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COMS W1002 Computing in Context: Digital
Humanities / Finance
Schelling’s Model of Segregation
Adapted from Frank McCown and Stanford’s Nifty Assignments repository! Many thanks to
Frank and Nifty!
Overview
Racial segregation has always been a pernicious social problem in the United States.
Although much effort has been extended to desegregate our schools, churches, and
neighborhoods, the US continues to remain segregated
(https://tcf.org/content/commentary/racial-segregation-is-still-a-problem/) by race and
economic lines. Why is segregation such a difficult problem to eradicate?
In 1971, the American economist Thomas Schelling
(https://en.wikipedia.org/wiki/Thomas_Schelling) created an agent-based model that might
help explain why segregation is so difficult to combat. His model of segregation showed that
even when individuals (or “agents”) didn’t mind being surrounded or living by agents of a
different race, they would still choose to segregate themselves from other agents over time!
Although the model is quite simple, it gives a fascinating look at how individuals might selfsegregate, even when they have no explicit desire to do so.
In this assignment, you will create a simulation of Schelling’s model. The user should be able
to set a number of parameters of the model and watch it go.
How the Model Works
Schelling’s model will now be explained with some minor changes. Suppose there are two
types of agents: X and O. The two types of agents might represent different races, ethnicity,
economic status, etc. Two populations of the two agent types are initially placed into random
locations of a neighborhood represented by a grid. After placing all the agents in the grid,
each cell is either occupied by an agent or is empty as shown below.
Now we must determine if each agent is satisfied with its current location. A satisfied agent
is one that is surrounded by at least a fractoin t of agents that are like itself. This threshold t
is one that will apply to all agents in the model, even though in reality everyone might have a
different threshold they are satisfied with. Note that the higher the threshold, the higher the
likelihood the agents will not be satisfied with their current location.
For example, if t = .3, agent X is satisfied if at least 30% of its neighbors are also X. If fewer
than 30% are X, then the agent is not satisfied, and it will want to change its location in the
grid. For the remainder of this explanation, let’s assume a threshold t of .3. This means every
agent is fine with being in the minority as long as there are at least 30% of similar agents in
adjacent cells.
The picture below shows a satisfied agent because 50% of X’s neighbors are also X (.5 > t).
In the pciture below, agent X is not satisfied because only 25% of its neighbors are X (.25 <
t). Notice that in this example empty cells are not counted when calculating similarity.
When an agent is not satisfied, it can be moved to any vacant location in the grid. Any
algorithm can be used to choose this new location. For example, a randomly selected cell
may be chosen, or the agent could move to the nearest available location.
In the image below, all dissatisfied agents have an asterisk next to them.
The next image shows the new configuration after all the dissatisfied agents have been
moved to unoccupied cells at random. Note that the new configuration may cause some
agents which were previously satisfied to become dissatisfied!
All dissatisfied agents must be moved in the same round. After the round is complete, a new
round begins, and dissatisfied agents are once again moved to new locations in the grid.
These rounds continue until all agents in the neighborhood are satisfied with their location.
Okay, so what do I have to do?
You will create code that simulates the Schelling model for two distinct populations.
Consider the following parameters for the Schelling model:
grid size: tuple of integers (n,m)
fraction of population 1: float between 0 and 1.
fraction of vacant sites in the grid: float betweein 0 and 1.
tolerance: float between 0 and 1
Write a function start(grid_size,pop,vacancy) that creates and returns a 2-D
numpy array of the appropriate size consisting of integers where each element of the array is
assigned as follows:
part of first demographic: 1
part of second demographic: -1
vacant: 0
The array your function returns should have the appropriate characteristics as specified by
the input parameters provided.
In [1]:
But wait, there’s more!
Write a second function next_round(arr,tolerance) that takes as input an n by m
array like the one you just created and returns a new 2-D array one step in the future where
all dissatisfied agents have been moved. Remember, since there may be more dissatisfied
agents than vacancies in the grid, you need to move them one at a time, this way each time
an agent is randomly assigned to a vacant site, a vacancy at a new location is created.
In [2]:
Last bit! (almost)
Finally write a function make_list(n) that returns a list of n numpy arrays where the first
array is created using start and the second using next_round on the first array and
the third using next_round on the second, and so on.
File ““, line 4
^
SyntaxError: unexpected EOF while parsing
File ““, line 4
^
SyntaxError: unexpected EOF while parsing
# write your function here:
def start(grid_size,pop,vacancy):
# write your function here:
def next_round(arr,tolerance):
In [3]:
Really last bit!
Try out your code. Create a list of length 100 using the parameter values:
size=(30,30)
pop=.5
vacant = .1
tolerance = .3
In class we will see how to visualize this evolution of the grid using matplotlib. Try it out! I’ve
included some code to help with this in the hw_files folder on Courseworks if you want to
get started early.
And finally, are there still dissatisfied agents in the grid? How could you write an alternative
function to make_list that makes a list exactly big enough so that in the final grid there
are no more dissatisfied agents. You don’t have to do this, but it wouldn’t be too hard.
In [ ]:
File ““, line 5
^
SyntaxError: unexpected EOF while parsing
# write your function here:
def make_list(n,grid_size,pop,vacancy,tolerance):
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