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 self-organization.

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 non-

smokers, 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 Modelcontinued

• 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 everytime step, so probability of a specific amount of accumulatedwealth approximately follows a Poisson distribution, evenwithout 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:

0-100 Social support = convince others to

maintain: 0-100• 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

• 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