Literature/1989/Kochen


 * Preface

The phenomenon of two strangers meeting in a strange place and discovering that they have a common acquaintance occurs surprisingly often. It is related to the equally counterintuitive fact that a chain of at most seven intermediaries, and more commonly two or three intermediaries -- friends of friends -- are sufficient to link most pairs of people in the world. This is the small world phenomenon. The name derives from the frequently heard comment of two freshly made acquaintance, on discovering that they have an acquaintance in common: "It is a small world, isn't it?"

This phenomenon is of great importance. Political influence is transmitted over such chains of acquaintances. If a person wishes to influence the passage of certain legislation, he may ask an acquaintance in Congress to state the case for him; if he does not know anyone in Congress well enough for this purpose, he may ask an acquaintance who does, to do it on his behalf. A job-seeker may ask an acquaintance or a friend of a friend (etc.) to put in a good word on his behalf; as Granovetter has shown, it is often "weak ties" or rarely contacted acquaintances that are called on and who are instrumental in this way. An entrepreneur relies on direct contacts and indirect contacts to build a clientele, sources of finance, a staff. The widespread availability of good connections, direct and indirect, and their systematic use, probably distinguishes mature societies from less developed ones, in which only a few make extensive use of personal networks.

The small world phenomenon is also of great scientific interest. It arouses our sense of wonder and it challenges us to explain it. The challenge is heightened by the difficulty of finding really satisfactory explanations. It appears to be a rather fundamental property of social structure and function. Understanding it, its origin, and its implications seems likely to shed light on many scientifically interesting and basic problems in sociology, political science, anthropology. Moreover, there is the tantalizing possibility that the small world phenomenon could shed light on the secret of how networks more generally give rise to emergent properties, such as the higher mental functions of neural nets and their analogs in social nets or computer nets.

Though many people have experienced, observed and thought about the small world phenomenon for a long time, it was Ithiel de Sola Pool who intended to subject it to scholarly and scientific study. It had long been a topic of party conversation and of recreational mathematics; the famous mathematician Paul Erdös, for example, defined the Erdös distance between two authors A, B of scientific papers as the number of intermediary co-authors (the smallest n, such that A co-authored at least one paper with some X or B, who co-authored at least one paper with X2 or B, ..., who co-authored at least one paper with Xn or B). Ithiel de Sola Pool, recognizing the mathematical nature of the small world problem -- to explain the small world phenomenon -- asked his political science colleague Karl Deutsch in 1957 to suggest a mathematician likely to engage in fruitful collaboration with him. Karl Deutsch introduced Pool and me for that purpose. He thus catalyzed what became a lifelong friendship and partnership in this research. The creation of that direct link by an intermediary is a fitting use of the small world phenomenon. It is also fitting that the foreword to this volume which commemorates de Sola Pool should be written by this eminent social scientist. (p. viii)

The reason we circulated draft manuscripts with our ideas and partial results for two decades prior to submitting one for publication was that we never felt we had "broken the back of the problem." This concern with the completeness, finality, conclusiveness of their work had troubled many researchers in this area who try to live up to their own high standards of social science. This includes several distinguished contributions to this volume. It was Linton Freeman's vision of an invisible college of social networks researchers and his founding of Social Networks to bring this about that led to the decision by Pool and me to "cut bait or fish" by combining our working papers into a manuscript. (p. viii)

Our unpublished working papers had stimulated the interest of one of the most creative social psychologists: Stanley Milgram. Having attained renown for his many ingenious experiments, notably those showing that many human subjects would follow an experimenter's instructions to inflict what they perceived to be pain on someone else (an actor), and even to increase its intensity, Milgram devised what has come to be known as "The Small World Method." The experimental instrument resembled a passport. On its first page was the description of a "target" person. specified by his or her picture. name, location, occupation, etc. A random sample of people in a location remote from that of the target person was chosen, and this "passport" given to each one. Each respondent (called an informant by some social scientists) was instructed to choose one of his or her acquaintances to whom to send the passport, with the intention that the recipient would count the target person among his or her acquaintances and, failing that, would forward it to an acquaintance likely to know the target. Each such respondent was to indicate in the passport whom he or she chose as a recipient, and why. By the time the target person received all the passport given .... (p. viii)

This remarkable confluence between the predominantly theoretical approach motivated by De Sola Pool, the predominantly experimental approach of Milgram, and the predominantly observational approach of Newcomb, combined with the fact that all three died in 1984, makes this commemorative volume a fitting testimonial to their legacy. (p. ix)

Networking is not just a name for talking to people; it is determining whom to talk to in different circumstances, and following leads and referrals in identifying such people.

Thus, this book has the following features;


 * 1) It bring together, in a coherent and up-to-date picture and in one place much of what is understood about the small world problem.
 * 2) It indicates the quality, vitality, and scope of this area as a leading edge of social science.
 * 3) It shows the centrality of the problem in modern life, and why understanding should be in the intellectual inventory of every educated person.
 * 4) It pays tribute to the pioneering contributions of Pool, Milgram, and Newcomb by showing how the seeds they planted are growing.
 * 5) It contains some very interesting and surprising facts.


 * Foreward I
 * The Small World Problem: The Growth of a Research Idea
 * Karl W. Deutsch


 * Foreward II
 * The Small World Method and Other Innovation in Experimental Social Psychology
 * Charles Kadushin


 * Part I.
 * Introduction      1

Chapter 1

 * Contacts and Influence      3
 * Ithiel de Sola Pool and Manfred Kochen

Chapter 2

 * Toward Structural Sociodynamics      52
 * Manfred Kochen

Part II. 
 * Uses of the Small World Phenomenon      65

Chapter 3

 * The Conditional Significance of Communication for
 * Interpersonal Influence      67
 * Ronald S. Burt and Tetsuji Uchiyama

Chapter 4

 * Applying the Small World Phenomenon to
 * Organizational Buying      88
 * Julia M. Bristor and Michael J. Ryan

Chapter 5

 * Toward a Sociometric Theory of Representation:
 * Representing Individuals Enmeshed in a Social
 * Network      100
 * Scott L. Feld and Bernard Grofman

Chapter 6

 * Modeling International Linkages      108
 * Paul R. Williamson

Chapter 7

 * International Networks, 1904-1950: The Small
 * World of Trade and Diplomacy      128
 * Michael D. Wallace and J. David Singer

Part III. 
 * The Experimental/Empirical Legacy      145

Chapter 8

 * Estimating Acquaintanceship Volume      147
 * Linton C. Freeman and Claire R. Thompson

Chapter 9

 * Estimating the Size of an Average Personal Network
 * and of an Event Subpopulation      159
 * H. Russell Bernard, Eugene C. Johnson,
 * Peter D. Killworth, and Scott Robinson

Chapter 10

 * Urban Social Networks: Some Methodological
 * Problems and Possibilities      176
 * Alden S. Klovdahl

Chapter 11

 * Social Relations in Luzon, Phillippines, Using the
 * Reverse Small World Method      211
 * Kirk R. Cuthbert

Part IV. 
 * Models and Conceptualizations      227

Chapter 12

 * The Smallworld Technique as a Theory-Construction
 * Tool      231
 * Nan Lin

Chapter 13

 * Agreement-Friendship Processes Related to
 * Empirical Social Macrostructures      239
 * Eugene C. Johnsen

Chapter 14

 * Two Regimes of Network Effects
 * Autocorrelation      280
 * Patrick Doreian

Chapter 15

 * Connectivity and the Small World Problem      296
 * John Skvoretz and Thomas J. Fararo

Chapter 16

 * Some Aspects of Epidemics and Social Nets      327
 * Anatol Rapoport and Yufei Yuan

Chapter 17

 * Approaches to Non-Euclidean Network
 * Analysis      349
 * George A. Barnett

Author Index      373

Subject Index      379

Wikipedia

 * Ithiel de Sola Pool
 * Stanley Milgram
 * Theodore Newcomb
 * Small world phenomenon
 * Small-world network
 * Six degrees of separation