Modeling Social Behavior

Mathematical modeling as something distinct from the main body of mathematics arose sometime in the 19th century, focused at first on problems from physics. Over the years it gradually incorporated questions in chemistry, and later in biology. Applications to the social sciences have been more recent. While we have more-or-less established laws in physics, chemistry and biology, the social world has been more difficult to characterize by accepted laws.

 

The author notes this in his preface: that the social sciences do not have broadly acknowledged theoretical foundations as physics and biology do. He proposes to offer a starting place for undertaking study of quantitative theory in the social sciences. The target audience consists of those working in the social, cognitive, and behavioral sciences. The author aims to identify tools for studying complex social systems that use mathematical and computational models. One of his goals is to develop a bridge between those who want to develop tools for modeling and others with strong mathematical and computational skills who want to apply them to the social sciences.

 

Because many readers may have little or no experience in mathematical modeling, the author goes to some lengths to explain the whys and wherefores of modeling in the social sciences, the benefits as well as the limitations. He says that models can be “doing violence to reality”, and wants his readers to understand that one sometimes needs to begin with simple nonrealistic models to be able to progress to more complex and realistic models.

 

Two types of modeling are described: agent-based and equation-based. Agent-based models use individual agents that are explicitly simulated as computational entities. This concept is first motivated by the example of flocking birds where the behavior of an individual bird is governed by a few simple rules. The first extended description of agent-based model deals with the question of how racial and ethnic segregation develops.

 

The author uses a programming tool called NetLogo for agent-based modeling, and makes all the code in the book available to students online. This gives students the capability to assemble a model with little or no background in programming. Agent-based and equation-based modeling are treated together as complementary tools throughout the book. For prerequisites, only proficiency with high school level algebra and probability are needed, although some calculus and statistics would be helpful.

 

The real meat of this book is in the examples, and they are very good. They range from the segregation example to contagion (of disease and innovation), the dynamics of opinion, cooperation (the prisoner’s dilemma and evolutionary dynamics), and coordination between groups.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.