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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.

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Dynamic Models of Segregation

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  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, 143-186.

  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, 143-186.

  5. Methods • Two experiments • Spatial Proximity Model • Bounded-Neighborhood Model Thomas Schelling (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143-186.

  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, 143-186.

  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, 143-186.

  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, 143-186.

  9. 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.

  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, 143-186.

  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, 143-186.

  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, 143-186.

  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, 143-186.

  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, 143-186.

  20. 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.

  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.

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