The viable system model and the viability theory: Collaborations paths

Abstract

The cybernetic viable system model (VSM) and viability theory (VT) are based on common assumptions. Both are tools for understanding and designing organizations. What, then, are the specific notions or concepts they share? What are their points of contact? To answer these questions, we identify the various mathematical concepts of control theory used in VSM and study the advances made in VT. We also summarize the various concepts in each approach. It is shown that VSM emphasizes general structures whereas VT puts the accent on the behaviour of particular dynamic systems. Our general conclusions are that: (1) VSM contributes important cybernetic concepts while VT provides precise notions of tychastic viability, viability and invariant sets as well as capture and absorption basins; and (2) control theory strongly enriched by system dynamics techniques is the most important theoretical and practical bridge between VSM and VT. These various characteristics of the two methods lend themselves to fruitful collaboration between them and form the basis of an attractive agenda for further research.

Keywords:

• Community OR
• soft OR
• system dynamics

Disclosure statement

The authors report there are no competing interests to declare.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 The extensions of VSM proposed by these authors may be briefly stated as follows. Schwaninger (2009) provides an in-depth treatment of cybernetic concepts such as the Conan-Ashby Theorem (ibid., p. 8), hierarchy versus heterarchy (ibid., p. 29) and team syntegrity (ibid., p. 115). Espejo and Reyes (2011) bring in the concepts of autopoiesis and allopoiesis (ibid., p. 14) and propose a methodology denoted VIPLAN for applying VSM in organizations (ibid., p. 115). Espinosa and Walker (2017) consider business-related concepts such as business sustainability and organizational network viability. Finally, basing themselves on VSM, Pérez-Ríos (2012) propose the concept of organizational pathology (ibid., p. 141) and apply the concept of team syntegrity (ibid., p. 201) to organizations.

2 $(\mathcal{H},〈·|·〉)$ is a Euclidean space with the induced norm $\left|\right|·\left|\right|.$

3 To simplify the notation we adopt the following conventions. When we say that a given property is (is not) satisfied in $[0,T],$ we mean that it is (is not) satisfied almost everywhere (a.e.) in $[0,T].$ Also, we write x for the function $x(·)$ and also for an element x(t) in $\mathcal{H}$ when what is meant is clear from the context.

4 We will see later why this quantity was chosen.

5 We consistently extend the formulation of control theory posed in Section 2.3.

6 Let $\mathcal{X}$ be a set, $g:\mathcal{X}\to [-\infty ,+\infty ]$ be a function, and $\xi \in \mathbb{R}.$ The lower level set of g at height ξ is the set ${\text{lev}}_{\le \xi } g\doteq \{x\in \mathcal{X}:g(x)\le \xi \}$ .

7 In Beer (1966) the word optimization appears seven times, but in every case it refers to decision-making techniques in support of a limited range of complex problems.

8 Indeed, one such paper Vahidi and Aliahmadi (2019, p. 23) propose a system dynamics model to represent VSM behaviour.