Butterfly Economics

Scientific research can often seem obscure and even pointless to outsiders. This is not so much due to the intellectual difficulty involved in understanding such activity, for it is widely accepted that this will inevitably be the case. It is rather that many of the topics which are examined seem to be almost designed to incur the scorn and wrath of the lay person. Before sitting down this morning to write these very words, for example, my eye fell on a report in a serious British newspaper. An American psychologist had been visiting the country to carry out a study of rams in the English Lake District. His research was complete. 'Ten per cent of all rams', he proclaimed solemnly, 'are homosexual.' Readers no doubt took consolation from the fact that this finding was obtained at the expense of the American taxpayer and not themselves.

Nor are such examples confined exclusively to the sciences. I have long admired Emily Brontë's novel Wuthering Heights. The opening chapters, in which Lockwood first encounters the ill-tempered Heathcliff and his assorted household, seem to me to be one of the finest pieces of comedy in the whole corpus of English literature. Realizing that not everyone shares this opinion, and in order to improve my understanding, I recently opened a modern work of literary criticism on Brontë's masterpiece. It was completely impenetrable. Many of the individual words were quite new to me, and whole sentences, indeed whole pages, appeared to lack any coherent meaning. I sought solace in the preface, where I learned that the density of the text was deliberate. 'The analysis of literature and culture', declared the author, 'is a task no less difficult, and no less demanding of a specialized language, than the study of sub-atomic particles.' I hastened immediately to a textbook on orthodox economic theory in an effort to restore my sanity.

In the mid-1980s, entomologists carried out a series of experiments with ants which, at first sight, appear equally esoteric. Two identical food sources were placed at an equal distance from a nest of ants, and were constantly replenished so that they always remained identical. In other words, every time an ant removed a grain from one of the sources, another was added to the pile. And the two piles were exactly the same distance from the nest. How would the ant colony divide itself between the two sources of food?

The experiments appear at first sight to be of little or no interest to anyone outside the world of biology. Even among biologists, ant behaviour is a pretty specialized topic. Yet the results of the experiments turned out to be fiendishly difficult to explain, and a proper understanding of them has widespread implications for behaviour far beyond that of the humble colony of ants, illuminating complex problems in human societies and economies, worlds living at the edge of chaos.

In the experiments there was, by design, absolutely no reason for the ants to prefer one of the sources to the other, so we might start by expecting that the ants would split evenly between them. A little reflection would lead us to think that, while this might very well be an outcome, any division would be possible. Suppose each ant emerges from the nest and visits one of the food piles at random. It is successful in obtaining food to bring back to the nest, and so on its next outing it has an incentive to revisit the site of its previous success. The pile is always replenished, so it will always obtain food from this site.

If this theory were correct, the distribution of the ants between the two piles could be analysed in just the same way as an experiment in tossing a fair coin and observing the split between heads and tails. The first time an ant comes out of the nest to look for food, its destination is given by the equivalent of a toss of a coin, and the design of the experiment gives it a strong incentive to keep revisiting its original choice. So, in theory, we could expect the colony to split in any proportion between the two piles. There would be a strong expectation that the split would be close to 50:50, because this is how a large number of tosses of a fair coin usually divide, but any distribution would be possible theoretically.

But the biologists had developed a more sophisticated version of this theory, based upon a known fact about ant behaviour. Once an ant has successfully found food – which it would, thanks to the design of the experiment – it will usually revisit the same site the next time and so on into the future. But when an ant which has found food returns to the nest, it physically stimulates another ant to follow it to the food source by chemical secretion. Some kinds of ant go even further and recruit whole groups to follow them, by laying a trail of secretions. So an ant emerging from the nest for the first time would be influenced in its decision by the trails of the ants it encounters on its journey.

In economic terms this means the behaviour of agents is influenced directly by the behaviour of others. In this example, the interaction between ants takes place at what we term the local level. No ant can ever observe the overall division of the colony between the two food sources, and so this cannot influence the choice of destination. But each ant is open to recruitment by the limited number of other ants which pass its immediate neighbourhood.

The situation is one in which, to introduce a technical term, positive feedback predominates. An ant goes out, finds food and encourages others to follow it back to its source. In this artificial experiment, the self-reinforcing mechanism is very strong, for each pile of food is constantly replenished. So the ants which are recruited find food with complete certainty, and return to recruit others. The more ants that visit any particular site, the greater the chance that yet more of them will visit it in future.

In other words, the consequences of actions by individual ants are enhanced by their influence on the behaviour of others, hence the phrase 'positive feedback'. The term is purely descriptive, and does not carry any overtones of approval or desirability. It applies to any system, such as that of our ant colony, in which the initial impact of actions or events tends to be magnified over time. Its opposite, 'negative feedback', is used to describe systems in which initial effects are dampened and smoothed away. As we shall see later in the book, almost the whole of conventional economic theory can be thought of as describing systems of negative feedback. But in the real world of the economy and society, positive feedback generally rules.

The crucial trail-laying quality of ants led to more subtle theoretical expectations of the proportions which visit each of the sites. The signals left by the creatures mean that the random choices of the first few ants to leave the nest could exercise a decisive influence on the behaviour of the whole colony. If the choice of each ant were purely random each time it left the nest, because of the very large number of ants, there is a probability of almost one – in other words, almost complete certainty – that the proportions will settle down very close to a 50:50 split. But suppose half a dozen ants went out, foraged and returned with food. These then left trails for the next group to follow, and so on. The random choices of a very small number of ants may not divide evenly between the two sites. Our fair coin tossed enough times will lead to an even split, but it is much less likely that a small number of tosses will give an equal number of heads and tails. (So with six tosses, the odds are against an even split.) The trails left by the first returning ants have a potential influence on the decisions of those emerging for the first time and, precisely because the random choice of a small number can influence the subsequent decisions of the whole group, the eventual proportions visiting the two sites may differ quite markedly from a 50:50 split.

A key feature of the biologists' theory was that the proportions in any given experiment would settle down to the pattern determined in the early stages of the food foraging process. There would be some random fluctuations around this for a short time, but the eventual outcome would be stable.

This theoretical framework is an important one. It predicts that, once a few more ants, for whatever reason, start to visit one of the sites rather than the other there will be a strong tendency for that site to become the favoured destination for more and more ants. Some of the early recruits to the other site might stay loyal, as it were, but we expect an unbalanced outcome to arise. And once this has arisen, the proportions will then remain fixed. Or, in the jargon, the system will stay locked in that particular solution.

In fact, what was seen to take place was a completely different outcome. Even when the experiment had been running for a long time, in ant terms, the proportion of the total ant population visiting any one site continued to fluctuate in an apparently random fashion. The proportions averaged out at one half, but this precise outcome was hardly ever observed, and the proportion was subject to constant change. Once a large majority of ants had visited one of the sites, the outcome tended to stay reasonably stable and exhibited small variations around that proportion for some considerable time. But the majority was always eroded and the ants switched to visiting the other site. Sometimes these shifts were not only very large – from, say, an 80:20 division at one pile to the reverse outcome of 20:80 – but also rapid.

The constant changes, often small but occasionally rapid and large, were entirely unexpected according to the biologists' theory. This conflict between the actual and theoretical outcomes led the experiment to be repeated in different ways. The exact recruitment mechanism which is used varies between species of ants, so different species were tried. The outcome was the same. Doubts then arose as to whether there was some subtle change in the food source which was the cause of the fluctuations, such as the piles not being replenished in an absolutely symmetrical way. So the experiment was tried with just one food source and two identical bridges, precisely the same distance away from the nest, and the proportion going over each of the bridges was observed. Again, the same pattern of behaviour was monitored.

The economist Alan Kirman, then based at the European University Institute in Florence, turned his mind to the problem. By definition, in circumstances such as the ant experiment, the idea that the system as a whole can be understood by the behaviour of a single, representative agent is a complete non-starter. For the overall outcome arises as a result of the interactions between individuals, and the changes in behaviour which they induce in one another. It is, quite literally, impossible to infer the behaviour of the group as a whole from an account of one of its individuals taken in isolation. Kirman has in fact been one of the world leaders in pioneering the development of interacting agent models in economics. But, to paraphrase the words of a popular song, what's ants got to do with it?

Kirman set up a theoretical model which gives an excellent account of the observed behaviour of the seemingly perverse ants. And it can also be stated quite simply. An ant coming out of the nest follows one of three possibilities: it visits the food pile it previously visited; it is persuaded by a returning ant to visit the other source; or, of its own volition, it decides to try the other pile itself. And this is almost all that is required to explain the complex and seemingly baffling phenomenon of the fluctuations in the proportions of ants visiting the respective piles.

I use these simple basic principles throughout the book to explain many social and economic problems. At any point in time an individual agent – whether an ant, a person, a company, or whatever – can follow one of three choices: to stay with its previous decision; to select an alternative of its own accord; or to be persuaded to switch to the alternative by the actions of others.

In such circumstances, no single outcome of an experiment will ever be identical to another, for the choices of individual ants are not fixed, but can be altered each time with given probabilities. This random element to the whole process means that each solution of Kirman's theoretical model, and the outcome of each practical experiment, is unique. But a typical simulation, or outcome, is plotted in Figure 1.1, which shows the proportion of ants visiting one of the food sources at any one time. The chart illustrates the typical patterns of constant small changes and occasional large shifts which are observed.

When its properties are examined more deeply, such simulated data exhibits characteristics which are entirely typical of situations in which the behaviour of any individual agent is influenced directly by the behaviour of others. In the short term, movements in the series are quite unpredictable. Even with completely accurate knowledge of the equations which describe the behaviour of the individual ants, it is not possible to predict with any degree of accuracy the direction of change of the proportion of ants which visit either of the food sources.

Indeed, in this particular system, non-predictability appears in its most extreme form. We can work out the probability of the very next ant about to collect food visiting a particular site, but we can never do any better than this. In other words, all we can ever say is that the next ant has a certain probability of visiting one site, and a certain probability of visiting the other. In the same way, with the toss of a fair coin, we can never do better than say that there is a probability that a head will appear, and one that a tail will appear. Any 'prediction' can be no better than a pure guess.

One way of looking at this is to see if we can draw any conclusions about the way the system will move from any given split of the colony between the sites. Look, for example, at what happens when the split is 55:45. Reading across from the point marked '55' on the left-hand axis, we can see a number of occasions on which this split occurred in this particular simulation of the model. The first time, the proportion of ants visiting site A then rose rapidly to over 60 per cent. The next time the 55:45 split happened, the proportion visiting this site subsequently fell by a small amount. Moving across to the peak at the far right of the chart, the proportion visiting site A rose by a small amount for a short time. But then, as it fell back through 55 it continued to fall quite sharply. In other words, the proportions we observe at any point in time give us no information about what will happen to the proportions in the immediate future.

But the system does have a very distinct pattern in the longer term. Figure 1.2 sets out for the ants model how much time the system spends at any given distribution of the ant colony between the food sources, whenever the experiment is run for a reasonable length of time. The precise shape of this distribution will vary according to the persuasiveness with which ants can convert others, and on the propensity of individuals to change their own minds.

Figure 1.2 shows the relative amounts of time which a proportion of the ant population spends at each site, when the propensity to switch behaviour is low. The bottom axis of the chart shows the percentage visiting site A, so when the value is close to zero, by implication almost 100 per cent of the ants are visiting site B, and vice versa. The left-hand axis of the chart shows the amount of time a particular proportion of the ants is observed visiting site A. The U-shape of the curve tells us that the ants spend much more time at extremes of the split between the two sites than they do at reasonably equal distributions. In other words, the colony spends much of its time in situations where either almost every ant visits site A and very few site B, or almost every ant visits site B and very few site A. In contrast, the occasions on which a split close to 50:50 is observed are relatively few and far between.

Figure 1.3 sets out the same kind of plot as Figure 1.2, but one feature has changed. In this case the propensities of the ants to switch behaviour are high.

Comparing Figures 1.2 and 1.3, a potential paradox appears to arise. In the first figure, ants have only a low propensity to change their behaviour and visit a different site, and in the second they are much more likely to switch. Yet in Figure 1.2, much more time is spent with most of the ants visiting either site A or site B than is the case in Figure 1.3, where the ants spend much more time split closer to 50:50 between the sites.

A first impression might suggest that a high likelihood of changing behaviour would drive the system to the extremes, rather than a low one. But in fact, if ants often change the site they visit, the chance of most of them ending up at one or other of the sites is very low, for the very reason that lots of them change their mind each period. In contrast, if changes are only occasional, once the proportion has drifted to an extreme split, it will take a very long time to change. It may take a long time to ever get into such a situation, but once there, the proportion will take even longer to be altered significantly.

The behaviour of individual ants, their direct influence on the behaviour of others, and the consequences of this interaction between individuals for the colony as a whole can be applied as a very general description, or model, of a wide range of economic and social phenomena. For the principles which govern the behaviour of ants also apply to humans. Much of the time, individuals face a limited number of choices in any particular situation. If there are more than two choices, this is just an extension of the fundamental ideas which can be readily incorporated. There are other extensions, complications and simplifications which we will come across in the course of this book as we consider different circumstances and different problems. But the essential principles of the ants model remain. In most circumstances, a person can either stay with the pattern of behaviour he or she previously followed (an ant visiting its previous site), can decide to switch of his or her own volition, or can be influenced into switching by the observed behaviour of others.

The consequences of this description of individual behaviour have, as we shall see, deep implications for the outcome for the human colony as a whole. Many important social and economic issues share the key characteristics of ant behaviour, of unpredictability in the short run merging imperceptibly over time into a form of regularity, of complex systems living at the edge of chaos.

The basic concepts involved in the ants model can be observed in many apparently disparate circumstances in the real world. My first two examples, from the restaurant trade and the film industry, may seem rather trivial, even though these areas of economic activity are becoming increasingly significant. But they do illustrate important principles which have far-reaching consequences not just for economics but for the other social sciences. Short-term prediction and control of the overall outcome is either very difficult or impossible, although there may be regularities that appear over time in terms of the proportions of time which the system spends at different outcomes. Even periods of apparent stability are characterized by persistent small changes, punctuated from time to time by large and rapid movements.

Several restaurants are often located very close together in a street. There may be a clear differentiation of their products – such as the nature of the cuisine, price level and so on – or there may be two or three offering very similar food at comparable prices. The custom of these restaurants tends to fluctuate in a seemingly inexplicable way. One month, one will be bursting at the seams, while another will be half empty, only for quite the opposite to be observed the following month. Of course, these particular kinds of food source do differ from those of our ants, in that the proprietors, far from trying to ensure that their sites are identical, will be constantly thinking about ways in which they can improve them and steal a march on their rivals. Yet the fluctuations in custom will often seem unconnected to their marketing efforts. For they are being driven by the same kind of dynamics which determines the outcome of the ants model. Potential customers hear a particular restaurant being praised or damned by their friends and neighbours, and may allow this to influence their choice when they next eat out. In other words, there is a probability that deciding which food source to visit will be influenced by meeting someone else who has visited one of them recently. Further, an individual restaurant-goer, no matter how loyal he or she has been to a particular outlet, may, like our ants, experiment with a different one through his or her own volition.

A substantial degree of uncertainty is therefore inherent in the process of judging, say, how many people will visit a restaurant in the coming week. This creates the same qualitative difficulties for the policy-maker – in this case the restaurant owner – as it does at more elevated levels in the economy. Short-term prediction is hard. And it is difficult to judge the immediate impact of a marketing ploy, for, in the absence of such an initiative, the underlying dynamics of the situation might have been about to deliver a sharp upturn or downturn in the level of bookings. So there is a distinct risk that the wrong conclusions may be drawn about the effect of such policies.

When this chapter was first being written, the film Anaconda emerged as an enormous and completely unexpected box office hit in the United States. Described by one film critic as 'a movie about huge snakes devouring a B-grade cast', it nevertheless took $43 million in cinema receipts in the first three weeks of its release. This is by no means untypical in the film industry. Indeed, during the process of revising the chapter, the low-budget British film The Full Monty, featuring as its key characters redundant steel workers from a depressed, industrial part of Britain, also became a major American hit. Tremendous successes emerge from nowhere, and films made with huge budgets, replete with glittering names, can flop. Recent examples of major commercial failures include Hudson Hawk and The Postman, despite massive funding and leading stars.

The American economists Arthur De Vany and W. David Wallis published an article in the Economic Journal in November 1996 using a more complicated version of the ants model to account for success or failure in the American cinema. They tested the model by comparing its properties with those of the weekly data provided by Variety's Top 50 films in America. The principle of positive feedback operated with devastating effect. During the nine months which they analysed, the top four films took over 20 per cent of all box office receipts, and the bottom four less than one hundredth of 1 per cent. The highest-grossing film had revenue of $49 million, whereas the film exactly in the middle (defined as the position where the number taking more than its revenue is the same as the number taking less) took only $300,000. And the worst performer had a total revenue of under $5,000, representing a ratio of 10,000:1 in favour of the most successful over the least.

The tremendous uncertainty surrounding the success or failure of a new release is reflected in the very brief tenure of studio heads. De Vany and Wallis attempted to contact nearly 400 film executives, but one third of their letters were simply returned with no forwarding address. A disaster with a major film can even bankrupt a studio, as happened, for example, with United Artists and Heaven's Gate.

The key to the whole process is interacting agents. Movie-goers make or break films by telling their friends, an activity which is reinforced by the role of reviewers. The ants leave a trail for others to follow, but here the word is spread through conversation and reading newspapers. In the orthodox economic theory of consumer behaviour, the tastes and preferences of individuals are given, and the individual then acts so as to maximize his or her 'utility' with respect to these tastes. In the film industry, when a new release is issued, consumers do not know in advance whether they will like it or loathe it. In conventional theory, the actions of individuals are held to reveal their true preferences, but here they have to discover what their preferences really are, which is why the opinions of others influence individual behaviour to such a high degree.