During the 1970s, Thomas Schelling proposed a simple model of agents, played on a two-dimensional grid. The basic model consists of red agents and green agents. Each color has a threshold that specifies the number of similar neighbors that must be the same color for the agent to be ‘happy’. For example, if the threshold is 0.5 and a red agent has 3 neighbors are red and 2 are green, then the agent is happy. If the agent is unhappy, then the agent randomly chooses an open cell, and moves there during the next time.
We can simulate the model with Netlogo, an agent-based modeling program. First, we set the number of agents and set up the model.
Next, we set the happiness threshold and simulate the system.
We see the agents segregate. The surprising thing about this system is that relatively small biases in the agent’s preferences translate to much larger segregation levels on the macro-level. For example, the agents in the simulation above are happy if 30% of their neighbors are like them, but the segregation for the system as a whole turns out to be over 70%. A threshold of 50% results in 90% segregation!
Schelling showed how the rules at the micro-level can have surprising results at the macro-level. Segregation emerges from the simple rules that individual agents follow.
Bill Rankin, a professor at Yale, makes maps of segregation in US cities. Looking at the maps, we see significant segregation in many cities. The Schelling model is still a model: real people don’t randomly move to a new neighborhood, but instead decide on a home location based on many other factors. Still, Schelling’s model shows one surprising mechanism that leads to segregation.
See more maps by Eric Fischer, inspired by Bill Rankin’s maps here.