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

Charlie Pilgrim*, Weisi Guo, Samuel Johnson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Article number4388
JournalScientific Reports
Issue number1
Publication statusPublished - 1 Dec 2020

Bibliographical note

Funding Information:
The study was funded by the EPSRC grant for the Mathematics for Real-World Systems CDT at Warwick (Grant Number EP/L015374/1) and the EPSRC grant for CoTRE - Complexity Twin for Resilient Ecosystems (Grant Number EP/R041725/1).

Publisher Copyright:
© 2020, The Author(s).

ASJC Scopus subject areas

  • General


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