44. Competing models? Deconstruct into building bricks?

Models are representations of theories. I write this as a modeller – someone who works on mathematical and computer models of cities and regions but who is also seriously interested in the underlying theories I am trying to represent. My field, relative say to physics, is underdeveloped. This means that we have a number of competing models and it is interesting to explore the basis of this and how to respond. There may be implications for other fields – even physics!

A starting conjecture is that there are two classes of competing models: (i) those that represent different underlying theories (or hypotheses); and (ii) those that stem from the modellers choosing different ways of making approximations in seeking to represent very complex systems. The two categories overlap of course. I will conjecture at the outset that most of the differences lie in the second (perhaps with one notable exception). So let’s get the first out of the way. Economists want individuals to maximise utility and firms to maximise profits – simplifying somewhat of course. They can probably find something that public services can maximise – health outcomes, exam results – indeed a whole range of performance indicators. There is now a recognition that for all sorts of reasons, the agents do not behave perfectly and way have been found to handle this. There is a whole host of (usually) micro-scale economic and social theory that is inadequately incorporated into models, in some cases because of the complexity issue – the niceties are approximated away; but in principle, that can be handled and should be. There is a broader principle lurking here: for most modelling purposes, the underlying theory can be seen as maximising or minimising something. So if we are uncomfortable with utility functions or economics more broadly, we can still try to represent behaviour in these terms – if only to have a base line from which behaviour deviates.

So what is the exception – another kind of dividing line which should perhaps have been a third category? At the pure end of a spectrum, ‘letting the data speak for themselves’. It is mathematics vs statistics; or econometrics vs mathematical economics. Statistical models look very different – at least at first sight – to mathematical models – and usually demand quite stringent conditions to be in place for their legitimate application. Perhaps, in the quantification of a field of study, statistical modelling comes first, followed by the mathematical? Of course there is a limit in which both ‘pictures’ can merge: many mathematical models, including the ones I work with, can be presented as maximum likelihood models. This is a thread that is not to be pursued further here, and I will focus on my own field on mathematical modelling.

There is perhaps a second high-level issue. It is sometimes argued that there are two kinds of mathematician: those that think in terms of algebra and those who think in terms of geometry. (I am in the algebra category which I am sure biases my approach.) As with many of these dichotomies, they should be removed and both perspectives fully integrated. But this is easier said than done!

How do the ‘approximations’ come about? I once tried to estimate the number of variables I would like to have for a comprehensive model of a city of 1M people and at a relatively coarse grain, the answer was around 1013! This demonstrates the need for approximation. The first steps can be categorised in terms of scale: first, spatial – referenced by zones of location rather than continuous space – and how large should the zones be? Second, temporal: continuous time or discrete? Third, sectoral: how many characteristics of individuals or organisations should be identified and at how fine a grain? Experience suggests that the use of discrete zones – and indeed other discrete definitions – makes the mathematics much easier to handle. Economists often use continuous space in their models, for example, and this forces them into another kind of approximation: monocentricity, which is hopelessly unrealistic. Many different models are simply based on different decisions about, and representations of, scale.

The second set of differences turn on focus of interest. One way of approximating is to consider a subsystem such as transport and the journey to work, or retail and the flow of revenues into a store or a shopping centre. The dangers here are the critical interdependencies are lost and this always has to be borne in mind. Consider the evaluation of new transport infrastructure for example. If this is based purely on a transport model, there is a danger than the cost-benefit analysis will be concentrated on time savings rather than the wider benefits. There is also a potentially higher-level view of focus. Lowry very perceptively once pointed out that models often focus on activities – and the distribution of activities across zones; or on the zones, in which case the focus would be on land use mix in a particular area. The trick, of course, is to capture both perspectives simultaneously – which is what Lowry achieved himself very elegantly but which has been achieved only rarely since.

A major bifurcation in model design turns on the time dimension and the related assumptions about dynamics. Models are much easier to handle if it is possible to make an assumption that the system being modelled is either in equilibrium or will return to a state of equilibrium quickly after a disturbance. There are many situations where the equilibrium assumption is pretty reasonable – for representing a cross-section in time or for short-run forecasting, for example, representing the way in which a transport system returns to equilibrium after a new network link or mode is introduced. But the big challenge is in the ‘slow dynamics’: modelling how cities evolve.

It is beyond the scope of this piece to review a wide range of examples. If there is a general lesson here it is that we should be tolerant of each others’ models, and we should be prepared to deconstruct them to facilitate comparison and perhaps to remove what appears to be competition but needn’t be. The deconstructed elements can then be seen as building bricks that can be assembled in a variety of ways. For example, ‘generalised cost’ in an entropy-maximising spatial interaction model can easily be interpreted as a utility function and therefore not in competition with economic models. Cellular automata models, and agent-based models are similarly based on different ‘pictures’ – different ways of making approximations. There are usually different strengths and weaknesses in the different alternatives. In many cases, with some effort, they can be integrated. From a mathematical point of view, deconstruction can offer new insights. We have, in effect, argued that model design involves making a series of decisions about scale, focus, theory, method and so on. What will emerge from this kind of thinking is that different kinds of representations – ‘pictures’ – have different sets of mathematical tools available for the model building. And some of these are easier to use than others, and so, when this is made explicit, might guide the decision process.

Alan Wilson

August 2016

43. Lowering the bar

A few weeks ago, I attended a British Academy workshop on ‘Urban Futures’ – partly focused on research priorities and partly on research that would be useful for policy makers. The group consisted mainly of academics who were keen to discuss the most difficult research challenges. I found myself sitting next to Richard Sennett – a pleasure and a privilege in itself, someone I’d read and knew by repute but whom I had never met. When the discussion turned to research contributions to policy, Richard made a remark which resonated strongly with me and made the day very much worthwhile. He said: “If you want to have an impact on policy, you have to lower the bar!” We discussed this briefly at the end of the meeting, and I hope he won’t mind if I try to unpick it a little. It doesn’t tell the whole story of the challenge of engaging the academic community in policy, but it does offer some insights.

The most advanced research is likely to be incomplete and to have many associated uncertainties when translated into practice. This can offer insights, but the uncertainties are often uncomfortable for policy makers. If we lower the bar to something like ‘best practice’ – see preceding blog 42 – this may involve writing and presentations which do not offer the highest levels of esteem in the academic community. What is on offer to policy makers has to be intelligible, convincing and useful. Being convincing means that what we are describing should evidence-based. And, of course, when these criteria are met, there should be another kind of esteem associated with the ‘research for policy’ agenda. I guess this is what ‘impact’ is supposed to be about (though I think that is half of the story, since impact that transforms a discipline may be more important in the long run).

‘Research for policy’ is, of course, ‘applied research’ which also brings up the esteem argument: if ‘applied’, then less ‘esteemful’ if I can make up a word. In my own experience, engagement with real challenges – whether commercial or public – adds seriously to basic research in two ways: first, it throws up new problems; and secondly, it provides access to data – for testing and further model development – that simply wouldn’t be available otherwise. Some of the new problems may be more challenging and in a scientific sense more important, than the old ones.

So, back to the old problem: what can we do to enhance academic participation in policy development? First a warning: recall the policy-design-analysis argument much used in these blogs. Policy is about what we are trying to achieve, design is about inventing solutions; and analysis is about exploring the consequences of, and evaluating, alternative policies, solutions and plans – the point being that analysis alone, the stuff of academic life, will not of itself solve problems. Engagement, therefore, ideally means engagement across all three areas, not just analysis.

How can we then make ourselves more effective by lowering the bar? First, ensure that our ‘best practice’ (see blog 42) is intelligible, convincing and useful; evidence-based. This means being confident about what we know and can offer. But then we also ought to be open about what we don’t know. In some cases we may be able to say that we can tackle, perhaps reasonably quickly, some of the important ‘not known’ questions through research; and that may need resource. Let me illustrate this with retail modelling. We can be pretty confident about estimating revenues (or people) attracted to facilities when something changes – a new store, a new hospital or whatever. And then there is a category, in this case, of what we ‘half know’. We have an understanding of retail structural dynamics to a point where we can estimate the minimum size that a new development has to be for it to succeed. But we can’t yet do this with confidence. So a talk on retail dynamics to commercial directors may be ‘above the bar’.

I suppose another way of putting this argument is that for policy engagement purposes, we should know where we should set the height of the bar: confidence below, uncertainty (possibly with some insights), above. There is a whole set of essays to be written on this for different possible application areas.

Alan Wilson

June 2016.

42. Best practice

Everything we do, or are responsible for, should aim at adopting ‘best practice’. This is easier said than done! We need knowledge, capability and capacity. Then maybe there are three categories through which we can seek best practice: (1) from ‘already in practice’ elsewhere; (2) could be in practice somewhere but isn’t: the research has been done but hasn’t been transferred; (3) problem identified, but research needed.

How do we acquire the knowledge? Through reading, networking, cpe courses, visits. Capability is about training, experience, acquiring skills. Capacity is about the availability of capability – access to it – for the services (let us say) that need it. Medicine provides an obvious example; local government another. How do each of 164 local authorities in England acquire best practice? Dissemination strategies are obviously important. We should also note that there may be central government responsibilities. We can expect markets to deliver skills, capabilities and capacities – through colleges, universities and, in a broad sense, industry itself (in its most refined way through ‘corporate universities’). But in many cases, there will be a market failure and government intervention becomes essential. In a field such as medicine, which is heavily regulated, the Government takes much of the responsibility for ensuring supply of capability and capacity. There are other fields, where in early stage development, consultants provide the capacity until it becomes mainstream – GMAP in relation to retailing being an example from my own experience. (See the two ‘spin-out blogs.)

How does all this work for cities, and in particular, for urban analytics? Good analytics provide a better base for decision making, planning and problem solving in city government. This needs a comprehensive information system which can be effectively interrogated. This can be topped with a high-level ‘dashboard’ with a hierarchy of rich underpinning levels. Warning lights might flash at the top to highlight problems lower down the hierarchy for further investigation. It needs a simulation (modelling) capacity for exploring the consequences of alternative plans. Neither of these needs are typically met. In some specific areas, it is potentially, and sometimes actually, OK: in transport planning in government; in network optimisation for retailers for example. A small number of consultants can and do provide skills and capability. But in general, these needs are not met, often not even recognised. This seems to be a good example of a market failure. There is central government funding and action – through research councils and particularly perhaps, Innovate UK. The ‘best practice’ material exists – so we are somewhere in between categories 1 and 2 of the introductory paragraph above. This tempts me to offer as a conjecture the obvious ‘solution’: what is needed are top-class demonstrators. If the benefits were evident, then dissemination mechanisms would follow!

Alan Wilson
June 2016

41 Foresight on The Future of Cities

For the last three years (almost), I have been chairing the Lead Expert Group of the Government Office for Science Foresight Project on The Future of Cities. It has finally ‘reported’, not as conventionally with one large report and many recommendations, but with four reports and a mass of supporting papers. We knew at the outset that we could not look forward without learning the lessons of the past, and so we commissioned a set of working papers – which are on the web site – as a resource, historical in the main, looking forwards imaginatively where possible. The ‘Foresight Future of Cities’ web site is at https://www.gov.uk/government/collections/future-of-cities.

During the project, we have worked with fourteen Government Department – ‘cities’ as a topic crosses government – and we have visited over 20 cities in the UK and have continued to work with a number of them. The project had several (sometimes implicit) objectives: to articulate the challenges facing cities from a long run – 50 years – perspective; to consider what could be done in the short run in evidence-based policy development to generate possibly better outcomes in meeting these challenges; to review what we know and what we don’t know – the latter implying that we can say something about research priorities; and to review the tools that are available to support foresight thinking.

We developed six themes that seemed to work for us throughout the project:

  • people – living in cities
  • city economies
  • urban metabolism – energy and materials flows and the sustainability agenda
  • urban form – including the issues associated with density and connectivity
  • infrastructure – including transport
  • governance – devolution and mayors?

What have we achieved? I believe we have a good conceptual framework and a corresponding effective understanding of the scale of the challenges. It is clear that to meet these challenges in the long term, radical thinking is needed to support future policy and planning development. The project has a science provenance and this provides the analytical base for exploring alternative future scenarios. Forecasting for the long term is impossible, inventing knowledge-based future scenarios is not. In our work with cities – Newcastle and Milton Keynes provide striking examples – we have been met with enthusiasm and local initiatives have produced high-class explorations, complete with effective public engagement. There is a link to the Newcastle report on the GO-Science website; the Milton Keynes work is ongoing.

Direct links to the four project reports follow. The first is an overview; the second a brief review of what we know about the science of cities combined with an articulation of research priorities; the third is, in effect, a foresighting manual for cities who wish to embark on this journey; and the fourth is an experiment – work on a particular topic – graduate mobility – since ‘skills’ figures prominently in our future challenges list.

An overview of the evidence


Science of Cities:


Foresight for Cities:


Graduate Mobility:


Alan Wilson

May 2016

40: Competing models

My immediately preceding blog post, ‘Truth is what we agree about’, provides a framework for thinking about competing models in the social sciences. There are competing models in physics, but not in relation to most of the ‘core’ – which is ‘agreed’. Most, probably all, of the social sciences are not as mature and so if we have competition, it is not surprising. However, it seems to me that we can make some progress by recognising that our systems of interest are typically highly complex and it is very difficult to isolate ideal and simple systems of interest (as physicists do) to develop the theory – even the building bricks. Much of the interest rests in the complexity. So that means that we have to make approximations in our model building. We can then distinguish two categories of competing models: those that are developed through the ‘approximations’ being done differently; and those that are paradigmatically different. Bear in mind also that models are representations of theories and so the first class – different ways of approximating – may well have the same underlying theory; whereas the second will have different theoretical underpinnings in at least some respects.

I can illustrate these ideas from my own experience. Much of my work has been concerned with spatial interaction: flows across space – for example, journey to work, to shop, to school, to health services, telecoms’ flows of all kinds. Flows decrease with ‘distance’ – measured as some kind of generalised cost – and increase with the attractiveness of the destination. There was even an early study that showed that marriage partners were much more likely to find each other if they lived or worked ‘nearer’ to each other – something that might be different now in times of greater mobility. Not surprisingly, these flows were first modelled on a Newtonian gravity model analogy. The models didn’t quite work and my own contribution was to shift from a Newtonian analogy to a Boltzmann one – a statistical averaging procedure. In this case, there is a methodological shift, but as in physics, whatever there is in underlying theory is the same: the physics of particles is broadly the same in Newton or Boltzmann. The difference is because Newton can deal with small numbers of particles, Boltzmann with very large numbers – but answering different questions. The same applies in spatial interaction: it is the large number methodology that works.

These models are consistent with an interpretation that people behave according to how they perceive ‘distance’ and ‘attractiveness’. Economists then argue that people behave so as to maximise utility functions. In this case the two can be linked by making the economists’ utility functions those that appear in the spatial interaction model. This is easily done – provided that it is recognised that the average behaviour is such that it does not arise from the maximisation of a particular utility function. So the economists have to assume imperfect information and/or, a variety of utility functions. They do this in most instances by assuming a distribution of such functions which, perhaps not surprisingly, is closely related to an entropy function. The point of this story is that apparently competing models can be wholly reconciled even though in some cases the practitioners on one side or other firmly locate themselves in silos that proclaim the rightness of their methods.

The same kind of system can be represented in an agent-based model – an ABM. In this case, the model functions with individuals who then behave according to rules. At first sight, this may seem fundamentally different but in practice, these rules are probabilities that can be derived from the coarser grain models. Indeed, this points us in a direction that shows how quite a range of models can be integrated. At the root of all the models I am using as an illustration, are conditional probabilities – a probability that an individual will make a particular trip from an origin to a destination. These probabilities can then be manipulated in different ways at different scales.

An argument is beginning to emerge that most of the differences involve judgements about such things as scale – of spatial units, sectors or temporal units – or methodology. The obvious example of the latter is the divide between statisticians and mathematicians, particularly as demonstrated by econometrics and mathematical economics. But, recall, we all work with probabilities, implicitly or explicitly.

There is perhaps one more dimension that we need to characterise differences in the social sciences when we are trying to categorise possibly competing approaches. That is when the task in hand is to ‘solve’ a real-world problem, or to meet a challenge. This determines some key variables at the outset: work on housing would need housing in some way as a variable and the corresponding data. This in turn illustrates a key aspect of the social scientists approach: the choice of variables to include in a model. We know that our systems are complex and the elements – the variables in the model – are highly interdependent. Typically, we can only handle a fraction of them, and when these choices are made in different ways for different purposes, it appears that we have competing models.  Back to approximations again.

Much food for thought. The concluding conjecture is that most of the differences between apparently competing models come from either different ways of making approximations, or  through different methodological (rather than theoretical) approaches. Below the surface, there are degrees of commonality that we should train ourselves to look for; and we should be purposeful!

Alan Wilson

May 2016