1. Dynamic Models of Segregation
Thomas C. Shelling
Reviewed by Hector Alfaro
September 30, 2008

2. SUMMARY

3. Goal
Study segregation that results from discriminatory individual behavior.
Results useful for any twofold analysis:
Black and white
Male and female
Students and faculty
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

4. Motivation Segregation may be organized or unorganized May occur from
Religion
Language of communication
Color
Correlations
Church  Neighborhoods
Difficult to find integrated neighborhoods.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

5. Methods Two experiments Spatial Proximity Model
Bounded-Neighborhood Model
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

6. Spatial Proximity Model
Two types of individuals: stars and zeros
Dissatisfied individuals denoted by dot over individual.
Neighborhood definitions vary, relative to individuals.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

7. Spatial Proximity Model
Results
Equilibrium reached.
Random sequences yield
5 groupings with 14 members
7-8 groupings with 9-10 members
Order does not matter
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

8. Spatial Proximity Model
Two-dimensional model
Order can vary
Top left to bottom right
Center outward
Results
Segregation occurs regardless of order
Extreme ratios lead to minority forming large clusters, disrupting majority.
Increasing neighborhood size  increases segregation
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

9. Spatial Proximity Model
Integration exhibits phenomena:
Requires more complex patterns
Minority is rationed
Dead space forms its own clusters
Left – upper & lower limits
Right – will settle
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

10. Bounded-Neighborhood Model
Neighborhoods are defined. An individual is either in or out.
Information is perfect, but intentions not known.
Most tolerant white
Both satisfied
Median white
Least tolerant white
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

11. Bounded-Neighborhood Model
Results
Only one stable equilibrium: all white or all black.
Can vary tolerance slope for more intersection
Can limit population to find more points of equilibrium.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

12. Bounded-Neighborhood Model
Results
Can study integration by interpreting results differently.
Producing equilibriums requires large perturbations (like changing population size) or concerted actions.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

13. Contributions
Can make predictions on changes to neighborhoods based on models.
Tipping phenomenon: new minority entering an established majority cause earlier residents to evacuate.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

14. ANALYSIS

15. Strengths
Broad study, results apply to any two groups one wishes to compare.
Models are easy to change and results may be easily reproduced: changing number of neighbors, satisfied/dissatisfied conditions, etc.
Results may be interpreted differently: segregation v. integration.

16. Strengths
Tolerance in bounded-neighborhood model is a relative measure – indicative of reality.
Results may be manipulated to achieve equilibrium.

17. Weaknesses Just a model, not based on studies of the population.
Perhaps too broad, makes it inapplicable to real life.
Spatial proximity versus bounded neighbor model not really comparing apples to apples: comparing interactions in multiple neighborhoods versus one neighborhood.

18. Weaknesses
Claim that we can study integration by reinterpreting the results: methods chosen particularly to study segregation. Different methods need be employed to study integration.
Ways to reach equilibrium are not practical: large perturbations nor concerted actions happen often in reality.

19. Weaknesses Schelling admits no allowance for:
Speculative behavior
Time lags
Organized action
Misperception
Information is not always perfect
Tipping studies outdated.
Models cannot handle complex interactions.
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1,

20. Comparison to CAS Cellular Automata Conway’s Game of Life Overall
Directly related to the linear distribution model.
Conway’s Game of Life
Much like the spatial proximity model.
Overall
Set of simple rules defined that result in complex behavior
Emergent patterns occur.
Stephen Wolfram (1983). Cellular Automata. Los Alamos Science, 9, 2-21.
Martin Gardner (1970). Mathematical Games. The fantastic combinations of John Conway's new solitaire game "life." Scientific American, 223, , October 1970.

21. Comparison to CAS Prisoner’s Dilemma
Indirect correlation: cooperation and defection may be compared to tolerance of an individual.
Further studies could superimpose the payoff matrix into Schelling’s segregation models.
Robert Axelrod (1980). Effective choice in the Prisoner's Dilemma. Journal of Conflict Resolution, 24:1, 3-25.

22. Comparison to CAS Schelling’s system exhibits:
Emergence
Multiple agents
Simple agents
Iteration
No adaptation, variation.
Research looking for unorganized individual behavior into collective results.