Diversity and Complexity (Primers in Complex Systems) - Softcover

Page, Scott E.

Softcover

ISBN 10: 0691137676 ISBN 13: 9780691137674

Verlag: Princeton University Press, 2010

Inhaltsangabe

This book provides an introduction to the role of diversity in complex adaptive systems. A complex system--such as an economy or a tropical ecosystem--consists of interacting adaptive entities that produce dynamic patterns and structures. Diversity plays a different role in a complex system than it does in an equilibrium system, where it often merely produces variation around the mean for performance measures. In complex adaptive systems, diversity makes fundamental contributions to system performance.

Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system.

• Provides a concise and accessible introduction


• Shows how diversity underpins robustness and fuels tipping points


• Covers all types of diversity


• The essential primer on diversity in complex adaptive systems

Über diesen Titel

Über die Autorin bzw. den Autor

Scott E. Page is the Leonid Hurwicz Collegiate Professor of Complex Systems, Political Science, and Economics at the University of Michigan and an external faculty member at the Santa Fe Institute. He is the author of The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies (Princeton).

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"Scott Page effectively illustrates the multiplicity of results from diverse aspects of complex systems. While all too many social scientists have tried to focus on making analysis simple, Page points out that this overlooks the great variety of relevant material in our social worlds. I am looking forward to having my students read it in my graduate seminar and encourage others to do so as well."--Elinor Ostrom, winner of the Nobel Prize in economics

"At once clear and precise, Page not only makes a persuasive case for the advantages of diversity in biological, ecological, and social systems alike, but also provides the reader with the analytical tools necessary to engage real-world debates in a rational, even quantitative manner. The result is a valuable primer on a difficult and important subject."--Duncan J. Watts, author of Small Worlds: The Dynamics of Networks between Order and Randomness

"Scott Page has performed a remarkable work of synthesis. The concepts of diversity and its implications for performance and growth are common to many fields, especially biology and economics. Page has drawn these illustrations together and shown the common elements and how each field illuminates others."--Kenneth J. Arrow, winner of the Nobel Prize in economics

"Page engagingly seduces readers into rather deep ideas in complex systems, including sophisticated mathematical formulas, by using a relaxed style with lots of examples. Yet the treatment is rigorous."--Simon A. Levin, Princeton University

"One of the book's many strengths is that it draws upon insights from seemingly disconnected areas of research and shows how they can be viewed within a common framework. Page's style is lively and conversational, making challenging subject matter quite readable, but without any sacrifice of rigor. He manages to convey both the excitement and difficulty of analyzing complex systems and the role of diversity within them."--Rajiv Sethi, Barnard College, Columbia University

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DIVERSITY AND COMPLEXITY

By Scott E. Page

PRINCETON UNIVERSITY PRESS

Copyright © 2011 Princeton University Press
All right reserved.
ISBN: 978-0-691-13767-4

Contents

Acknowledgments..........................................................................ixPrelude: The Meaning of Diversity........................................................11. On Diversity and Complexity...........................................................162. Measuring Diversity...................................................................543. The Creation and Evolution of Diversity...............................................794. Constraints on Diversity..............................................................1275. Variation in Complex Systems..........................................................1486. Diversity's Inescapable Benefits I: Averaging.........................................1677. Diversity's Inescapable Benefits II: Diminishing Returns to Types.....................1838. Diversity's Impact in Complex Systems.................................................1969. Parting Thoughts......................................................................249Bibliography.............................................................................257Notes....................................................................................271Index....................................................................................281

Chapter One

ON DIVERSITY AND COMPLEXITY

Armageddon is not around the corner. This is only what the people of violence want us to believe. The complexity and diversity of the world is the hope for the future. —MONTY PYTHON'S MICHAEL PALIN

In this chapter, I pose and answer some basic questions. What is diversity? What is complexity? And, why link diversity and complexity—what does one have to do with the other? First, diversity. Diversity applies to populations or collections of entities. A ball bearing cannot be diverse. Nor can a flower. Diversity requires multitudes. Cities are diverse; they contain many people, organizations, buildings, roads, etcetera. Ecosystems are diverse because they contain multiple types of flora and fauna.

When scientists speak of diversity, they can mean any of three characteristics of a population. They can mean variation in some attribute, such as differences in the length of finches' beaks. They can mean diversity of types, such as different types of stores in a mall. Or they can mean differences in configuration, such as different connections between atoms in a molecule.

Complexity proves to be a much more problematic concept. As mentioned in the Prelude, complexity can be loosely thought of as interesting structures and patterns that are not easily described or predicted. Systems that produce complexity consist of diverse rule-following entities whose behaviors are interdependent. Those entities interact over a contact structure or network. In addition, the entities often adapt. That adaptation can be learning in a social system, or natural selection in an ecological system. I find it helpful to think of complex systems as "large" in Walt Whitman's sense of containing contradictions. They tend to be robust and at the same time capable of producing large events. They can attain equilibria, both fixed points and simple patterns, as well as produce long random sequences.

To provide an example of the type of analysis that follows, I begin with an example of how diversity contributes to complexity in economics. Imagine an exchange market—a bazaar in which people bring wheelbarrows of goods to trade. This example demonstrates how diversity can reduce volatility in a system and also produce complexity. In an exchange market, diversity can enter in three ways: (1) in what the agents bring to buy and sell, their endowments; (2) in the agents' preferences for the different goods; and (3) in the ways the agents adapt to information, specifically prices.

If the market had no diversity, not much would happen. If everyone had identical endowments and preferences, then no one would have any reason to trade. So, we need diversity on at least one of these dimensions just to make the market come to life. Let's add diversity to both endowments and preferences so that agents bring different goods to market and desire different bundles of goods as well. In such a market, we need some mechanism for prices to form. Following standard economics, let's assume that there exists a market maker, who calls out prices with the intent of producing equilibrium trades.

Once we introduce the market maker, we have to take into account how agents respond to prices. Let's start by assuming no diversity. If all of the agents react in the same way, then prices will be volatile. They'll jump all over the place. This volatility results from everyone reacting in the same way to a price that's too low, resulting in a massive increase in demand and a similar rise in price. Gintis (2007) shows that diversity in the learning rules reduces this volatility. Later in the book, I provide a simple model involving negative and positive feedbacks that explains the stabilizing effect of variability in responses. Here, I just wish to raise the point that diversity can stabilize.

This model can be made even more complex. Kirman and Vriend (2001) add realism by dispensing with the market maker. Instead, they allow individual buyers and sellers to strike up relationships with one another. With this added realism, diversity has more subtle effects. If buyers differ in the price at which they value the goods, then buyers with relatively high values tend to pay higher prices. Furthermore, high value buyers exhibit less loyalty than buyers with low values. In this model, diversity produces complexity through the web of connections and reputations that emerge from the system. Without diversity, nothing interesting happens. With diversity, we get relatively stable market prices, but when we look at the agents and how they behave, we see a complex system.

In the remainder of this chapter, I begin with brief overviews of what is meant by diversity and complexity. I then describe how diversity contributes to complexity with some specific examples including the spatial prisoner's dilemma. I conclude the chapter by describing what I call the assemblage problem—the fact that many complex systems are assembled, typically from the bottom up. The fact that complex systems are assembled complicates empirical tests of the benefits of diversity.

Characterizing Diversity

There are many ways to characterize diversity. Each affects how much diversity we see in a particular situation. I may walk into a furniture store and see tremendous diversity in style. You may walk in and see no diversity at all—just a bunch of bedroom furniture. In this section, I describe several categorizations of types of diversity as well as some common measures of diversity.

One logical starting place for thinking about how to categorize diversity is to distinguish between continuous and discrete differences. The weights of the members of a murder of crows or of a parliament of owls vary. These differences in weight can take on any real value; hence we can think of them as a continuous variable. Alternatively, we can think of diversity as the number of types or as the distribution across those types. For...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 0691137676
• ISBN 13: 9780691137674
• Einband: Taschenbuch
• Anzahl der Seiten: 291
• Kontakt zum Hersteller: Princeton University Press; https://press.princeton.edu/books; ; 7th Floor, New South Building; PRINCETON; NJ; 8544; USA
• Verantwortliche Person: Nicht verfügbar