which they are embedded; which itself is dynamically changing as events unfold. Effectively interpreting such emergent processes of change requires nonlinear models that identify feedback loops and the networks of connections present.15

1. Political Complexity. (2017). Google Books. Retrieved 22 June 2017, from

2. Kiel, L. (2000). The evolution of nonlinear dynamics in political science and public administration: Methods, modeling and momentum. Discrete Dynamics In Nature And Society, 5(4), 265-279. doi:10.1155/s1026022600000571

3. Political Complexity. (2017). Google Books. Retrieved 22 June 2017, from

4. Dictionary, s. (2017). synergy Meaning in the Cambridge English Dictionary. Retrieved 22 June 2017, from

5. Synergy – organization, system, company, business, system, History of synergy, Individuals and synergy. (2017). Retrieved 22 June 2017, from

6. Feedback Loop: Definition & Examples – Video & Lesson Transcript | (2017). Retrieved 22 June 2017, from

7. “Complex Social Systems” Martin Hilbert. (2017). YouTube. Retrieved 22 June 2017, from

8. (2017). Retrieved 22 June 2017, from,issue-3/pdfs/dobre.pdf

9. Usó-Doménech, J., Nescolarde-Selva, J., & Lloret-Climent, M. (2014). “Unintended effects”: A theorem for complex systems. Complexity, 21(2), 342-354. doi:10.1002/cplx.21609

10. Civil Society. (2014). Retrieved 22 June 2017, from

11. totalitarianism | government. (2017). Encyclopedia Britannica. Retrieved 22 June 2017, from

12. Social Emergence – Cambridge University Press. (2017). Retrieved 22 June 2017, from

13. Agent Based Modeling and Simulation . (2017). Retrieved 22 June 2017, from

14. A Study in Complexity. (2017). Retrieved 22 June 2017, from

15. Political Complexity. (2017). Google Books. Retrieved 22 June 2017, from