The University of Warwick, Centre for Doctoral Training in Mathematics for Real-World Systems, Coventry, CV4 7AL, UK.
Cranfield University, Centre for Autonomous and Cyberphysical Systems, Cranfield, MK43 0AL, UK.
Sci Rep. 2020 Mar 9;10(1):4388. doi: 10.1038/s41598-020-61196-8.
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.
协调的人类行为发生在各种不同的社会组织结构中，可以将这些结构视为具有“管理者”影响“下属”的权力结构。组织内部的政策变化会在整个结构中引发级联效应，这可能是可取的，也可能是不可取的。随着组织规模、复杂性和结构的变化，系统动态也会发生变化。在这里，我们考虑将组织建模为有向分层图的多数规则动态，其中有向边表示影响。我们利用一种称为营养不连贯性参数 q 的拓扑度量，有效地衡量组织中权力结构的分层。我们表明，该度量可以限制行为的范围。q 值较低时（例如暴政）会快速达成共识，q 值中等时（例如民主）则达成共识较慢，而 q 值较高时（例如无政府状态）则无法达成共识。我们通过对罗马军队、美国政府和医疗保健组织等不同案例的分析、数值和实证研究来研究这些状态。我们的工作表明，在考虑社会影响动态模型时，营养不连贯性参数是有用的，这对组织的设计和分析具有广泛的影响。
