Applications of Cellular Automata in the Social Sciences

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Applications of Cellular Automata in the Social
Sciences

• Eileen Kraemer
• Fres1010
• University of Georgia

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Social Automata

• Agent-based models
• In contrast to global descriptive model, the
  focus is on local interactions by agents
• Assumptions
• Agents are autonomous bottom-up control of
  system
• Agents are interdependent
• Agents follow simple rules
• Agents adapt, but are not optimal

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Schelling Segregation Model (SSM)

• first developed by Thomas C. Schelling
  (Micromotives and Macrobehavior, W. W. Norton and
  Co., 1978, pp. 147-155).
• one of the first constructive models of a
  dynamical system capable of self-organization.

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Schellings Segregation Model

• placed pennies and dimes on a chess board
• moved them around according to various rules.
• interpreted board as a city, each square
  representing a house or a lot.
• interpreted pennies and dimes as agents
  representing any two groups in society
• (two races, two genders, smokers and
  non-smokers, etc.
• neighborhood of an agent consisted of the squares
  adjacent to agents location. (8 for inside, 3 or
  5 for edge)

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SSM

• Rules could be specified that determined whether
  a particular agent was happy in its current
  location.
• If it was unhappy, it would try to move to
  another location on the board, or possibly just
  exit the board entirely.

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SSM

• found that the board quickly became strongly
  segregated if the agents' "happiness rules" were
  specified so that segregation was heavily
  favored.
• also found that initially integrated boards
  tipped into full segregation even if the agents'
  happiness rules expressed only a mild preference
  for having neighbors of their own type.

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SSM

• Mild preference to be close to others similar to
  oneself leads to dramatic segregation
• Conflict between local preferences and global
  solution
• Nobody may want a segregated community, but it
  occurs anyway

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Schellings Segregation Modelcontinued

• Model
• 2-D lattice with Moore neighborhoods
• Two types of individuals
• If lt 37 of neighbors are of an agents type,
  then the agent moves to a location where at least
  37 of its neighbors are of its type

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Schellings Segregation Model
A perfectly integrated, but improbable, community
A random starting commmunity with some discontent.
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Schellings Segregation Model
A community after several generations of
discontented people moving.
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Sugarscape (Epstein Axtell)

• Explain social and economic behaviors at large
  scale through individual behaviors (bottom-up
  economics)
• Agents
• Vision high is good
• Metabolism low is good
• Movement move to cell within vision with
  greatest sugar
• GR grow sugar back with rate R
• Replacement Replace dead agent with random new
  agent

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Wealth Distribution

• Uniform random assignments of vision and
  metabolism still results in unequal, pyramidal
  distribution of wealth
• Start simulation with number of agents at the
  carrying capacity
• Random life spans within a range, and death from
  starvation
• Replace dead agent with new agent with random new
  agent

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Wealth Distribution
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Wealth Distribution Lorenz Curves
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Wealth Distribution Gini Ratio
Y cumulated proportion of wealth X cumulated
proportion of population G 0 everybody has
same wealth G1 All is owned by one individual
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Why an Unequal Distribution of Wealth?

• Epstein Axtell
• Agents having wealth above the mean frequently
  have both high vision and low metabolism. In
  order to become one of the very wealthiest agents
  one must also be born high on the sugarscape and
  live a long life.

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Why an Unequal Distribution of Wealth?

• This is part of the story, but not completely
  satisfying if vision and metabolism variables are
  uniformly or normally distributed
• Multiplicative effect of variables?

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Binomial distribution

• Binomial function describes the probability of
  obtaining x occurrences of event A when each of N
  events is independentof the others, and the
  probability of event A on any trial is P

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Poisson Distribution

• Poisson distribution approximates Binomial if P
  is small and N is large (e.g. accidents, prairie
  dogs, customers). The probability of obtaining x
  occurrences of A when the average number of
  occurrences is l is

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Skewed Binomial and Poisson Distributions
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Re Wealth Distribution
Every agent picks up wealth with a small
probability on every time step, so probability of
a specific amount of accumulated wealth
approximately follows a Poisson distribution,
even without any differences between agents.
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Population Change in Sugarscape

• Sexual reproduction
• Find neighboring agent of opposite sex. Children
  based on parents attributes. Bequeath share of
  wealth to child.
• Fitter values become more frequent in
  population
• Fitness as emergent (not a function as in Genetic
  Algorithms)
• Fitness as sustainable coevolution with ones
  environment

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Fluctuations in Population

• If all agents have high vision, overgrazing may
  occur, leading to extinction
• Natural oscillations in population even with
  constant growth of sugar
• Constant population if childbearing starts 12-15,
  ends 40-50 (F) or 50-60 (M),natural death 60-100,
  and only bear children if wealth gt birth wealth
• Oscillations if childbearing ends 30-40 (F) or
  40-50 (M). Why?

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Oscillations in Population
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Cultural Transmission in Sugarscape

• Cultural heritage series of 1 and 0 tags.
• E.g. 100010010
• Transmission
• Randomly select one tag and flip it to neighbors
  value
• Cultural groups by tag majority rule
• Red group if 1sgt0s, else Blue
• Considerable variability within a group
• Typical behavior one group dominates over time

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• Friend if similar and neighbor.
• Friends tend to stay close
• Does similarity affect who we interact with?
  (Coleman, 1965)
• - adopt friends smoking habits, and choose
  friends by habits
• Does similarity affect proximity or vice versa?
• Are all agents equally connected? Hubs?
• What is the role of far friends? Small-worlds?
• Does group affect tags? Greater coherence with
  time?

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Cultural Imperialism
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Friends Stay Close
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Social Influence

• Groups do not always regularly increase their
  uniformity over time
• Minority opinions continue to exist
• Group polarization sub-groups resist
  assimilation
• Contrast with rich-get-richer models of cultural
  transmission

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Social influence on opinion

• Conformity (Sherif, Asch, Crutchfield, Deutsch
  Gerard)
• Active community association members correlate
  better with their communitys vote (.32) than
  nonmembers (0) (Putnam, 1966)
• marginalization

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MIT housing study

• MIT housing study with random court assignments
  (Festinger, 1950)
• 38 of residents deviated from modal attitude
  within housing court
• 78 of residents deviated from cross-court
  attitude
• Four characteristics of group opinion
• Consolidation reduction of diversity of opinion
  over time
• Clustering people become more similar to their
  neighbors
• Correlation attitudes that were originally
  independent tend to become
• associated (social and economic conservatism)
• Continuing diversity Clustering protects
  minority views from complete consolidation

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Sherif (1936) norms

• When judging amount of movement of a point of
  light (autokinetic effect), estimates converge
  when made in group

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Nowaks Celluar Automata Model of Social Influence

• Each person is a cell in a 2-D cellular automata
• Each person influences and is influenced by
  neighbors
• Immediacy proximity of a cell
• Attitude 0 or 1
• Persuasiveness convince others to switch 0-100
• Social support convince others to maintain
  0-100
• Change opinion if opposing force gt supporting
  force

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Social Influence

• NONumber of opposing neighbors,
• Pi Persuasiveness of neighbor i,
• Si supportiveness of neighbor i,
• didistance of neighbor

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• Does everybody have same number of
• neighbors? Hubs?
• Does everybody only connect to
• neighbors? Small-worlds?
• Is assumption of no movement
• plausible or innocuous?
• Are attitudes well represented by a
• single binary bit?
• Is there a reaction-formation to
• majority opinions?

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Consolidation increases with time
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Polarization Small deviations from 50 are
accentuated