Playing Pool

Predicting outcomes on three different pool tables

Imagine a pool table. In the end I’m going to ask you to imagine three different ones, but for now we’ll go one by one.

The first pool table operates like the ones you’ve played on, assuming you’ve ever played pool. It’s flat and stable; you hit a white ball into the coloured balls and they roll off in different directions, bouncing off the “walls” of the table and off each other. One or two may go down into a pocket.

So assume that this table and the balls and pockets represent a “system” that you’re interested in. You can think of yourself here as a combination of analyst (e.g. academic) and influencer (policy-maker). To make the balls go where you want them, you need to know enough about how the system works — particularly, how the component parts of it interact — to be able to make sensible predictions of what how the system ends up after you propel the white ball into it at a certain angle and velocity.

This first table is a representation of what’s often referred to as a “complicated problem”: it has many moving parts, and hence there are many potential interactions to consider when analysing the impact of hitting the white ball into the coloured balls. But it has largely mechanical properties, which means in principle at least, things are largely predictable. (Which is, of course, why skilful pool players are skilful; they have both the ability to control the cue ball, and to understand the impact of sending it in a particular direction and at a particular speed, with given spin.)

Simplifying outrageously, this is the sort of problem (and the sort of system) that many engineers deal with professionally. As analyst, you can make meaningful—and in this case, deterministic—predictions of how the system will respond to an intervention (being hit with the white ball). As an influencer, trying to have a particular impact on the system to achieve an end result, you know what needs to be done; you simply need to have sufficient skill with the cue to achieve that result.

Now imagine a second table. Let’s mix things up a bit, making them different than how we normally think of a pool table. We’ll start with balls that vary with size. Inside the balls are magnets (or something similar) that either attract or repel balls around them. Now imagine the difficulty in accurately predicting from one given strike of the white ball how the coloured balls will respond and where they will settle? To make matters worse, what if the surface of the table is no longer smooth and flat, but undulates slowly providing one more source of motion for all the balls? And what if this undulation is also sensitive to where the balls move, so that as weight accrues in any given spot, the table sags slightly and rises elsewhere?

If you want to relate this kind of table to academic disciplines, it might seem like you’re comparing Newtonian physics (the first table) to relativity (the second), since those of us who know next to nothing about physics might remember those pictures of flat grids that become bumpy when astronomically large bodies are in the vicinity.

But in fact, this second table is more like the kind of system that biologists and ecologists study. The balls now interact more like simple living creatures, and the system they operate in is not “exogenous” but interdependent. What the balls do determines how the table surface operates, which feeds back on the balls’ movement, and so on.

What table two captures are the features of a complex (but not yet adaptive) system, or equivalently, a self-organising system. It will potentially display features of such systems, including: possible feedback loops between the movement of the table surface and the movements of the balls; emergent properties, patterns that cannot be predicted from first principles but that emerge from the interplay of the various elements of the system; thresholds, whereby a gradual and incremental adjustment of the system suddenly turns into a major transformation; and, fundamentally, unpredictability, in that making a precise and accurate prediction of the final result of knocking a white ball into the (initially stabilised) set of coloured balls is not possible.

(One way to make this system “adaptive” would be to give the balls some consciousness and capacity for self-propulsion, along with capacity for simple learning.)

A third table looks for our purposes like the first one, flat and stable. The key difference here is that now the coloured balls are conscious, self-aware and fully able to move themselves. As they see you move towards them, holding the cue and the white ball, they start anticipating and calculating. If you’re trying to predict the outcomes of your strike, you cannot do it mechanically as you might with the first table; you have to figure out what the balls want, and what they think you’re about to do.

If the coloured balls want to be struck by the white ball — let’s label this the “subsidy case” — they’ll line up as best they can to receive the strike you’re about to send their way. They may struggle with each other for the best position, and they may be making judgements about what direction you’re most likely to send the white ball, with their different guesses resulting in a distribution of balls around the table. If the balls don’t want to be struck by the white ball — let’s label this the “tax case” — the balls will attempt to move out of the way, or to hide behind other balls in order not to be directly hit. Who gets to be most exposed is hard to say without knowing how the balls are likely to move in anticipation of, and then as a result of, your strike of the white ball.

Things get yet more complex if the balls are of different sizes, can move at different speeds, and possibly even can combine, with two balls merging into a single one to become bigger. (This merging might be by mutual consent, or a larger ball may “swallow up” a smaller one.) Every ball’s mobility may range from instantaneous to delayed (representing “costs of adjustment”). If the table surface has some of the properties of the second table, yet more unpredictability is created.

This third table shows the difficulties facing economics and the various social sciences, grappling with human behaviour, where humans are able to strategise and to forecast.

The second and third tables have one thing in common; they are representations of self-organising systems, as opposed to fundamentally mechanical ones. The key difference between them is the difference in autonomy of action of the agents. Scientists used to complexity theory and the analysis of complex systems do not often appreciate the extra dimensions and degrees of difficulty that is added agents with detailed cognitive capabilities, able to anticipate, to strategise, and to consciously interact. Economists, in turn, are often oblivious to the insights that can emerge from complex systems analysis, involving network interactions, feedback loops, thresholds and path dependence.

At this point it is worth noting that the point here is not to assign particular disciplines to particular tables. As one example, lots of problems in physics look like “complicated problems” writ large, essentially very elaborate versions of the first table; but as soon as (for example) chaotic dynamics are involved, there can be feedback loops and sensitive dependence on initial conditions, making predictions of the impacts of a shock hard to make, and we’re more in the world of table 2. This is the case even without “conscious agents”; the balls can simply be particles, and still operate and interact in ways that can be labelled “complex.” Meanwhile, many natural scientists using experimental methods do not involve themselves in complex systems modelling, but in tackling specific problems in controlled settings. But the move from laboratory to field will involve more complicating factors and reduce the degree of predictability of the impacts of particular actions.

In a follow-up post to this, I will discuss how modelling in economics actually moves between the various scenarios and strategies described above. There are times (i.e. partial equilibrium, CGE, micro-simulation modelling) where economics operates as if analysing a “complicated” rather than a “complex” problem. In at least some major areas of macroeconomics, the emphasis is on table 3, with highly reasoning agents making subtle decisions, but the “landscape” flattened out for convenience. In some areas (such as with the use of agent-based modelling in a number of fields, and the analsis of networks), the landscape is made more complex, but the decision-making is often somewhat simplified.

Note that I’ve said nothing about the standard aspects commonly regarded as being key to economics, like scarcity, markets, pricing, or equilibrium. This is about the nature of systems, and strategies to analyse them; but those features of economics will feature. More to come.