# Chaos Theory in the Social Sciences

Foundations and Applications

Publication Year: 1996

Published by: University of Michigan Press

#### Contents

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pp. vii-viii

#### Introduction

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pp. 1-15

The social sciences, historically, have emulated both the intellectual and methodological paradigms of the natural sciences. From the behavioral revolution, to applications such as cybernetics, to a predominant reliance on the certainty and stability of the Newtonian paradigm, the social sciences have followed the lead of the natural sciences. This trend continues as new discoveries...

#### Part 1: Chaotic Dynamics in Social Science Data

#### 1. Exploring Nonlinear Dynamics with a Spreadsheet: A Graphical View of Chaos for Beginners

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pp. 19-29

The mathematical foundation of chaos theory and the unique vernacular of this new science can deter some researchers from exploring the dynamics of nonlinear systems. Terms such as periodicity, sensitive dependence on initial conditions, and attractors are not the usual vernacular of the social sciences. However, the modem microcomputer and electronic spreadsheet software...

#### 2. Probing the Underlying Structure in Dynamical Systems: An Introduction to Spectral Analysis

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pp. 31-51

This chapter examines one method of investigating the underlying dynamics of time-series data. It introduces the reader to spectral analysis, a tool for evaluating the frequency properties of a time series. This is distinguished from the analysis of the properties of time series in the time domain, which is...

#### 3. Measuring Chaos Using the Lyapunov Exponent

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pp. 53-66

At some point in time, all scientific things must be measured and calibrated--even chaos. The Lyapunov characteristic exponent, A, is the clearest measure to prove the existence and to quantify chaos in a dynamical system or time series. Chaos exists when A is positive, and this indicates the system under investigation is sensitive to initial conditions. A dictionary would suggest...

#### 4. The Prediction Test for Nonlinear Determinism

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pp. 67-88

One of the more interesting problems of modem empirical economics is what one might call the forecasting paradox: Standard linear statistical models of economic phenomena invariably fit very well in sample. However, results for out-of-sample prediction are typically much worse than one might expect given the in-sample fit. This problem has been known in the profession since...

#### 5. From Individuals to Groups: The Aggregation of Votes and Chaotic Dynamics

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pp. 89-116

The aggregation of individual preferences into a group choice is one of the most significant questions in political science. How citizens combine and weigh their interests and desires toward a societal agreement is the foundation of democratic theory. However, the individual-group connection is not as straightforward as early democratic theorists assumed. The process of reaching a societal agreement between a group of individuals, each with their own...

#### Part 2: Chaos Theory and Political Science

#### 6. Nonlinear Politics

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pp. 119-137

That chaos may be a part of elementary politics is evidenced by highly exploratory work in the fields of electoral behavior, game theory, axiomatic choice theory, and conflict analysis. The social dynamical processes that may induce chaos, methods of investigating large-scale collective behavior, and some implications for political science research are outlined in this essay....

#### 7. The Prediction of Unpredictability: Applications of the New Paradigm of Chaos in Dynamical Systems to the Old Problem of the Stability of a System of Hostile Nations

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pp. 139-163

The social sciences have long tried to emulate the procedures and results of the physical sciences--the laws of economic detenninism of Marx come immediately to mind. To a large extent, the science of international relations has not been successful in this emulation; its capability of predicting the outcome of international competition (war or peace?) has been very limited. Perhaps this is because too many variables seem to be required, intuitively, to...

#### 8. Complexity in the Evolution of Public Opinion

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pp. 165-196

Be that as it may, we often study such phenomena as though they were static. Cross-sectional analyses continue to dominate disciplinary research, for two reasons. First, we typically choose to analyze cross-sectional data. Exemplary are the many analyses of year-specific surveys of the electorate during presidential and off-year elections (see Huckfeldt and Sprague 1987; Cohen et al. 1991; and examples based on specific National Election Studies),...

#### Part 3: Chaos Theory and Economics

#### 9. Chaos Theory and Rationality in Economics

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pp. 199-213

A central assumption in economic theory is that of rational behavior by economic agents, although this has been widely criticized by many noneconomists. Since the work of Muth (1961), this assumption has increasingly taken the form of rational expectations, that agents over time on average accurately predict the future. This somewhat simplistic formulation of the assumption...

#### 10. Long Waves 1790–1990: Intermittency, Chaos, and Control

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pp. 215-236

There are two contending views of economic dynamics. Insights into their validity may be provided via concepts of catastrophe and chaos. The dominant paradigm is that optimizing behavior produces an economy that is inherently equilibrating, tending toward steady-state growth in the absence of random shocks. Such shocks, in the Slutsky-Frisch-Tinbergen view, are transfonned into cyclical oscillations through the filtering properties of the economy's...

#### 11. Cities as Spatial Chaotic Attractors

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pp. 237-269

Developments in the mathematical theory of dynamical stability and bifurcation
theory have considerably influenced developments throughout the social
sciences. S.ources have been either the field of *structural stability* emanating
from catastrophe theory (see Thorn 1975; Zeeman 1977), mathematical chaos
(see Lorenz 1963; May 1976; Guckenheimer and Holmes 1983; Thompson...

#### Part 4: Implications for Social Systems Management and Social Science

#### 12. Field-Theoretic Framework for the Interpretation of the Evolution, Instability, Structural Change, and Management of Complex Systems

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pp. 273-294

Policy making and decision making and other aspects of the management of complex systems are becoming increasingly difficult. Management philosophies, approaches, and techniques were developed during simpler times. However, complex systems are dynamic rather than static, evolve or are driven into domains of instability, and emerge into new structures. There is...

#### 13. Social Science as the Study of Complex Systems

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pp. 295-323

Despite three decades of development in the physical sciences, the social sciences are only now coming to grips with deterministic chaos and its world-view. Several explanations have been given for this hesitance. Positivists, appealing to Comtean doctrine, conceptualize the sciences as constituting a developmental hierarchy. Mathematics, physics, and astronomy, envisioned...

#### References

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pp. 325-345

#### Contributors

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pp. 347-349

E-ISBN-13: 9780472022526

E-ISBN-10: 0472022520

Print-ISBN-13: 9780472084722

Print-ISBN-10: 0472084720

Page Count: 360

Illustrations: 100 tables, figures

Publication Year: 1996