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):
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.
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.
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?
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.