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 ). 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 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 (F) or (M),natural death , and only bear children if wealth > birth wealth  Oscillations if childbearing ends (F) or (M). Why?

Oscillations in Population

Cultural Transmission in Sugarscape Cultural heritage: series of 1 and 0 tags.  E.g 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:  Social support = convince others to maintain: 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