By Steven Lade
What do you think about mathematical modelling of ‘wicked’ or complex problems? Formal modelling, such as mathematical modelling or computational modelling, is sometimes seen as reductionist, prescriptive and misleading. Whether it actually is depends on why and how modelling is used.
Here I explore four main reasons for modelling, drawing on the work of Brugnach et al. (2008):
- Prediction
- Understanding
- Exploration
- Communication.
I start with mental models – the informal representations of the world that we all use as we go about both our personal and professional lives – and then move on to formal models.
Mental models
We are all modellers! We all use mental models every day for a variety of different purposes:
- To make quantitative predictions about the future. For example, if I throw the ball this fast, where will it land? How much money would my house sell for?
- To understand things that happened. For example, why did the cake I baked not turn out like expected? Why was Donald Trump elected as president in the USA, against many expectations?
- To explore alternative versions of our worlds. For example, what if I added a room to my house? What is life like for someone living in another country?
- To communicate. Communication is nothing more than the construction and sharing of mental models via language, and we use it every day. For example, when we talk about love, the weather, justice, our garden, or tax, we use representations of these concepts that are at least partially shared among those involved in the conversation.
Formal models
All these purposes can also be fulfilled by formal models.
Prediction is the model purpose most commonly associated with formal modelling, though in wicked problems prediction should be treated cautiously and with full understanding of the model’s assumptions.
Understanding is the model purpose most commonly used in traditional science, to test hypotheses against observations.
The remaining two purposes, exploration and communication, are of the most relevance for wicked problems, yet are arguably the most underappreciated.
Exploration using formal models is nothing more than a reasoning tool to support our own mental modelling capacity for exploration. The effects of complex system dynamics features such as multiple interacting feedbacks can be difficult to anticipate and may even be counter-intuitive: that’s why they’re considered ‘complex’.
An example can be seen in research on how different poverty-environment relationships affect which poverty alleviation strategies are likely to be effective (Lade et al., 2017). We showed that in situations where poor people degrade their environment—usually because they have no choice—asset inputs may help break that cycle of poverty. But in situations where poor people maintain their environment, and agricultural intensification leads to increased environmental degradation, asset inputs may be counterproductive and even reinforce poverty, requiring other strategies.
Finally, sometimes the process of constructing the formal model can be just as valuable as the model itself. Participatory model construction encourages communication of each participant’s mental models, thereby developing awareness of others’ perspectives and possibly challenging one’s own mental model. In an earlier blog post, Jen Badham and Gabriele Bammer described how jointly designing formal models can help stakeholders draw out differences in their mental models of a complex system. For example, a modelling process could help draw out the different understandings that farmers and government policy-makers have of an agricultural system and the different challenges that they face when interacting with this complex system.
In summary, mathematical models have a valuable place even in complex systems with wicked problems, especially when used for exploration and communication. As with any tool, the key is to be aware of why you’re using them.
Why do you model? Do you have other modelling purposes to share? Or additional examples of the reasons for modelling described above?
References:
Brugnach, M., Pahl-Wostl, C., Lindenschmidt, K. E., Janssen, J. A. E. B., Filatova, T., Mouton, A., Holtz, G., van der Keur, P. and Gaber N. (2008). Complexity and Uncertainty: Rethinking The Modelling Activity. U.S. Environmental Protection Agency Papers, 72. (Online): http://digitalcommons.unl.edu/usepapapers/72
Lade, S. J., Haider, L. J., Engström, G. and Schlüter, M. (2017). Resilience offers escape from trapped thinking on poverty alleviation. Science Advances, 3, 5: e1603043. (Online) (DOI): https://doi.org/10.1126/sciadv.1603043
Biography: Steve Lade is a researcher at the Stockholm Resilience Centre, Stockholm University, Sweden and an Honorary Senior Lecturer at the Fenner School of Environment and Society, Australian National University in Canberra, Australia. He uses complex systems tools to study the resilience and sustainability of human and natural systems including fisheries, poverty traps and the Earth system. He is currently funded by a young researcher mobility grant from the Swedish Research Council Formas.
I think we make these categories more precise in the joint paper at https://www.jasss.org/22/3/6.html
A comment on “What do you think about mathematical modelling of ‘wicked’ or complex problems?”
Facing reality I will explain the free choices before one could model something mathematically….
You cannot escape the first choice: saying “yes” or “no” to something that you can experience. If a stakeholder brings you in a certain environment and says: “do you experience this”? Then you have two choices: you could say “yes” or you could say “no”. Implicitly we suppose that you are honest in your judgement.
If a stakeholder brings you in two distinct environments and says: “do you experience “this” in the first being more (or less) “this” than in the second”? Then you have two choices: you could say “yes” or you could say “no”. Implicitly we suppose that you are honest in your judgement again.
If you want that communication is predictable (because you are honest) then this introduces a constraint. If you say “yes” to the question “do you experience “this” in the first being more “this” than in the second”, AND if you say “yes” to the question “do you experience “this” in the second being more “this” than in the third”, then you should say “yes” to the question “do you experience “this” in the first being more “this” than in the third”.
This constraint is thus an ordering. Honest communication implies this predictability. It is not straightforward that stakeholders use the same ordering, it depends on what they can experience in the relevant environments and how they apply symbols (or words) to it. Already this should be researched by everybody with respect for stakeholders.
Now we can go a step further. The stakeholder who brought you in two distinct environments could use this distinction as a unity, meaning: all distinctions can be expressed as multiples (or fractions) of this “first” distinction. The multiples now code the order.
Only after those two steps some mathematics can be used in the act of modeling “that “something” was understood”, but not all of mathematics, because a zero is not defined yet.
The next step is to define a zero, a point that is not questionable at all because it is the point where I stand and it is different from the point where you stand.
Mathematical modelling is thus not straightforward at all.
Walter
Thorbjørn: could you post a few references for us? I am struggling to find some. Your ideas about ‘planning discourse platforms and procedures’ sounds interesting
Christopher: Thanks for your interest. There are some papers on Acdemia.edu — (Thorbjoern Mann) for example the most recent version on the Planning Discourse “P D S S – R E V I S E D… “; I also have WordPress blog ‘https://Abbeboulah.com’ that tries to treat these issues in more conversational ‘Tavern Talk’ language. An older book ‘The Fog Island Argument’ (XLibris), a 2010 article in ‘Informal Logic’ journal, and a more voluminous book ‘Rigatopia’ also deal with those topics.
I agree with your comments about the usual formal models — with regard to ‘wicked’ problems (in the sense formulated by Rittel and Webber). They were of course talking about social problems: design , planning, policy-making, more than problems in, say, the natural sciences where understanding of the nature of systems in reality is the key concern. A main aspect of wicked problems is that the (context) information about who is affected by the problem and how is ‘distributed’ in the population rather than being documented in data bases and expert knowledge textbooks. Thus, the main tool for eliciting that knowledge is discourse — most importantly, the planning discourse with its pros and cons about plan proposals, and differing ideas about the nature of the problems.
The traditional ‘systems’ and scientific formal models usually do not show or reference arguments. The models give the appearance that all controversies and issues have been ‘settled’ — so that the predictive simulations can be run effectively and without contradictory assumptions (which of course are the key ingredients of pros and cons…) The modeler must have taken the side of one party or the other in the inherent controversies.
I have written some articles about this — in Academia.edu. The task is to develop planning discourse platforms and procedures in which systems models have an important role — for example, in providing discourse participants with a visual overview of all the variables end relationships in the system. Or models that accommodate argumentative discourse… Traditional ‘debates’ notoriously do not provide adequate overview and understanding, leading speakers to the temptation to nudge the process towards decisions based on the ‘last word’ in the discussion ‘framed’ by the first entries…
Great comments! Thanks for adding a layer to my explanations. I agree that formal models are sometimes seen as ‘the truth’ and used as a source of definitive knowledge about the future. That’s why I prefer to use models in explorative (or communication) mode that can investigate the consequences of different assumptions or arguments. Then the modeller doesn’t need to ‘pick a side’. Any tools you have to better communicate or illustrate different stakeholder assumptions in a model would be very welcome!
Thanks, Steve. About your question (last sentence): I see the answer less in specific tools than in the way modeling is embedded in the process. I have been working on a better platform for (public) planning and policy-making, where the task is to arrive at a common plan, often to simply agree on whether to accept or reject a plan proposal. That involves bringing out and then evaluatiing (‘weighing’) the arguments, the pros and cons that inform the community about the problem the plan aims to address, and how it affects different people. That information serves as one source of the information needed. to build the model. Another aspect is this: in considering what I call the typical planning argument pattern, consisting of three main premises: one claiming that the plan will produce or imply a certain outcome; given assumed conditions; the second posits the desirability or undesirability of that outcome (the ‘ought’-premise) and the third premise — usually unstated as ‘taken for granted’ — the assumption that the conditions under which the first premise holds will indeed be ‘given’. Taking that premise seriously will reveal that its adequate description should consist of the ‘whole system’ of variables, forces, relationships of the context / environment of the plan: a model, of course. So in theory, each argument might produce a slightly different model. And then of course, within a discourse set up to accommodate argumentation, all assumptions of each such model would be open to questioning, discussion.
Those are only two instances of the relationships between the discourse and systems modeling. The latter should accompany the discourse throughout its process, since each new piece of information or suggestion to adapt the plan under discussion will require adjustment of the models or any ‘unified’ model that will eventually represent the entire range of pertinent information produced in the discourse.
But the design of the planning discourse support platform would provide a ‘toolkit’ of various techniques, tools, for participants to draw upon, for purposes such as the one you are asking about, applicable as needed in the judgment of participants.
My WordPress blog ‘Abbeboulah.com’ and a set of articles on Acdemia.edu contain ideas on these issues.
Steve. Thanks for this posting. I think the more we understand that we are constantly using cognitive or formal models to understand and communicate the more we can increase multi-stakeholder communication and collaboration. I think it would be profitable to flesh out similarities and differences between mental models (or cultural models) and formal models. Perhaps we should reconsider viewing mental or cultural models as informal, versus formal. Both of these terms have many connotations that may not be helpful. Very helpful posting!
Interesting Michael! What do you think some of the major differences between mental/informal/cultural models and formal models are?
A big difference between mental and formal models is burden of proof. We use mental models everyday and handle the inaccuracies and uncertainties involved without even thinking about it. On the other hand, a lot of effort has to go into making formal models acceptable, e.g. through “validation”.
I think a promising avenue of work is to demonstrate how formal models can be used in the same ways that mental models are used – minimising the burden of validation – which ties in well with the idea of exploration.
I was recently introduced to these two (related) papers on the topic:
Hodges, J. S. (1991). Six (or so) Things You Can Do With a Bad Model. Operations Research, 39(3), 355-365.
https://www.rand.org/pubs/notes/N3381.html
Hodges, J. S., & Dewar, J. A. (1992). Is it You or Your Model Talking? A Framework for Model Validation(R-4114-AF/A/OSD). Retrieved from Santa Monica, CA, USA: http://www.rand.org/pubs/reports/2006/R4114.pdf
Thanks Joe for the very useful (and entertainingly titled) references!
Hi Steven, these are great! Perhaps I would add two: 1. storing of information. Since the information & knowledge about the system modelled accumulates in the model. 2. development of alternatives.
Moreover, in the introduction to my dissertation, I wrote as follows “Modeling can support problem solving in various ways. For instance, models can help to generate alternatives or solution candidates, to evaluate alternative policies or systems, and to automate routine decision making (see, e.g. Brill et al. 1982, Pidd 1999). In general, developing and using models can help to organize one’s thinking and to increase understanding of the situation under study (see, e.g. Rubinstein 1975).”, which may be of relevance to this discussion! http://sal.aalto.fi/publications/pdf-files/tlah17_public.pdf
BR, Tuomas
Interesting point! I hadn’t thought about storage. Have you seen cases where stakeholders have gone back to use the information stored in the model (as opposed to the model output itself)? I don’t doubt you, but it would be interesting to hear about an example.
Thanks Steve, this is an excellent summary of some of the ‘other’ reasons to model. I think the most common experience of modelling is economic or weather predictions, and of course statistical models for researchers. This tends to mean that the prediction is much more front of mind but the other reasons are much more useful for my work. Some blog readers may also be interested in this recent JASSS paper http://jasss.soc.surrey.ac.uk/22/3/6.html (open access) that has seven reasons with a systematic but brief look at each.
Thanks very much Jen for the link, that is a fantastic new paper that I hadn’t seen.
Agree ….really simple but useful blog. Will follow up on the references thank you
Hi Steven, this is a really good explanation. I particularly like your comment that communication is a process of sharing mental models. If we can explore that concept with decision makers we can understand that our mental model is an abstraction and only reflect parts of ‘reality out there’. With that understanding we can justify the need for diversity within teams what work together to manage complex issues.
Hi Bonnie, completely agree! “All models are wrong, but some are useful” is usually a statement about formal models but completely applies to mental models too. Diversity and co-management are absolutely necessary.