By Bruce Edmonds
Vagueness and refutation
A model is basically composed of two parts (Zeigler 1976, Wartofsky 1979):
- A set of entities (such as mathematical equations, logical rules, computer code etc.) which can be used to make some inferences as to the consequences of that set (usually in conjunction with some data and parameter values)
- A mapping from this set to what it aims to represent – what the bits mean
Whilst a lot of attention has been paid to the internal rigour of the set of entities and the inferences that are made from them (1), the mapping to what that represents (2) has often been left as implicit or incompletely described – sometimes only indicated by the labels given to its parts. The result is a model that vaguely relates to its target, suggesting its properties analogically. There is not a well-defined way that the model is to be applied to anything observed, but a new map is invented each time it is used to think about a particular case. I call this way of modelling “Suggestivism”, because the model “suggests” things about what is being modelled.
This is partly a recapitulation of Popper’s critique of vague theories in his book “The Poverty of Historicism” (1957). He characterised such theories as “irrefutable”, because whatever the facts, these theories could be made to fit them. Irrefutability is an indicator of a lack of precise mapping to reality – such vagueness makes refutation very hard. However, it is only an indicator; there may be other reasons than vagueness for it not being possible to test a theory – it is their disconnection from well-defined empirical reference that is the issue here.
Some might go as far as suggesting that any model or theory that is not refutable is “unscientific”, but this goes too far, implying a very restricted definition of what ‘science’ is. We need analogies to think about what we are doing and to gain insight into what we are studying, e.g. (Hartman 1997) – for humans they are unavoidable, ‘baked’ into the way language works (Lakoff 1987). A model might make a set of ideas clear and help map out the consequences of a set of assumptions/structures/processes. Many of these suggestivist models relate to a set of ideas and it is the ideas that relate to what is observed (albeit informally) (Edmonds 2001). However, such models do not capture anything reliable about what they refer to, and in that sense are not part of the set of the established statements and theories that is at the core of science (Arnold 2014).
The dangers of suggestivist modelling
As above, there are valid uses of abstract or theoretical modelling where this is explicitly acknowledged and where no conclusions about observed phenomena are made. So what are the dangers of suggestivist modelling – why am I making such a fuss about it?
Firstly, that people often seem to confuse a model as an analogy – a way of thinking about stuff – and a model that tells us reliably about what we are studying. Thus they give undue weight to the analyses of abstract models that are, in fact, just thought experiments. Making models is a very intimate way of theorising – one spends an extended period of time interacting with one’s model: developing, checking, analysing etc. The result is a particularly strong version of “Kuhnian Spectacles” (Kuhn 1962) causing us to see the world though our model for weeks after. Under this strong influence it is natural to confuse what we can reliably infer about the world and how we are currently perceiving/thinking about it. Good scientists should then pause and wait for this effect to wear off so that they can effectively critique what they have done, its limitations and what its implications are. However, often in the rush to get their work out, modellers often do not do this, resulting in a sloppy set of suggestive interpretations of their modelling.
Secondly, empirical modelling is hard. It is far easier (and, frankly, more fun) to play with non-empirical models. A scientific culture that treats suggestivist modelling as substantial progress and significantly rewards modellers that do it, will effectively divert a lot of modelling effort in this direction. Chattoe-Brown (2018) displayed evidence of this in his survey of opinion dynamics models – abstract, suggestivist modelling got far more reward (in terms of citations) than those that tried to relate their model to empirical data in a direct manner. Abstract modelling has a role in science, but if it is easier and more rewarding then the field will become unbalanced. It may give the impression of progress but not deliver on this impression. In a more mature science, researchers working on measurement methods (steps from observation to models) and collecting good data are as important as the theorists (Moss 1998).
Thirdly, it is hard to judge suggestivist models. Given their connection to the modelling target is vague there cannot be any decisive test of its success. Good modellers should declare the exact purpose of their model, e.g. that is analogical or merely exploring the consequences of theory (Edmonds et al. 2019), but then accept the consequences of this choice – namely, that it excludes making conclusions about the observed world. If it is for a theoretical exploration then the comprehensiveness of the exploration, the scope of the exploration and the applicability of the model can be judged, but if the model is analogical or illustrative then this is harder. Whilst one model may suggest X, another may suggest the opposite. It is quite easy to fix a model to get the outcomes one wants. Clearly, if a model makes startling suggestions – illustrating totally new ideas or making a counter-example to widely held assumptions – then this helps science by widening the pool of theories or hypotheses that are considered. However most suggestivist modelling does not do this.
Fourthly, their sheer flexibility of as to application causes problems – if one works hard enough one can invent mappings to a wide range of cases, the limits are only those of our imagination. In effect, having a vague mapping from model to what it models adds in huge flexibility in a similar way to having a large number of free (non-empirical) parameters. This flexibility gives an impression of generality, and many desire simple and general models for complex phenomena. However, this is illusory because a different mapping is needed for each case, to make it apply. Given the above (1)+(2) definition of a model this means that, in fact, it is a different model for each case – what a model refers to, is part of the model. The same flexibility makes such models impossible to refute, since one can just adjust the mapping to save them. The apparent generality and lack of refutation means that such models hang around in the literature, due to their surface attractiveness.
Finally, these kinds of model are hugely influential beyond the community of modellers to the wider public including policy actors. Narratives that start in abstract models make their way out and can be very influential (Vranckx 1999). Despite the lack of rigorous mapping from model to reality, suggestivist models look impressive, look scientific. For example, very abstract models from the Neo-Classical ‘Chicago School’ of economists supported narratives about the optimal efficiency of markets, leading to a reluctance to regulate them (Krugman 2009). A lack of regulation seemed to be one of the factors behind the 2007/8 economic crash (Baily et al 2008). Modellers may understand that other modellers get over-enthusiastic and over-interpret their models, but others may not. It is the duty of modellers to give an accurate impression of the reliability of any modelling results and not to over-hype them.
How to recognise a suggestivist model
It can be hard to detangle how empirically vague a model is, because many descriptions about modelling work do not focus on making the mapping to what it represents precise. The reasons for this are various, for example: the modeller might be conflating reality and what is in the model in their minds, the researcher is new to modelling and has not really decided what the purpose of their model is, the modeller might be over-keen to establish the importance of their work and so is hyping the motivation and conclusions, they might simply not got around to thinking enough about the relationship between their model and what it might represent, or they might not have bothered to make the relationship explicit in their description. Whatever the reason the reader of any description of such work is often left with an archaeological problem: trying to unearth what the relationship might be, based on indirect clues only. The only way to know for certain is to take a case one knows about and try and apply the model to it, but this is a time consuming process and relies upon having a case with suitable data available. However, there are some indicators, albeit fallible ones, including the following.
- A relatively simple model is interpreted as explaining a wide range of observed, complex phenomena
- No data from an observed case study is compared to data from the model (often no data is brought in at all, merely abstract observations) – despite this, conclusions about some observed phenomena are made
- The purpose of the model is not explicitly declared
- The language of the paper seems to conflate talking about the model with what is being modelled
- In the paper there are sudden abstraction ‘jumps’ between the motivation and the description of the model and back again to the interpretation of the results in terms of that motivation. The abstraction jumps involved are large and justified by some a priori theory or modelling precedents rather than evidence.
How to avoid suggestivist modelling
How to avoid the dangers of suggestivist modelling should be clear from the above discussion, but I will make them explicit here.
- Be clear about the model purpose – that is does the model aim to achieve, which indicates how it should be judged by others (Edmonds et al 2019)
- Do not make any conclusions about the real world if you have not related the model to any data
- Do not make any policy conclusions – things that might affect other people’s lives – without at least some independent validation of the model outcomes
- Document how a model relates (or should relate) to data, the nature of that data and maybe even the process whereby that data should be obtained (Achter et al 2019)
- Be explicit as possible about what kinds of phenomena the model applies to – the limits of its scope
- Keep the language about the model and what is being modelled distinct – for any statement it should be clear whether it is talking about the model or what it models (Edmonds 2020)
- Highlight any bold assumptions in the specification of the model or describe what empirical foundation there is for them – be honest about these
Models can serve many different purposes (Epstein 2008). This is fine as long as the purpose of models are always made clear, and model results are not interpreted further than their established purpose allows. Research which gives the impression that analogical, illustrative or theoretical modelling can tell us anything reliable about observed complex phenomena is not only sloppy science, but can have a deleterious impact – giving an impression of progress whilst diverting attention from empirically reliable work. Like a bad investment: if it looks too good and too easy to be true, it probably isn’t.
 We often use the word “model” in a lazy way to indicate (1) rather than (1)+(2) in this definition, but a set of entities without any meaning or mapping to anything else is not a model, as it does not represent anything. For example, a random set of equations or program instructions does not make a model.
Bruce Edmonds is supported as part of the ESRC-funded, UK part of the “ToRealSim” project, grant number ES/S015159/1.
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