A dynamic network model of societal complexity and resilience inspired by Tainter's theory of collapse

Abstract

In the past twenty years several events disrupted global economies and social well-being and generally shook the confidence in the stability of western societies such as during the 2008 financial crisis and its economic aftermath. Here, we aim to identify and illustrate underlying drivers of such societal instability or even consequential collapse. For this purpose we propose a low-dimensional and stylised model of two classes of networked agents (termed "labourers" and "administrators" hereafter) that is inspired by Joseph Tainter's theory of collapse of complex societies. We numerically model the dynamics of societal complexity, measured as the share of "administrators", which is assumed to affect the productivity of energy-producing 'labourers". We show that collapse becomes increasingly likely if the model society's complexity continuously increases in response to external stresses that emulate Tainter's abstract notion of problems that societies need to solve. We additionally provide an analytical approximation of the system's dominant dynamics which matches well with the numerical experiments, thus, allowing for a precise estimate of tipping points beyond which societal collapse is triggered. The administration's ability for increasing productivity of labour shows to be the most influential parameter for longer survival times which is additionally fostered by a minimum level of social connectivity. Finally, we show that agents' stochastic transitions between labour force and administration, i.e. social mobility, can increase the survival time of the modeled society even further. Our work fosters the understanding of socio-ecological collapse and illustrates its potentially direct link to an ever increasing complexity in response to external shocks or stress via a self-reinforcing feedback.