Transcript Dynamic Models of Segregation

Dynamic Models of Segregation
Thomas C. Shelling
Reviewed by Hector Alfaro
September 30, 2008
SUMMARY
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, 143-186.
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, 143-186.
Methods
• Two experiments
– Spatial Proximity Model
– Bounded-Neighborhood Model
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143-186.
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, 143-186.
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, 143-186.
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, 143-186.
Spatial Proximity Model
• Integration exhibits phenomena:
– Requires more complex patterns
– Minority is rationed
– Dead space forms its own clusters
Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143-186.
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, 143-186.
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, 143-186.
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, 143-186.
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, 143-186.
ANALYSIS
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.
Strengths
• Tolerance in bounded-neighborhood model is
a relative measure – indicative of reality.
• Results may be manipulated to achieve
equilibrium.
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.
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.
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, 143-186.
Comparison to CAS
• Cellular Automata
– 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, 120-123, October 1970.
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.
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.