Dynamic Models of Segregation

Thomas C. Shelling

Reviewed by Hector AlfaroSeptember 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 matterThomas 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.

Median white

Most tolerant white

Least tolerant white

Both satisfied

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.