Chaos Theory in the Social Sciences Chaos Theory in the Social Sciences Foundations and Applications Edited by L. Douglas Kiel and Euel Elliott Ann Arbor THE UNIVERSITY OF MICHIGAN PRESS First paperback edition 1997 Copyright © by the University of Michigan 1996 All rights reserved Published in the United States of America by The University of Michigan Press Manufactured in the United States of America © Printed on acid-free paper 2004 7 6 5 4 No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, or otherwise, without the written permission of the publisher. A CIP catalog record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Chaos theory in the social sciences : foundations and applications / edited by L. Douglas Kiel and Euel Elliott, p. cm. Includes bibliographical references (p. ). ISBN 0-472-10638-4 (he : alk. paper) 1. Social sciences—Mathematical models. 2. Chaotic behavior in systems. I. Kiel, L. Douglas, 1956- . II. Elliott, Euel W., 1951- . H61.25.C48 1995 300'. 1'51—dc20 95-35470 CIP ISBN 0-472-08472-0 (pbk. : alk. paper) To Our Parents Contents Introduction Euel Elliott and L. Douglas Kiel Part 1. Chaotic Dynamics in Social Science Data 1. Exploring Nonlinear Dynamics with a Spreadsheet: A Graphical View of Chaos for Beginners L. Douglas Kiel and Euel Elliott 2. Probing the Underlying Structure in Dynamical Systems: An Introduction to Spectral Analysis Michael McBurnett 3. Measuring Chaos Using the Lyapunov Exponent Thad A. Brown 4. The Prediction Test for Nonlinear Determinism Ted Jaditz 5. From Individuals to Groups: The Aggregation of Votes and Chaotic Dynamics Diana Richards Part 2. Chaos Theory and Political Science 6. Nonlinear Politics Thad A. Brown 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 Alvin M. Saperstein 8. Complexity in the Evolution of Public Opinion Michael McBurnett Part 3. Chaos Theory and Economics 9. Chaos Theory and Rationality in Economics J. Barkley Rosser, Jr. viii Contents 10. Long Waves 1790-1990: Intermittency, Chaos, and Control 215 Brian J. L. Berry and Heja Kim 11. Cities as Spatial Chaotic Attractors 237 Dimitrios S. Dendrinos 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 273 Kenyon B. De Greene 13. Social Science as the Study of Complex Systems 295 David L. Harvey and Michael Reed References 325 Contributors 347 Introduction Eue I Elliott and L. Douglas Kiel The social sciences, historically, have emulated both the intellectual and methodological paradigms of the natural sciences. From the behavioral revo­ lution, 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 discov­ eries in the natural sciences have led to a reconsideration of the relevance of the Newtonian paradigm to all natural phenomena. One of these new discov­ eries, represented by the emerging field of chaos theory, raises questions about the apparent certainty, linearity, and predictability that were previously seen as essential elements of a Newtonian universe. The increasing recogni­ tion by natural scientists of the uncertainty, nonlinearity, and unpredictability in the natural realm has piqued the interest of social scientists in these new discoveries. Chaos theory represents the most recent effort by social scientists to incorporate theory and method from the natural sciences. Most importantly, chaos theory appears to provide a means for understanding and examining many of the uncertainties, nonlinearities, and unpredictable aspects of social systems behavior (Krasner 1990). Chaos theory is the result of natural scientists' discoveries in the field of nonlinear dynamics. Nonlinear dynamics is the study of the temporal evolu­ tion of nonlinear systems. Nonlinear systems reveal dynamical behavior such that the relationships between variables are unstable. Furthermore, changes in these relationships are subject to positive feedback in which changes are amplified, breaking up existing structures and behavior and creating unex­ pected outcomes in the generation of new structure and behavior. These changes may result in new forms of equilibrium; novel forms of increasing complexity; or even temporal behavior that appears random and devoid of order, the state of "chaos" in which uncertainty dominates and predictabil­ ity breaks down. Chaotic systems are often described as exhibiting low- dimensional or high-dimensional chaos. The former exhibit properties that may allow for some short-term prediction, while the latter may exhibit such