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.
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