Download Applications of Cellular Automata in the Social Sciences

Applications of Cellular Automata in
the Social Sciences
Eileen Kraemer
Fres1010
University of Georgia
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
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 selforganization.
Schelling’s 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 nonsmokers, etc.
• neighborhood of an agent consisted of the
squares adjacent to agent’s location. (8 for inside,
3 or 5 for edge)
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.
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.
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
Schelling’s Segregation Model
continued
• Model
 2-D lattice with Moore neighborhoods
 Two types of individuals
 If < 37% of neighbors are of an agent’s
type, then the agent moves to a location
where at least 37% of its neighbors are of
its type
Schelling’s Segregation
Model
A perfectly integrated,
but improbable,
community
A random starting
commmunity with some
discontent.
Schelling’s Segregation Model
A community after several generations of
discontented people moving.
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
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
Wealth Distribution
Wealth Distribution: Lorenz Curves
Wealth Distribution: Gini Ratio
Y = cumulated
proportion of wealth
X = cumulated
proportion of
population
G = 0: everybody has
same wealth
G=1: All is owned by
one individual
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.”
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?
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:
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:
Skewed Binomial and Poisson
Distributions
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.
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
one’s environment
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 > birth wealth
 Oscillations if childbearing ends 30-40 (F) or 40-50
(M). Why?
Oscillations in Population
Cultural Transmission in
Sugarscape
• Cultural heritage: series of 1 and 0 tags.
 E.g. 100010010
• Transmission:
 Randomly select one tag and flip it to neighbor’s value
• Cultural groups by tag majority rule:
 Red group if 1s>0s, else Blue
• Considerable variability within a group
• Typical behavior: one group dominates over time
• Friend if similar and neighbor.
 Friends tend to stay close
• Does similarity affect who we interact with?
(Coleman, 1965)
 - adopt friend’s 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?
Cultural Imperialism
Friends Stay Close
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
Social influence on opinion
• Conformity (Sherif, Asch,
Crutchfield, Deutsch & Gerard)
 Active community association
members correlate better with their
community’s vote (.32) than
nonmembers (0) (Putnam, 1966) –
• marginalization
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
Sherif (1936) norms
• When judging amount of movement of a point
of light (autokinetic effect), estimates converge
when made in group
Nowak’s 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: 0100
 Social support = convince others to maintain: 0100
• Change opinion if opposing force >
supporting force
Social Influence
NO=Number of opposing neighbors,
Pi= Persuasiveness of neighbor i,
Si= supportiveness of neighbor i,
di=distance 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?
Consolidation increases with time
Polarization: Small deviations
from 50% are accentuated