Racist Model

In trying to decide what courses to take next semester, I did some exploring on complex systems modeling. I created a lame model of two distinct classes of people (or things) who have a certain dislike for one another and prefer to be surrounded with a certain number of like individuals within an arbitrary radius. An distributed number of individuals of both categories are initially randomly placed on a grid. Each individual then scans the area of certain radius around them, figures the percentage of individuals like them relative to the total number of individuals within the scan radius, then makes a decision to move based on an arbitrary threshold. The individual them moves to some randomly chosen open space on the grid within a certain move radius.

I am assuming that the model represents to distinguishable groups who have some dislike for one another. Consider African Americans and white people, Hutus and Tutsis, poor people and rich people, Republicans and Democrats, etc. Upon seeing that an unacceptable percentage of the people around them are of the other category, they then can only move within a certain distance, assuming that resources are limited or moving too far will remove them from some desirable geographic proximity to work, resources, etc.

The model is quite simple, but the results are rather interesting. First we start with a 100 x 100 grid, yielding 10,000 possible occupable spaces. We assume 5000 total individuals, and a 50/50 distribution of each group. Placing them randomly, we obtain an initial grid that looks something like this:

Blue represents an unoccupied space, and yellow and red represent spaces occupied by one of the groups.

I started by assuming that individuals would not tolerate any less than 50 percent representation of their group within a radius of 10 squares. If they happen to occupy a square where the percentage of their own group compared to the total number of individuals within 10 squares is less than 50 percent, they will move to a randomly selected open square somewhere within a 20 square radius of their present position. I repeat this process 25 times. At the end, we see that even after 25 steps, people have already formed segregated clusters of individuals that are not necessarily contiguous. In fact, the entire grid is completely segregated after a mere 10 steps:

Adjusting the parameters a bit, we increase the percentage that people will tolerate to 80%. We can see that given a higher level of “racism” and a dense population, groups have a more difficult time clustering and are thus relegated to a life of constant movement and avoidance, with no resolve. I found this behavior to be true given a smaller population, and even a wider radius of movement. Given a higly level of intolerance for the other group, individuals have a difficult time forming clusters but there is little stability.

Assuming a high tolerance for the other group, leads to the opposite effect, leaving more individuals happy with their present position and less willing to move. This leads to high stability and less segregation, as one would expect.

The “sweet spot” for total segregation appeared to be approximately 50% tolerance. Individuals are happy as long as they make up 50% of the community, but this level of tolerance leads to the highest level of segregation overall. It is assumed that if an individual were to randomly move to an area occupied by the other group, they would immediately move as they felt overwhelmed by the presence of a majority that consisted of individuals of a group other than their own.

I also ran a model assuming that one group only made up for a quarter of the overall population and a moderate level of racism. The results were interesting. The minority group was forced to maintain a nomadic existence while the majority group hardly moved at all. When adjusting for extreme levels of racism, the majority group clusters almost immediately and the whole grid basically becomes a segregated urban area after approximately 25 steps. I call this the Jackson, Mississippi model.

My conclusions were simple and expected, but I was surprised that even this simple model was able to bear them out. High levels of racism lead to high levels of instability but low clustering due to the random nature of movement in the model. Low levels of racism lead to low clustering, but high stability of movement. Moderate levels of racism that we likely see within the US, lead to high levels of segregation and clustering with high levels of stability as people, once they have clustered are unlikely to leave what they consider to be a favorable situation. When creating a less than even distribution of groups, the minority group must maintain a nomadic state of existence, while the majority group remains fixed. Having a high level of racism under these conditions, creates a segregated society as seen above demonstrating the interplay between racist attitudes and imbalance in group representation.