Apparent Strength Conceals Instability in a Model for the Collapse of Historical States

Citation: Lawson DJ, Oak N ( Apparent Strength Conceals Instability in a Model for the Collapse of Historical States Daniel John Lawson 0 Neeraj Oak 0 Gennady Cymbalyuk, Georgia State University, United States of America 0 1 Heilbronn Institute, School of Mathematics, University of Bristol , Bristol , United Kingdom , 2 Bristol Centre for Complexity Sciences, University of Bristol , Bristol , United Kingdom An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We examine political disintegration across eras, cultures and geographical scale to form a simple hypothesis that can be expressed verbally yet formulated mathematically. Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion. In lieu of precise data we verify our model using sensitivity analysis. We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree. - Funding: DJL was funded by the Heilbronn Institute for Mathematical Research and NO by Bristol Centre for Complexity Sciences. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. History has witnessed the rise and fall of countless empires, dynasties and regimes. What governs these apparently inevitable processes has been discussed across the eras [1]. Whilst growth and power seem naturally self-reinforcing, reversal into decline or collapse has impacted every state and culture not present today. Further, the fate of a nation is often tied closely to the fate of its leading class; the sudden collapse of one often leads to a similar collapse of the other [2,3]. Within a state, influence and power are often distributed unequally. Political change is affected by many factors including visible achievements and failures, deliberate manipulation, accidents of fate and external forces. Historically, stable political states can enjoy long periods of relative growth and internal stability during which the leading class can gain a larger and larger share of the wealth and resource [4,5]. However, the process of mounting inequality has clearly not continued forever. Power may also change rapidly, and with great impact on the fate of apparently stable states. Whilst we do not apply our model to contemporary conflict, the clarity provided by modern media during the Arab Spring of 2011 [6,7] illustrates the lack of simplicity in these transitions. In many cases, rebellion operated without a unified name or organisation long before any form of leadership emerged (for example, in Libya [8]), signifying a decentralised process. We are interested in why social disorder appears rapidly from an apparently stable state. Is there a generality describing when dissident movements will receive support and when they will be ignored? Actual success of rebellion movements means acquiring military power, which is strongly dependent on technology and social structure. Those with the military power may join the rebellion if it is in their interests to do so. During peace this may seem implausible, but the toll of rebellion may rapidly change the situation. External factors are important in determining when a state fails. Pressure from other states is clearly important and we will consider examples that involve state aggression and warfare. Many collapse events have been linked to environmental factors such as local or global climate change [913] and long term degradation of resource [14] (although there is still controversy, e.g. [15]). Such external forces clearly catalyse disorder, and are frequently a proximal cause for collapse. However, this alone does not explain why stresses are sometimes resisted and sometimes cause calamity. For example, Sassanid Persia thrived during periods in which the neighbouring Roman empire experienced agricultural decline [16]. Many collapse events occur in the absence of environmental pressure [17], with external conquest, internal conflict, or poor social, political and economic institutions playing a greater role instead. We hypothesise a dynamical process behind the social conditions that can make unrest more likely to accelerate, which will interact with external stresses. Our model is complementary to other theories of collapse [18] by providing a game-theory or economic explanation for social assumptions. Collins [19,20] emphasises the importance of areas at the fringe of empires, so called marchlands, which tend to be the incubators of new regimes or polities. The thirteenth century author Ibn Khaldun [21] describes a concept he calls asabiya or group feeling in which loyalties are nested within a state. The metaethnic frontier theory of Turchin [22] combines these hypotheses. As we predict that power equality can lead to stability, the most cohesive states should emerge from marchlands and tight-knit groups with high asabiya. Thus our economic model predicts the emergence of asabiya. We join a recent trend of providing mathematical models for historical hypotheses (some excellent examples are [2326]). Mathematical modelling cannot replace historical investigation, and general principles of civil conflict and disunity can be understood [27,28] without the need for modelling. However, mathematics provides formal reasoning that aids generalisation and guides intuition in complex situations. A mathematical theory of collapse is a first step towards a statistically sound, data-driven comparison between hypotheses (a feat we do not attempt here). Our model is too general to be the full explanation for any specific scenario, so we consider a wide range of documented collapse events that contain qualitative similarities without claims about the critical factors in any given situation. Conceptually the model is qualitative and robustly explored by considering numerous precise instantiations, which acts as a sensitivity analysis [29] helpful for supporting (but not confirming) conclusions from qualitative data. A qualitative model of collapse Consider a number of actors playing a repeated public goods game, in which cooperators enter their resource into a public pool to be redistributed according to influence, which changes over time. Defectors obtain lower mean payoff but are not subject to redistribution. The game dynamics (Figure 1) draw on three vital qualitative assumptions: 1. Inequality of in (...truncated)