Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy

TL;DR

This paper explores how the structure of hierarchical organizations influences social influence dynamics, identifying regimes from tyranny to anarchy using a topological measure called trophic incoherence, supported by analytical, numerical, and empirical case studies.

Contribution

It introduces the trophic incoherence parameter as a key measure to predict influence regimes in hierarchical social networks, bridging theory and real-world applications.

Findings

Low q leads to fast consensus (tyranny)

Mid q results in slow consensus (democracy)

High q causes no consensus (anarchy)

Abstract

Coordinated human behaviour takes place within a diverse range of social organisational structures, which can be thought of as power structures with "managers" who influence "subordinates". A change in policy in one part of the organisation can cause cascades throughout the structure, which may or may not be desirable. As organisations change in size, complexity and structure, the system dynamics also change. Here, we consider majority rule dynamics on organisations modelled as hierarchical directed graphs, where the directed edges indicate influence. We utilise a topological measure called the trophic incoherence parameter, q, which effectively gauges the stratification of power structure in an organisation. We show that this measure bounds regimes of behaviour. There is fast consensus at low q (e.g. tyranny), slow consensus at mid q (e.g. democracy), and no consensus at high q (e.g. anarchy). These regimes are investigated analytically, numerically and empirically with diverse case studies in the Roman Army, US Government, and a healthcare organisation. Our work demonstrates the usefulness of the trophic incoherence parameter when considering models of social influence dynamics, with widespread consequences in the design and analysis of organisations.