To illustrate these points, let’s look at an important social problem, that of racial segrega-tion. Racial segregation is a persistent phenomenon in many cities in many countries. In the US, for example, while more than one-half of Black Americans now live in middle- or upper-income households, segregation in housing has persisted in major cities. The natural explanation for this phenomena would be that individuals are racist and prefer to avoid living with people of another race. Thus, segregation is no more than a macro- phenomenon that reflects, in a consistent way, people’s individual sentiments. But Tom Schelling, the 2005 Nobel Prize winner in economics whose influence permeates much of what we now call complex economics, showed, once again, that the relationship between micro- and macro-behaviour is not so simple. He argued that the degree of segregation which we observe is far from reflecting individual views. At the end of the 1960s, he introduced a model of segregation (a good summary of the variants of his model is given in Schelling (1978)), which showed essentially that even if people have only a very mild preference for living with neighbours of their own colour, as they move to satisfy their preferences, complete segregation can occur.
To see what is at work here, it is worth looking in some detail at the model that Schelling introduced. It can be explained simply and intuitively, and this is one of the features of Schelling’s contributions that makes them so appealing and which generated such surprise. A fuller account of this surprising relationship between micro-features and aggregate phenomena in the segregation model or, to use Schelling’s original phrase, the relationship between ‘micromotives and macrobehavior’, can be found in the paper by Pancs and Vriend (2007).
The basic idea is this: take a large chess board and place a certain number of dark and light counters on the board, leaving some free spaces. The basic assumption is that each counter prefers to be on a square where, at most, four of his eight neighbours are of a different colour than his own. As long as fewer than half of their neighbours are of a dif-ferent colour from their own, the individual is happy, or has high utility, as mainstream economists might say. However, if the number of different-coloured neighbours passes this threshold, then the individual becomes unhappy.
At each step an individual is drawn at random, and if they are unhappy, that is, have low utility, they move to the nearest unoccupied space where their utility will be higher.
An example of what happens over ‘time’ (i.e. over the course of many individual steps) is illustrated in Figure 7.1, which shows segregation developing rapidly.
Indeed, Schelling showed that the result would, in general, be complete segregation.
This is, in some sense, rather surprising in that the segregated outcome does not reflect the relative tolerance of the individuals. However, as Vinkovic and Kirman (2006) point out, a physicist would not be so surprised: oil and water do not naturally tend to mix, and such a mixture rapidly sorts out into two separate layers. They develop a simple physical analogy to the Schelling puzzle, which shows clearly what is going on. It is sometimes useful for economists to cast a glance at other disciplines!
The results above resulted from just one of the many possible ‘utility functions’ that we might use to determine how individuals behave in this environment. Perhaps more surprising is what happens when all individuals instead prefer perfectly balanced neigh-bourhoods, such that their utility is only high when exactly half of their neighbours share their own colour. The result of conducting the same experiment with individuals of this type is illustrated in the lower panels of Figure 7.2.
The result can be compared to the outcome of the original utility function, shown in the upper panels. The situation in the lower panels looks remarkably similar: almost total segregation. Nevertheless, at the micro level, the situations could not be more different.
With the original utility function, there is almost no movement after a certain point in
Figure 7.1 Segregation emerging from ‘non-discriminatory’ preferences
Source: Pancs and Vriend (2007)
Figure 7.2 Segregation with differ Source: Pancs and Vriend (2007)
time. The great majority of the individuals are happy and have no incentive to move. Yet with the new utility function, the individuals in the population are constantly moving.
From a distance the situation looks like a static one comparable to the original experi-ment, but in the second experiexperi-ment, almost nobody is happy and people are constantly looking for a better square. The reason for this is obvious: an exact balance of neigh-bours between the two colours is easily disturbed. As soon as one person moves, the fine balance is destroyed, thereby creating an incentive to move for all former neighbours.
Thus, the similarity between the two models is illusory, because macro similarity is not equivalent to micro similarity.
Many of the key lessons of Complexity Economics can be learnt from analysing this very simple model and its variations. We see that systems of interacting particles or
‘agents’ can have a tendency to self-organize, the results of which may be very different from what one might have anticipated and may not be socially satisfactory from the aggregate point of view.