Contribution D—“Show WASAN makes contributions to the theory of PSMs by showing how horizontal recursion can be used to represent interactions and meta-systemic issues across multiple modelled systems”. The concept of recursion and recursive systems was developed in WASASN to show how WASAN can contribute to the PSM theory. It is no coincidence that recursion is a central principle in Question 2 of the four pillar framework. To make the case for including WASAN as a PSM, the project wanted to show that along with sharing the same defining criteria as PSMs, WASAN could advance these central features and therefore make contributions to the body of the PSM theory. WASAN contributing to the theory of recursion shows commonality between WASAN and the existing PSMs and how WASAN influences other PSMs. For the author, this final proof that WASAN is a PSM and when shown in combination with the other contributions of this thesis will
cement WASAN as a generic PSM. The remainder of this section will introduce recursion as a systems modelling concept to be expanded in Chapter 5.
Recursion helps OR modellers to explain how complex hierarchically- interdependent units can be represented across multiple models. Typically, the relationship between recursive models is conceived as being vertical, where one model is linked to higher-level or lower-level equivalents. In these cases, we could say the lower level model is nested within the higher level model as the lower level model would have to form part of the higher level model. An example is presented in Figure 9, which shows Hoverstadt's (2008) 12 vertical levels of recursion within the Chilean Government. Each hierarchical level contains and is contained within a nested system. As the model is that of the Chilean Government, the Whole Nation is the highest level; however, if the purpose of the model were different, the model could expand to include other nations and beyond. Similarly, in Figure 9, the smallest unit is the worker, but, if required, the concept of recursion could go further and draw on biology to identify sub-systems that constitute the worker. One of the benefits of recursion is that it “allows elegant representation of organisations” (Jackson, 2003 p.87). Building a larger model without using recursion would mean the emergent properties of the individual systems would become more difficult to identify (Tejeida-padilla & Badillo-pin, 2010).
At each recursion level in Figure 9, the system is conceptualised in the same manner so the same structural/analytical rules can be applied to each level. This means that a model could be built at any level using the same modelling conventions with linkages being established across the models at different vertical levels. Beyond OR, other fields do not think of recursion as only a vertical property and use recursion in a more flexible manner to represent vertical or horizontal relationships between phenomena. In these settings, horizontal relationships refer to the analysis of continuous units on the same hierarchical plane, for example, a
supply chain. This thesis will reconsider the nature of recursion in OR modelling, expanding the usual definition to include horizontal modelling of units on the same hierarchical plane.
Figure 9 Twelve levels of recursion in Chile (from Hoverstadt, 2008)
OR modellers analyse situations by constructing models that represent and build knowledge on a problem (Mingers, 2003). A model is “an external and explicit representation of part of reality as seen by the people who wish to use that model to understand, to change, to manage and to control that part of reality” (Pidd, 2009 p.10). The elements included in the model reflect what is considered important to build an understanding of the situation by the modellers (Lane & Oliva, 1998). PSMs such as SSM and SODA recognise that situations exist in a wider environment and contain sub-levels (Ackermann, 2012). This is shown in the four pillar framework
through Question 2: “Does the approach acknowledge there are systems at different
hierarchical levels to the one being modelled?”Thus, recursion may be a useful tool to formally model the higher and lower systems in this hierarchy and thereby develop an understanding of the context to ensure that model outcomes are more politically and cognitively feasible.
When examining the impact that recursion has on OR, we do not examine PSMs as they do not describe recursion being at their heart. The strongest presence of recursion is in VSM (Beer, 1981) which places recursion high in its
constitution for how communication flows across functional units and between levels of systems. In VSM, recursion explains how complex systems are comprised of multiple nested subsystems that are autonomous, adaptable, self-regulatory, and self-organising (Watts, 2009). Like PSMs, VSM builds qualitative models and thus it is a more appropriate analogue through which to learn about the potential for recursion in PSMs.
In VSM, recursion is considered vertical, with the relationship between modelled systems spanning up and down the organisational hierarchy. This research project uses the concepts from recursion from VSM, but instead of only considering vertical relationships between models, it introduces horizontal recursion as a new type of recursion that is applicable to PSMs. Horizontal recursion uses the same modelling convention, but analyses other systems on the same hierarchical plane so the relationship between the analysed systems is horizontal not vertical. Thus, horizontal recursion examines systems upstream and downstream to model those using the same principles and structures. These models can be linked to move from one system model to another on the same horizontal plane and thereby model how one system can impact (and be impacted by) another. WASAN models systems that are impacted by upstream and downstream systems; therefore, to model these systems side-by-side, recursion must be used to ensure that the emergent properties of individual level systems are not lost in a meta-model.
This approach to model building creates a wider systemic understanding of the causes or impacts one unit can have on another on the same hierarchical plane. Broadening the definition of recursion to include horizontal recursion gives a new way for model builders to understand and represent the relationship between different systems and the models that reflect these.