|Ivars Peterson's MathTrek|
April 12, 1999
Computer simulation offers a powerful tool for studying human social behavior, contends Richard J. Gaylord of the University of Illinois at Urbana-Champaign. A theoretical physicist turned computational sociologist, Gaylord has developed models of social phenomena that focus on interactions between individuals, each having his or her own identity, traits, tastes, and memories.
"In setting up a simulation of a group of people, we create a society of individuals," Gaylord notes.
That means generating a list numerically characterizing each individual represented in the model, putting the digital "people" on a grid (one individual per lattice site), then allowing them to interact according to a set of rules specifying what happens as they move about on the grid.
"The system is decentralized in that there is no central authority deciding which individuals will remain where they are, which individuals will move, and to where they will move," Gaylord and Louis J. D'Andria of Wolfram Research in Champaign, Ill., remark in Simulating Society: A Mathematica Toolkit for Modeling Socioeconomic Behavior.
The approach used by Gaylord and D'Andria is an example of agent-based modeling. Researchers typically start with a grid on the computer screen, coloring in any units of the grid occupied by individuals, or agents. The researchers define the landscape, set the rules, and characterize the agents. They then step back to observe what happens as the swarming agents, left on their own in these simulations, move about and interact according to their programmed predilections. From the patterns that emerge, investigators believe they can glean insights into human social and economic behavior.
Reminiscent of the "Game of Life" invented by John H. Conway of Princeton University, agent-based models provide plenty of opportunities for experimentation. Seemingly minor changes in interaction rules can lead to radical population shifts. Individuals with certain traits can end up dominating a given artificial society.
To do your own simsociety modeling, it helps to start with simple scenarios, such as a group of interacting individuals milling about on a square grid, like a checkerboard. Gaylord and D'Andria, for example, populate the grid in such a way that an empty site has a value of zero and a site occupied by an individual has a value determined by a list representing the individual's characteristics. That list might include a numerical name tag identifying the individual, a number specifying the direction the individual is facing, a 0 or 1 designating "bad" or "good" behavior, and so on.
In a simple "mixing-bowl" model, the smoothly graduated shading from the top to the bottom of the grid (left), after many time steps, turns into a thorough mixing of the population (right) via the random movement of the system's individuals.
That's just the beginning. Gaylord and D'Andria focus on models of how people come to develop shared values based on ideas, beliefs, likes and dislikes, or attitudes. "One possible mechanism for the spreading of values through a population is through a sort of contagious process, occurring as individuals come into contact with one another and interact," they say. "This interaction results in a form of imitative behavior sometimes referred to as cultural transmission or social learning."
Gaylord and D'Andria start with a model originally proposed by Robert Axelrod of the University of Michigan in Ann Arbor. In this case, an agent has five attributes, or features, each of which has an integer value (called a trait) ranging from 1 to 10. At each time step, a randomly chosen agent in turn randomly selects an agent on a neighboring site. A comparison between the values of corresponding features of the two agents determines the outcome. If the traits of each corresponding feature are the same, nothing happens. If any of the traits differ, a cultural interaction occurs with a probability equal to the fraction of features that share the same value (reflecting their degree of cultural similarity).
For example, if the active agent's features are [3, 2, 1, 7, 5] and the selected agent's features are [4, 8, 1, 2, 5], there is a 40 percent probability that the agents will interact culturally because the values of the third and fifth features of the two agents are the same.
A cultural interaction is carried out by randomly choosing one of the features of the active agent having a different value from the value of the selected agent's corresponding feature and changing the active agent's feature value to the selected agent's value. For example, if the second feature is chosen, the active agent would end up with the feature traits [3, 8, 1, 7, 5].
Axelrod packed his square grid with agents and allowed no movement in the model. Gaylord and D'Andria relax those constraints by filling only a fraction of the squares and permitting mobility. They also allow two-way exchange of traits during a cultural interaction.
"In our variant of the Axelrod model, individuals roam around a lattice, carrying with them cultural attributes, and altering these attributes as they engage in bilateral interactions with individuals they encounter along the way," the researchers say. The system evolves for a specified number of time steps or until all the agents have identical attribute lists.
This particular model shows no convergence of attributes. It appears that mobility helps maintain diversity. Only by severely restricting random walks or increasing the population density sufficiently to suppress easy movement do repeated interactions between neighbors gradually bring about a coming together of values.
In these four snapshots from a cultural-transmission simulation, different colors represent different lists of values. Empty sites are gray.
It's possible to try out all sorts of variants. Gaylord and D'Andria have investigated, for instance, what would happen if the number of values shared between two facing agents is ignored and instead a value is randomly chosen and changed based on how similar the chosen value is for the two individuals. In another variant, social status determines the direction of value transmission.
"We don't try to model the universe," Gaylord insists. "We keep it simple yet try to get an accurate representation of a social situation or type of behavior. We aim for the essence of that behavior."
It's an endlessly fascinating lab-scale playing field for social experimentation.
Copyright 1999 by Ivars Peterson
Axelrod, R. 1997. The Complexity of Cooperation: Agent-Based Models of Competition and Cooperation. Princeton, N.J.: Princeton University Press.
Epstein, J.M., and R. Axtell. 1996. Growing Artificial Societies: Social Science from the Bottom Up. Washington, D.C.: Brookings Institution Press and Cambridge, Mass.: MIT Press.
Gaylord, R.J., and L.J. D'Andria. In press. Transmitting culture: Part II. Mathematica in Education and Research.
______. 1998. Transmitting culture: Part I. Mathematica in Education and Research 7(No. 4):56.
______. 1998. Simulating Society: A Mathematica Toolkit for Modeling Socioeconomic Behavior. New York: Springer-Verlag.
Johnson, G. 1999. Mindless creatures acting "mindfully." New York Times (March 23).
Peterson, I. 1998. The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics. New York: W.H. Freeman.
______. 1996. The gods of Sugarscape. Science News 150(Nov. 23):332. (Available at http://www.sciencenews.org/sn_arch/11_23_96/bob1.htm)
Information about Mathematica modeling can be found at http://www.wolfram.com.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.