Social and Economic Networks

Matthew O. Jackson

• Publisher: Princeton University Press
• Year: 2010
• ISBN:
  9781400833993
• Topic: Economía
• Subtopic: Microeconomía

Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function.
This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.

PART I

BACKGROUND AND FUNDAMENTALS OF NETWORK ANALYSIS

CHAPTER 1

Introduction

This chapter introduces the analysis of networks by presenting several examples of research. These examples provide some idea not only of why the subject is interesting but also of the range of networks studied, approaches taken, and methods used.

1.1

Why Model Networks?

Social networks permeate our social and economic lives. They play a central role in the transmission of information about job opportunities and are critical to the trade of many goods and services. They are the basis for the provision of mutual insurance in developing countries. Social networks are also important in determining how diseases spread, which products we buy, which languages we speak, how we vote, as well as whether we become criminals, how much education we obtain, and our likelihood of succeeding professionally. The countless ways in which network structures affect our well-being make it critical to understand (1) how social network structures affect behavior and (2) which network structures are likely to emerge in a society. The purpose of this monograph is to provide a framework for an analysis of social networks, with an eye on these two questions.

As the modeling of networks comes from varied fields and employs a variety of different techniques, before jumping into formal definitions and models, it is useful to start with a few examples that help give some impression of what social networks are and how they have been modeled. The following examples illustrate widely differing perspectives, issues, and approaches, previewing some of the breadth of the range of topics to follow.

FIGURE 1.1 Network showing fifteenth-century Florentine marriages. Data from Padgett and Ansell [516] (drawn using UCINET).

1.2

A Set of Examples

1.2.1 Florentine Marriages

The first example is a detailed look at the role of social networks in the rise of the Medici in Florence during the 1400s. The Medici have been called the “godfathers of the Renaissance.” Their accumulation of power in the early fifteenth century in Florence was orchestrated by Cosimo de’ Medici even though his family started with less wealth and political clout than other families in the oligarchy that ruled Florence at the time. Cosimo consolidated political and economic power by leveraging the central position of the Medici in networks of family intermarriages, economic relationships, and political patronage. His understanding of and fortuitous position in these social networks enabled him to build and control an early forerunner to a political party, while other important families of the time floundered in response.

Padgett and Ansell [516] provide powerful evidence for this consolidation by documenting the network of marriages between some key families in Florence in the 1430s. Figure 1.1 shows the links between the key families in Florence at that time, where a link represents a marriage between members of two families.¹

During this time the Medici (with Cosimo de’ Medici playing the key role) rose in power and largely consolidated control of business and politics in Florence. Previously Florence had been ruled by an oligarchy of elite families. If one examines wealth and political clout, however, the Medici did not stand out at this time and so one has to look at the structure of social relationships to understand why the Medici rose in power. For instance, the Strozzi had both greater wealth and more seats in the local legislature, and yet the Medici rose to eclipse them. The key to understanding the family’s rise, as Padgett and Ansell [516] detail, can be seen in the network structure.

If we do a rough calculation of importance in the network, simply by counting how many families a given family is linked to through marriages, then the Medici do come out on top. However, they only edge out the next highest families, the Strozzi and the Guadagni, by a ratio of 3 to 2. Although suggestive, it is not so dramatic as to be telling. We need to look a bit closer at the network structure to get a better handle on a key to the success of the Medici. In particular, the following measure of betweenness is illuminating.

Let P (ij) denote the number of shortest paths connecting family i to family j.² Let P_k (ij) denote the number of these paths that include family k. For instance, in Figure 1.1 the shortest path between the Barbadori and Guadagni has three links in it. There are two such paths: Barbadori-Medici-Albizzi-Guadagni and Barbadori-Medici-Tornabuon-Guadagni. If we set i = Barbadori and j = Guadagni, then P(ij) = 2. As the Medici lie on both paths, P_k(ij) = 2 when we set k = Medici, and i = Barbadori and j = Guadagni. In contrast this number is 0 if k = Strozzi, and is 1 if k = Albizzi. Thus, in a sense, the Medici are the key family in connecting the Barbadori to the Guadagni.

To gain intuition about how central a family is, look at an average of this betweenness calculation. We can ask, for each pair of other families, on what fraction of the total number of shortest paths between the two the given family lies. This number is 1 for the fraction of the shortest paths the Medici lie on between the Barbadori and Guadagni, and 1/2 for the corresponding fraction that the Albizzi lie on. Averaging across all pairs of other families gives a betweenness or power measure (due to Freeman [255]) for a given family. In particular, we can calculate

for each family k, where

if there are no paths connecting i and j, and the denominator captures that a given family could lie on paths between as many as (n − 1)(n − 2)/2 pairs of other families. This measure of betweenness for the Medici is .522. Thus if we look at all the shortest paths between various families (other than the Medici) in this network, the Medici lie on more than half of them! In contrast, a similar calculation for the Strozzi yields .103, or just over 10 percent. The second-highest family in terms of betweenness after the Medici is the Guadagni with a betweenness of .255. To the extent that marriage relationships were keys to communicating information, brokering business deals, and reaching political decisions, the Medici were much better positioned than other families, at least according to this notion of betweenness.³ While aided by circumstance (for instance, fiscal problems resulting from wars), it was the Medici and not some other family that ended up consolidating power. As Padgett and Ansell [516, p. 1259] put it, “Medician political control was produced by network disjunctures within the elite, which the Medici alone spanned.”

This analysis shows that network structure can provide important insights beyond those found in other political and economic characteristics. The example also illustrates that the network structure is important for more than a simple count of how many social ties each member has and suggests that different measures of betweenness or centrality will capture different aspects of network structure.

This example also suggests other questions that are addressed throughout this book. For instance, was it simply by chance that the Medici came to have such a special position in the network, or was it by choice and careful planning? As Padgett and Ansell [516, footnote 13] state, “The modern reader may need reminding that all of the elite marriages recorded here were arranged by patriarchs (or their equivalents) in the two families. Intra-elite marriages were conceived of partially in political alliance terms.” With this perspective in mind we then might ask why other families did not form more ties or try to circumvent the central position of the Medici. We could also ask whether the resulting network was optimal from a variety of perspectives: from the Medici’s perspective, from the oligarchs’ perspective, and from the perspective of the functioning of local politics and the economy of fifteenth-century Florence. We can begin to answer these types of questions through explicit models of the c...