SOC 147 University of Southern California LEC10 Structural Balance Theory Paper **This paper should be formatted with section headings. Before diving into the articles, you should introduce them. Strong summaries of each article which identify the authors’ main purpose and theoretical contributions. Direct incorporation of Lecture material.**
The document should have 1 inch margins, a Times New Roman 12 point font, and a minimum of 2,500-3,000 + (200-250) word count.
There are 3 Parts to the paper. Readings:
Part 1 deals with Rawlings and Friedkin “The Structural Balance Theory of Sentiment Networks”
Part 2 deals with Blau “A Macrosociological Theory of Social Structure”
The Format/Structure of your document should be as follows:
Title: SOC147
Part 1: Rawlings and Friedkin “The Structural Balance Theory of Sentiment Networks”
Section 1.1: The Authors’ Main Points
Section 1.2: Comments on the authors’ main points in relation to taking in account Professor Friedkin’s Lectures
Part 2: Blau “A Macrosociological Theory of Social Structure”
Section 2.1: The Authors’ Main Points
Section 2.2: Comments on the author’s main points in relation to and taking in account Professor Friedkin’s Lectures
Part 3: An additional 200-250 words that comment on LECTURE 9 “Groupthink, cults, and making monsters”. The number of words in your submitted midterm paper would have a (2,500-3,000) + (200-250) word count .
Your need not attend to the mathematical equations that are presented in this paper; you need only understand what problem or phenomena the mathematics is addressing.
NO QUOTES! DO NOT CLOSELY PARAPHRASE! PUT IT INTO YOUR OWN WORDS, AS IF YOU WERE DESCRIBING THE AUTHOR’S AND PROFESSOR FRIEDKIN’S MAIN POINTS TO SOMEONE WHO KNEW NOTHING ABOUT THE SUBJECT.
Citation style: citations to my lectures should be (NEF, Week #), and citations to published articles should be (Author(s) last name(s) with an “et al. ” if there are more than two authors, and the year of the publication), for example, (and Bargh and Ferguson, 2000) (Friedkin et al., 2016) The Structural Balance Theory of Sentiment
Networks: Elaboration and Test1
Craig M. Rawlings
Northwestern University
Noah E. Friedkin
University of California, Santa Barbara
Structural balance theory attends to a group’s network of sentiments
and posits that this network alters over time toward particular structural forms. Current work on the theory is focused on understanding
the mechanisms that alter sentiments as a function of the configuration of sentiments in which they are embedded. Although the theory assumes tension reduction mechanisms, there has been no effort to directly
measure and model the temporal changes of individuals’ relational tensions that are predicted by the theory. This article elaborates and tests
balance theory with an empirical analysis of its posited interpersonal
tensions and their reductions via a sentiment conversion process. In addition, the authors open a new line of inquiry on the theory’s scope conditions and point to a community commitment condition that is involved in the realization of structural balance. Their analysis draws
on a unique suite of multiwave measures obtained from the Urban Communes Data Set.
Georg Simmel posed an interesting, seemingly simple, question: what are
the implications of enlarging a dyadic relationship to a triad of individuals?
His insight, which might be stated as “social structure matters,” was that the
1
Earlier versions of this article were presented at the annual meetings of the American
Sociological Association in Chicago and the Sunbelt Conference of the International
Network for Social Network Analysis in Newport Beach, California. We thank John Levi
Martin and the AJS reviewers for insightful comments on prior drafts. Direct correspondence to Craig Rawlings, Department of Sociology, Northwestern University, 1810 Chicago Avenue, Evanston, Illinois 60208. E-mail: craig.rawlings@northwestern.edu
© 2017 by The University of Chicago. All rights reserved.
0002-9602/2017/12302-0005$10.00
510
AJS Volume 123 Number 2 ( September 2017): 510– 548
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Structural Balance of Sentiment Networks
enlargement of the smallest social group to a triad is a profound qualitative
change of group condition that has ramifications for all three dyadic relationships and all three individuals (Simmel [1922] 1955, 1950 [ca. 1902–
17]). Lines of investigation subsequent to Simmel’s analysis of the triad
have reinforced this insight. The triad cannot be understood as decomposable into three dyadic relationship systems but is itself a system in which the
three dyadic systems are nested. Lines of investigation have generalized
Simmel’s analysis by nesting triads in a social network. As with Simmel,
these lines of investigation attend to structural forms. In structural balance
theory, which is the focus of this article, the network is composed of interpersonal sentiments. The theory applies to groups in which every individual
has either a positive or a negative orientation toward every other individual
of the group. In such groups, the configuration of sentiments in each triad
can be classified as one of 16 possible types. Structural balance theory posits
that some types of triads are forbidden and others are permitted on the basis
of four rules. The theory shows that these rules have remarkable nonintuitive implications for the macrostructure of the group’s sentiment network.
Thus, Simmel’s triad is the stepping stone to an understanding of the macrostructure organization of sentiment relations.
Structural balance theory has been elaborated over generations of investigators. It continues to advance in work by sociologists and investigators in
the natural and engineering sciences with publications in premier general
scientific journals, such as the Proceedings of the National Academy of Sciences (Antal, Krapivsky, and Redner 2005; Abell and Ludwig 2007; Szell,
Lambiotte, and Thurner 2010; Marvel et al. 2011). The sustained and ongoing interest in this theory is its implication that a social network of interpersonal sentiments has a natural evolution toward particular generic forms of
balanced social organization at the macrolevel. Yet puzzles remain. Current
work on the theory is focused on understanding the mechanisms that alter
sentiments as a function of the configuration of sentiments in which they are
embedded.
Balance theory was initiated by Heider (1946). He analyzed a simple P-O-X
system composed of two persons P and O, with a fixed symmetric positive or
negative P-O relationship, who are oriented differently in sign to the same object X. Heider focused on P’s response to different states of this constrained
system. Newcomb (1961), attending to Heider’s work, proposed an A-B-X
system with more moving parts. The A-B sentiment symmetry constraint
is relaxed, A or B’s signed orientation to X may alter, and A or B’s sentiments
toward one another may alter. In Cartwright and Harary’s (1956) advancement of balance theory, the object X is another individual, and all triads of
individuals are nested in a sentiment network in which each individual has
an alterable positive or negative sentiment toward every other individual.
This is a system with many moving parts. It is in Cartwright and Harary’s
511
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
American Journal of Sociology
work that Simmel’s triad surfaces in an especially interesting way and where
the macrostructural implications of balance theory are formalized. The set of
assumptions involved in their analysis is now referred to as the classic model
of structural balance. Using the term “friend” to designate a positive sentiment and the term “enemy” to designate a negative sentiment, the classic balance model defines a sentiment network as balanced if it contains no violations of four assumptions:
(A1)
(A2)
(A3)
(A4)
A friend of a friend is a friend,
A friend of an enemy is an enemy,
An enemy of a friend is an enemy,
An enemy of an enemy is a friend.
In these terms, the assumptions are evocative of maxims that appear in various cultures. The four rules permit some types of triads and forbid others.
Cartwright and Harary showed that only two generic forms of sentiment network macrostructure are possible under these rules. The sentiment network
must be either a network of all-positive sentiments or a network of individuals partitioned into two cliques with all-positive within-clique sentiments
and all-negative between-clique sentiments. This discovery has sustained the
interest in balance theory.
Davis and Leinhardt (1972) generalized the Cartwright-Harary model.
They formalized the distinction of 16 possible types of triads. Then, in a brilliant analysis, they arranged the four rules of the classic model as a tuple {A1,
A2, A3, A4}—that is, an ordered set—and sequentially dropped assumptions
to consider the macrostructure implications of the sequence of reduced tuples
{A1, A2, A3}, {A1, A2}, and {A1}. They showed that each reduction includes
the macrostructure implications of all larger tuples as special cases. One rule,
denoted above as {A1} and referred to as the transitivity assumption, includes
the macrostructure implications of the larger tuples as special cases. On the
basis of this single rule, (1) all macrostructures have one or more cliques
(the entire structure may be one clique) within which relations are all positive;
(2) the relations between pairs of cliques are either all negative or asymmetric;
(3) every member of a clique has an identical sentiment toward every member
of the macrostructure; and (4) if cliques are joined by asymmetric relations,
then a hierarchical form of macrostructure exists.
The empirical evidence on groups that has been amassed to assess balance
theory presents strong support for the following restricted statements: (1) the
probability of a positive i → k sentiment is more likely when a sequence
i → j → k of positive sentiments exists than when such a sequence does
not exist, and (2) the probability of an intransitive triad (one of the seven types
of triads that violate transitivity) is lower than the probability of a triad that is
not intransitive (one of the nine types of triads that do not violate transitivity).
512
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Structural Balance of Sentiment Networks
See, for example, the findings of Hallinan (1974), Sørenson and Hallinan
(1976), Davis (1979), Hallinan and Hutchins (1980), Doreian and Krackhardt
(2001), and Kossinets and Watts (2009). We believe that it is accurate to characterize all other predictions of the theory as being in an unsettled state.
Unresolved puzzles arise concerning the mechanisms that alter a sentiment network and put it on a trajectory toward structural balance. The theory suggests the existence of such a temporal evolution, but it does not specify the mechanism that alters sentiments. Empirical tests of whether such an
evolution occurs require the collection of longitudinal data on networks of
interpersonal sentiments, and such tests are rare. The few longitudinal studies that have been conducted have not connected the dynamics of sentiment
change to the management of the relational tensions that the theory posits
are associated with particular configurations of sentiments. Without the
demonstration that such a mechanism exists, the validity of the theory
may be questioned, and it has been. Feld (1981) and Feld and Elmore
(1982) have suggested that relational tensions are not relevant and that
the evidence on a transitivity bias in observed social networks is largely explained by the social-structural contexts (“foci”) that give rise to clusters and
inequalities in popularity, rather than by tension reduction responses to violations of balance theory rules.
We believe that relational tensions are associated with structural violations of the rules of balance theory and that the temporal evolution of a sentiment network is the epiphenomenon of responses to tensions that reduce
violations of balance theory rules. But the available evidence to support this
belief is scanty. Experimental social psychologists have investigated the extent to which certain imagined triads are perceived as stressful by subjects
(Aderman 1969; Crano and Cooper 1973; Fuller 1974). This evidence suggests that, when subjects imagine being put in particular positions of various balanced and imbalanced triadic situations, they associate conditions of
imbalance with more imagined unpleasantness than under more balanced
conditions. These findings on imagined tensions have obvious limitations in
terms of being extended to interpersonal tensions in naturally occurring
groups, but they do suggest a plausible link between perceived imbalances
and tension reduction motivations. They also do not attend to the question
whether individuals’ responses to perceived tensions are sentiment conversions that reduce violations of balance theory rules.
CONTRIBUTION
Recent theoretical work on balance theory mechanisms has reinforced a
long-standing call for more empirical evidence on the dynamics of sentiment change that shift macrostructures toward generic forms of balance
(Opp 1984). Although the theory assumes tension reduction mechanisms,
513
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
American Journal of Sociology
there has been no effort to empirically investigate the linkages of sentiment
structures and relational tensions. In this article, we report the first effort to
directly measure relational tensions and model the linkages and temporal
changes of individuals’ sentiment structures and relational tensions. A suite
of new findings are reported on a set of open questions. We do not know
whether differences of exposure to violations of balance theory rules, which
all balance theory models assume are a source of tension, are associated
with individuals’ perceptions of relational tensions and how such perceptions lead to observed sentiment conversions. Can temporal shifts toward
structural balance emerge in the absence of individuals’ perceptions of interpersonal tensions? Are all of the violations entertained in the four rules
of the classic balance model similarly associated with perceived relational
tensions and, in turn, with sentiment conversions? Does the empirical evidence favor automatic or deliberative (optimizing) sentiment conversion responses to perceived relational tensions? Furthermore, no evidence exists
on the scope conditions of sentiment structure evolution; that is, are mechanisms that alter group macrostructures toward greater balance more likely
under some group-level conditions than others?
We find systematic evidence of temporal reductions of violations of balance theory rules and linkages of structural violations with relational tensions. The evidence supports the assumption of purposeful actors, entailed
in some of the recent work on mechanisms of sentiment network evolution,
who alter sentiments on the basis of the relative tension reduction payoffs of
converting particular sentiments. In addition, we open a new line of inquiry
on the theory’s scope conditions. We find that a community commitment
condition is importantly involved in the realization of structural balance,
whereby balance theory mechanisms depend on the extent to which a group
is composed of individuals who are committed to the group as a social unit.
Our findings are based on the unique suite of multiwave measures in the
Urban Communes Data Set (Zablocki 1980; Martin, Yeung, and Zablocki
2001). Below, we describe the theoretical framework of balance theory, and
the current work on it, in more detail. Then we lay out hypotheses, our measures and method, findings, and conclusions.
THEORETICAL FRAMEWORK
Rules of Structural Balance
Sentiments are an important special case of attitudes that are positive or
negative cognitive orientations of some strength. Positive interpersonal sentiments and their relational correlates (sustained contact, reciprocity, trust,
and influence) are the essential bases of small primary groups, and they
form the backbone of larger social structures (Homans 1950; Granovetter
1973; Krackhardt 1992; Friedkin 1998; Lawler 2001; Martin 2009). The
514
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Structural Balance of Sentiment Networks
scope condition of balance theory is a group in which all individuals have a
positive or negative orientation of some strength toward every other member of the group. This condition is more likely to be satisfied in small groups
of mutually acquainted individuals than in large groups where ubiquitous
mutual acquaintance is more problematic (Davis 1963). Balance theory relaxes the assumption of all-positive sentiments, and, in so doing, it allows
the simultaneous existence of social cohesion and social conflict, that is, the
ubiquitous duality that has stimulated the development of sociological theory since the inception of the discipline (Durkheim [1893] 1933). Balance
theory suggests that stable macrostructures may exist that include both positive and negative interpersonal sentiments.
In the literature on balance theory, it is the structural form of a triad—
that is, its configuration of positive and negative relations among three individuals—that determines whether the triad microstructure is balanced.
The existence of a negative sentiment in the triad does not automatically define it as unbalanced. In turn, a balanced macrostructure may contain numerous triads in which there is one or more negative sentiments. It is the
configuration of positive and negative sentiments in the microstructures
of triads and in the macrostructure containing the triads that determines
whether the network as a whole is in a state of structural balance.
The development of balance theory rests on its analysis of four maxims.
The classic model of balance theory disallows (“forbids”) any violations of
the four rules. Generalizations of balance theory disallow a subset of these
four rules. The clusters model forbids violations of {A1, A2, A3}, the
ranked clusters model forbids violations of {A1, A2}, and the transitivity
model forbids only violations of {A1}. This ordered relaxation of constraints
allows the appearance of more constrained models as special cases. The
transitivity model allows the other three models as special cases.2
Table 1 shows the 16 types of triads that are possible in any group of three or
more individuals. The four rules of balanced sentiment structures “forbid”
subsets of these 16 types, on the basis of the occurrence of at least one violation
of the rules, and “permit” the remaining types. The convention is to represent
the 16 types of triads in a simplified form: only positive sentiments are displayed, with the understanding that the absence of a positive sentiment implies the presence of a negative sentiment. These triads are characterized by
three numbers, indicating the number of mutual (M), asymmetric (A), and null
(N) ties, and symbols that discriminate triads with identical MAN numbers—
transitive (T), up (U), down (D), and cyclic (C)—when required. Only two triads (300 and 102) do not violate any of the four rules, a condition that when
stipulated for all triads in a group leads to the classic model’s implication of
united or bifurcated macrostructures.
2
See Johnsen (1985) for a useful analysis of the logic involved in the sequence of the models.
515
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
TABLE 1
Four Rules of Structural Balance and Forbidden Triads
Triad Type
Triad Label
………
300
……….
102
………..
003
A4
A3
A2
A1
Forbidden
……….
120D
Forbidden
……….
120U
Forbidden
………
030T
Forbidden
Forbidden
………
021D
Forbidden
Forbidden
………
021U
Forbidden
Forbidden
………
012
Forbidden
………
021C
Forbidden
………
111U
……..
111D
………
030C
Forbidden
………
201
Forbidden
Forbidden
Forbidden
120C
Forbidden
Forbidden
Forbidden
210
Forbidden
Forbidden
Forbidden
……..
………
Forbidden
Forbidden
Forbidden
Forbidden
Forbidden
Forbidden
Forbidden
Forbidden
This content downloaded from 128.111.128.129 on April 21, 2018 09:28:16 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Structural Balance of Sentiment Networks
For a particular group with n members, a “triad census” distributes the
group’s observed “n choose 3” triads among these 16 types. The number of
triads that are distributed among these 16 types increases rapidly with the size
of a group; for example, for groups of size 5, 10, 20, and 40, the number of
triads is 10, 120, 1,140, and 9,880, respectively. Analyses of distributions of
observed triads among the 16 possible types have regularly indicated a strong
bias toward transitivity, which is the only rule that is assumed by all four
models of structural balance. Note that in table 1, s…
Purchase answer to see full
attachment