rawlings friedkin balance

8/9/2019 Rawlings Friedkin Balance

1/48

The Balance Theory of Sentiment Relations

Craig M. Rawlings1Department of Sociology

University of California, Santa Barbara

Noah E. FriedkinDepartment of Sociology, and

Center for Control, Dynamical Systems and Computation, College of Engineering,

University of California, Santa Barbara

Manuscript Under ReviewPlease do not cite or quote without permission.

Key words: Balance Theory; Social Networks; Social Psychology; Structure; Group Dynamics

[10,446 Words]

1Corresponding author. Contact: Sociology Dept., SSMS 3005, University of California, Santa

Barbara, CA 93106;[email protected];(805) 895-2892
mailto:[email protected]:[email protected]:[email protected]:[email protected]


2/48

The Balance Theory of Sentiment Relations

Abstract

The sentiment relation exists in all human interactions as a signed cognitive orientation of one

individual toward another, and it exists in all groups of acquainted individuals as a network of

signed cognitive orientations among the groups members. Balance theory attends to network

structures of sentiments and posits that these structures alter over time in response to individuals

efforts to locate themselves in social positions that are tension free. In small social groups, where

all individuals have a positive or negative orientation toward every other member of the group,

these efforts are constrained to sign changes of orientation. Balance theory presents the

surprising claim that negative sentiments may be tension free. The theory is structural in its

treatment of tension as a property of the configuration of sentiments, and is supported by a body

of empirical findings. However, the findings do not include supports for the theoryspostulate

that changes of sentiment are triggered by the interpersonal tensions of particular configurations

of sentiment relations. This paper advances balance theory with a unique set of findings obtained

with longitudinal data on sentiment structures and measures of interpersonal tensions.


3/48

1

INTRODUCTION

Research on social structures includes a classic and enduring line of work on how structures of

positive and negative interpersonal sentiments develop and shift over time among individuals.

Interpersonal sentiments are an important special case of attitudes that are positive or negative

cognitive orientations of some strength toward particular objects. Studies in cognitive science

suggest that individuals have an automatic positive or negative evaluative response to all

perceived objects, including other individuals. Kahneman (2003: 701) remarks that

The evidence, both behavioral (Bargh, 1997; Zojonc, 1998) and neurophysiological (see,e.g., LeDoux, 2000), is consistent with the idea that the assessment of whether objects are

good (and should be approached) or bad (and should be avoided) is carried out quicklyand efficiently by specialized neural circuitry. Several authors have commented on theinfluence of this primordial evaluative system (here included in System 1) on the

attitudes and preferences that people adopt consciously and deliberately (Epstein, 2003;

Kahneman et al. 1999; Slovic et al. 2002; Wilson, 2000; Zajonc, 1998).2

Positive interpersonal sentiments and their relational correlates (sustained contact, reciprocity,

trust, and influence) are the essential basis of small primary groups, and they form the backbone

of larger social structures (Friedkin 1998; Granovetter 1973; Homans 1950; Krackhardt 1992;

Lawler 2006; Martin 2009). Every structure of positive sentiments presents a complement

structure of non-positive interpersonal sentiments. In a small primary group with all positive

sentiments, this non-positive complement structure is absent. More generally, in small groups of

individuals who are all acquainted with one another, all individuals have a positive or negative

orientation of some strength toward every other member of the group. In larger social structures,

some non-positive complement structure is a characteristic feature of sentiment structures,

including instances where no sentiment exists among unacquainted individuals. The

simultaneous existence of social cohesion and social tension is a ubiquitous duality that has

2Kahneman distinguishes two systems, 1 and 2, and locates the hard work of logic and reasoning in

System 2. A simple example of System 2 activity is a countdown by sevens from 100.


4/48

2

stimulated the development of sociological theory since the inception of the discipline

(Durkheim 1933[1893]; Simmel 1950[c. 1902-17], 1955[1922]). One of these lines of research is

balance theory.

Initially formulated by Heider (1946), balance theory has been an ongoing focus of

interest because it links the analysis of micro- and macro-level social structures and presents

subtle and important implications of their linkage. Its scope condition is a group of acquainted

individuals with signed sentiments toward every member. It posits a natural process of structural

transformation in which individuals responses to their local relational tensions eventuate in

macro-structures composed of one or more cliques with all positive within-clique sentiments and

asymmetric interfaces with other cliques, if other cliques are formed. Between-clique sentiments

for an ordered pair of cliques are either all positive or all negative. A balanced sentiment

structure is a network that is either a clique or a network with multiple cliques, such that all

members of a clique have aligned (structurally equivalent) sentiments on all network members.

Moreover, a balanced sentiment structure with multiple cliques must be a hierarchical status

order if a set of between-clique asymmetric positive interfaces connects all cliques. With these

and other implications, it is not surprising that sociologists have long been intrigued by this

theory and contributed to its exploration. The insights of Davis (1963, 1967, 1970) were

particularly instrumental in this development. However, the investigation of the theory has been

limited by the absence of data on the structural dynamics posited by the theory and direct

measures of the local relational tensions that the theory assumes (see Abell 1968; Opp 1984).

This article is an effort to move beyond the current limitations of the empirical literature

on balance theory. With longitudinal data, we examine changes of sentiments in small, naturally-

occurring groups. We test the proposition that individuals within such groups tend to reduce their


5/48

3

exposure to intransitive triadic configurations of sentiments. We directly address the motivations

for such reductions, i.e., that individuals seek to reduce and/or avoid relational tensions by

resolving intransitive configurations of sentiments. Our data are based on twenty urban

communes in the years 1974 and 1975 (Martin, Yeung, & Zablocki 2001; Zablocki 1980). These

data deal with community-oriented groups of all acquainted individuals where the proposed

structural dynamics of sentiments are likely to be pronounced. With these data, if we cannot find

evidence supportive of the theorys emphasis on tension-related structural transformations, then

the premises of the theory are called into question. Our balance theory approach to this famous

and unusual data set is the first application of balance theory to it.

3

In the next four sections, we

detail balance theory, present our hypotheses, describe the data on communes and methods used

to test these hypotheses, and report our findings. Our discussion considers some extensions and

elaborations of our findings and their limitations, and outlines some directions of future work.

BALANCE THEORY

Heiders initial formulation of balance emphasized the micro-dynamics of individuals

perceptions of other individuals positive or negative orientations toward an object. Perceived

disagreement of orientation is a source of tension, which is reduced by changes of sentiment

toward greater alignment. When the object of orientation is a particular individual, relational

tension exists given perceived disagreements of interpersonal sentiments toward that individual.

Considering all such perceived sentiments in a social group, various adjustments of sentiments

lead, under Heiders assumptions, to the same conclusion, i.e., the sentiment structure of a group

will evolve into a structure of all positive sentiments or into a structure composed of precisely

3See Bradley (1999) for a sustained investigation of these communes with respect to their varying levelsof charisma, and analyses which include a comparison of positive sentiment structures in more and less

charismatic communes.


6/48

4

two hostile subgroups. Extensions of Heiders approach have relaxed some of its assumptions,

and shifted its focus away from an individuals perceptions of relationships toward a structural

analysis of networks composed of sentiment relations that are either positive or negative

(Cartwright and Harary 1956; Davis 1963; Davis & Leinhardt 1972; Holland & Leinhardt 1970).

Moreover, these generalizations relax Heiders strong assumptions concerning the local

structural conditions that trigger relational tension, and each successive generalization includes

prior models as special cases. The development of the theory presents an orderly advancement of

work across generations of investigators.

The orderly development of balance theory rests on its analysis of four structural

postulates. Let +Sij indicate that individual is sentiment toward individualjis positive, and

letSij indicate that it is negative:

(1) A friend of a friend is a friend, i.e., if +Sij and +Sjk, then +Sik;

(2) A friend of an enemy is an enemy, i.e., if Sij and +Sjk, then Sik;

(3) An enemy of a friend is an enemy, i.e., if +Sij andSjk, then Sik;

(4) An enemy of an enemy is a friend, i.e., if Sij andSjk, then +Sik.

Classical balance theory disallows (forbids) any violations of the above rules. Generalizations of

classical balance theory disallow a subset of these four rules and are referred as models. All these

generalizations include the first rule, which is known as transitivity. A violation of this rule

intransitivityexists when +Sij, +Sjk, and Sik. The most general model only disallows

violations of transitivity, and it is referred to as the transitivity model.4 The transitivity model

includes all other models, based on these rules, as special cases of structural balance that do not

violate transitivity.

4Johnsen (1985) presents an additional generalization for large-scale groups that relaxes the assumption

of transitivity.


7/48

5

Note that these rules present particular ijktriadic configurations of sentiments. All

generalizations minimally include the postulate that a triad, and the larger sentiment structure in

which it is embedded, is unbalanced if there exists three individuals i,j, and kamong whom the

sequence ikjof positive sentiment relations exists, but the ijpositive sentiment relation

does not. Triads that present at least one violation of transitivity are referred to as intransitive

triads with respect to their configurations of sentiment relations. The transitivity model assumes,

as do all other models, that intransitive configurations of sentiment relations in triads generate

relational tensions that the individuals involved in them are motivated to resolve.

-- Insert Figure 1 Here --

Figure 1 shows the sixteen types of triads that are possible when considering all possible

ijkconfigurations of sentiments, seven of which present at least one instance of intransitivity.

The convention is to represent these sixteen types in a simplified form: only the configuration of

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 numberstransitive (T), up (U), down (D), and cyclic

(C)when required. Every triad must be one of these sixteen types. For a particular group with n

members, a triad census distributes the groups observed nchoose 3 triadic configurations of

sentiments among these sixteen types. The number of triads that are distributed among these

sixteen types increases rapidly with the size of a group; e.g., for groups of size 5, 10, 20 and 40,

the number of triads is 10, 120, 1,140 and 9,880, respectively.

The various models of balanced sentiment structures forbid subsets of these sixteen

types and permit the remaining types (Holland & Leinhardt 1970; Johnsen 1986). The classic


8/48

6

and most restrictive model permits only the 300 and 102 types. The most prominent relaxation of

the stringent assumptions of this classic model forbids triads that present one or more instances

of a violation of transitivity and permits all other triads. Seven triad types violate transitivity at

least once, and a triad may have as many as three intransitive sequences of positive and non-

positive sentiments within the triad (as does the 030C triad). The remaining nine triad types are

divided into two classes: transitive and vacuously transitive triads. The distinction is based on

whether or not the configuration of relations in a triad presents at least one instance of an ikj

sequence. If there is no such sequence, then the structural condition for a violation of transitivity

does not exist and the triad is defined a vacuously transitive because it does not violate

transitivity. We will occasionally remind the reader of this important distinction. Vacuously

transitive triads are not posited to be sources of relational tensions.

What researchers consider the permitted vs. forbidden triads in a given approach is based

on largely unexplored linkages between triadic configurations of sentiments and relational

tensions. Heiders view of balance was quite restrictive on this matter, while later formulations

were more relaxed. For example, Newcombs (1968) and Holland and Leinhardts (1970) models

were based in part on a different set of assumptions regarding what should be a tension-laden

configuration. Thus, a triad of type 003 (where there are no positive sentiments) is not taken as a

tension-laden configuration in any of the generalizations of the classic balance model. In the

transitivity model, such empty triads, and vacuously transitive triads in general, are assumed to

be tension free. Negative sentiments are not,perse, treated as sources of relational tension. In

the transitivity model, where relational tensions are strictly associated with intransitivity, these

tensions may be resolved by the conversions of one or more positive sentiments into negative

sentiments, or vice versa. For example, an intransitive situation in which a friend of friend is not


9/48

7

a friend (+Sij, +Sjk, and Sik) may be resolved by the conversion of the negativeSik sentiment

to the positive +Sik sentiment , or by the conversion of the +Sij sentiment to the negative Sij

sentiment.

While the pressures for some form of cognitive consistency in sentiments toward objects

may in some respect be universal (Festinger 1957; Greenwald et al. 2002; Homans 1950; Osgood

& Tannenbaum 1955), situations that are tension-laden in one culture or institutional context

may be tension-free in another.5 The hypothesized pressures of balance theories appear to be

especially tailored to explain dynamics within groups with little functional differentiation (Davis

1963). Such groups are most likely to realize the kinds of triadic heuristics that shape transitivity,

because the absence of a positive sentiment is likely more problematic than in more complexly

differentiated groups where it is easier to discount certain sentiments relations (Martin 2009), or

to have weak ties of acquaintanceship that dont elicit the same demands in time and emotional

intensity that generate transitive pressures (Granovetter 1973).

With a few notable exceptions (Srenson & Hallinan 1976: Doreian & Krackhardt 2001),

empirical studies testing the postulates of balance theory have been cross-sectional, and the few

longitudinal studies have not connected sentiment alignments to the underlying mechanism at the

heart of the theorynamely, the management of relational tensions. The lack of empirical

evidence directly linking the modification of sentiment structures to relational tensions in groups

is an important gap. With no available evidence on tensions, some investigators have proposed

that tensions are not relevant and that transitivity is largely explained by the socialcontexts that

give rise to clusters and inequalities in popularity, rather than by tension reduction responses

(Feld 1981; Feld & Elmore 1982). These two viewpoints are not incommensurate. Whatever the

5For example, see Hage (1976) for a cultural context that appears consistent with Heiders early

formulations of balance.


10/48

8

conditions that set up a sentiment network, balance theory applies to an understanding of the

temporal structural trajectory of the network. In balance theory, the temporal evolution of

clusters and inequalities of positive sentiments are the epiphenomena of tension reduction

responses that alter social structure. Finally, we have found no comparative studies that examine

evolving triadic sentiment structures in multiple, relatively-bounded, naturally-occurring groups

where such assertions might be adjudicated.

Tests of the predictions of balance theory require the collection of longitudinal data on

networks of interpersonal sentiments; and such data are rare. Researchers have employed

experimental designs to probe the merits of the theory (Aderman 1969; Crano & Cooper 1973;

Fuller 1974; Press, Crockett, & Rosenkrantz 1969), and more recently have employed computer

simulations to explore possible processes that govern the evolution of sentiment structures (Anat,

Krapivsky, & Redner 2006; Hummon & Doreian 2003; Montgomery 2009; van Rijt 2011; Wang

& Thorngate 2003). The empirical evidence on groups that has been amassed to assess balance

theory presents overwhelming support for the following restricted statements: (a) if there exists

three individuals i,j, and kamong whom the sequence ijkof positive sentiment relations

exists, then the existence of an ikpositive relation is more likely than when the sequence i

jkof positive sentiment relations does not exist6and (b) the probability of an intransitive triad

(one of the seven types of triads that violate transitivity) is lower than the probability of a triad is

not intransitive (one of the nine of types of triads that dont violate transitivity). See, for

example, the findings of Davis (1979), Doreian & Krackhardt (2001), Hallinan (1974) Hallinan

6One indication of the relatively settled state of this finding is the implementation of transitivity as a

regular structural feature in stochastic actor-centered models of tie formation (see Snijders, van de Bunt,& Steglich 2010).


11/48

9

& Hutchins (1980), and Srenson & Hallinan (1976). We believe that it is accurate to

characterize all other predictions of the theory as being in an unsettled state.

HYPOTHESES

In balance theory, negative sentiments do not suffice to adduce relational tensions. Relational

tensions are triggered by particular structural configurations of sentiments. Sentiments are

directed ijcognitive orientations that can only be altered by individual i. The proximate

structural configurations that trigger relational tensions felt by individual iare the triadic

configurations of sentiments in which individual iis embedded. To the extent that an individual

is embedded in tension laden triadic configurations, the individual will be motivated to alter the

signs of his or her orientations toward specific other individuals. This is the logic that underlies

our hypotheses. Hence, after documenting the temporal reduction of intransitive triads posited by

balance theory (Hypothesis 1), we focus on individuals extents of direct exposure to

intransitivity and their felt relational tensions (Hypotheses 2-3). The general intent and unique

contribution of Hypotheses 2-3 is the grounding of balance theory postulates on individual-level

motivations to reduce the felt relational tensions associated with their exposure to intransitive

sentiment configurations of sentiments. We frame these hypotheses in terms of the transitivity

model of balance, which draws on the information provided by positive versus non-positive

sentiments.

Temporal Decline of Intransitive Triads

Numerous cross-sectional studies present evidence supporting the conclusion that small

group sentiment dynamics are based in part on the dictates of transitivity. Longitudinal studies of


12/48

10

sentiment structure have shown that transitive closure (i.e ikand kjties of positive sentiment lead

to an ijtie of positive sentiment) is a significant factor in shaping the relational correlates of

positive sentiments, such as friendships and voluntary work relations (Dahlander & McFarland

2013; Hallinan 1974; Hallinan and Hutchins 1980; Homans 1950; Kossinets & Watts 2009;

Newcomb 1961). Balance theory goes beyond tie formation models in predicting that there is a

general shift of the sentiment structure of relatively boundedgroupstoward configurations of

positive sentiments that do not violate transitivity. Support for this prediction can be found in

Srenson and Hallinan (1976), which detailed changing reports of friendship among a class of 28

sixth graders. Their analysis also showed that groups do not hopfrom unbalanced to balanced

sentiment structures and that shifts toward greater balance involve transitions of particular ijk

triads through states of intransitivity. Doreian and Krackhardts (2001) reanalysis of Newcombs

longitudinal data on 17 members of a fraternity likewise obtained support for the structural

postulates of balance theory. However, their findings were based on rank-order measuresrather

than dichotomous measuresof positive sentiments, and the authors chose not to examine

changes in the triad census for this group, examining instead the likelihood of moving toward

transitivity given various pre-transitive triadic states. Consistent with balance theorys

emphasis on group-level shifts and these previous empirical findings, we hypothesize that

H1: The proportion of triadic configurations that violate transitivity declines over time

among the enduring members of group.

Note that this hypothesis does not assert that transitivity necessarily increases over time,

only that intransitivity decreases. For example, a group may resolve tension-laden configurations


13/48

11

of intransitive sentiment relations by shifting to 003 configurations, in which no positive

sentiments exist among three persons, and other vacuously transitive configurations, and in so

doing lower the proportion of transitive triadic configurations of positive sentiments in the group.

The configurations of sentiments among the enduring members of a group should manifest a

temporal decline of intransitivity regardless of any intransitivity generated by the loss or addition

of members. Thus, an important aspect of this hypothesis is that a decline of intransitivity in the

enduring subset of groups is insensitive to group turnover.

Dyad-Level Sentiments and Tensions in Intransitive Environments

Proposed temporal mechanisms of intransitivity reduction include processes that treat the

group (or each individual in it) as an optimizing balance-seeking strategic actor who rewires the

groups structure of positive sentiments to eliminate intransitivity (Abell & Ludwig 2007; Antal,

Krapivsky, & Redner 2005; Kulakowski, Gawronski, & Gronek 2005; Marvel et al. 2011; Wang

& Thorngate 2003; see also Macy & Willer 2002). There is currently no empirical evidence that

supports or erodes these proposals. Moreover, we can find no empirical study that involves a

direct measure of the relational tensions in naturally-occurring groups that are assumed to

motivate posited structural changes of sentiment relations. Experimental social psychologists

have investigated the extent to which certain imaginedtriads are perceived as tension-laden by

subjects (Aderman 1969; Crano & Cooper 1973; Fuller 1974). This evidence suggests that, when

subjects imagine being put in particular positions ofvarious balanced and imbalanced triadic

situations, they associate conditions of intransitivity with more imagined unpleasantness than

under conditions that do not violate transitivity. Although these findings on imagined tensions


14/48

12

have obvious limitations, they do serve to indicate that a tension avoidance and reduction

hypothesis is intuitively plausible in applications to triadic configurations of positive sentiments.

The key premise is that individuals(not networks) seek to reduce relational tensions

when social environments present intransitivity (e.g. Hallinan & Hutchins 1980). Each i toj

sentiment relation (positive or non-positive) is contextualized by n-2 other individuals. Each of

these other individuals sets up an ijk triad with a particular configuration of sentiments, so that

the i toj sentiment is embedded in a social environment of n-2 sentiment configurations.

Controlling for the i toj sentiment (positive or non-positive), this social environment may

generate an i toj tension relation that is is tension and notjs. Among acquainted individuals, a

positive i toj sentiment may be either tension-laden or tension-free; similarly, a non-positive

sentiment may also be either tension-laden or tension-free. In balance theory, this tension

variable depends on the extent to which the itojsentiment is embedded within local (triadic)

intransitive configurations of sentiments. Thus, exposure to intransitivity is based on the subset

of nchoose 3 ijktriads that contain a particular ijordered pair. Sentiment conversion is a more

or less visceral reaction to local imbalance; sentiment conversion also may be informed by the

calculated payoffs of converting a particular sentiment relation with respect to the conversions

reduction of the individuals level of exposure to intransitivity. These two factors (visceral versus

rational conversion responses) are likely to be correlated in real world datathat is, individuals

with sentiments that are embedded in a larger number of intransitive triads are likely to have

greater payoffs in reducing those intransitivities through sentiment conversions. But, in particular

instances of i toj sentiment, a visceral conversion may or may not be an optimal conversion.


15/48

13

Threeresearchable hypotheses, theoretically central to balance theory, may be formulated

at the dyad-level. We begin with the hypothesized relationship between intransitivity and

tensions, and then formulate two hypotheses on sentiment conversions:

H2a: The probability of an ij relational tensionincreases with the extent to which the i

to j positive or non-positive sentiment is embedded in intransitive triadic configurations

of sentiments that include the particular i to j sentiment.

H2b: The probability of an ijsentiment conversion (positive to non-positive or vice

versa) increases with the extent to which the i to j positive or non-positive sentiment is

embedded in intransitive triadic configurations of sentiments that include the particular i

to j sentiment.

H2c: The probability of an ijsentiment conversion (positive to non-positive or vice

versa) increases with the extent to which the payoff of that sentiment conversion is a

reduction in the proportion of intransitive triadic configurations of sentiments that

include the particular i and j sentiment.

Individual-Level Reductions in Exposure to Intransitivity and Relational Tensions

Our third set of hypotheses is framed at the individual-level, because the key assertion of

balance theory is that individuals gravitate toward social structural positions that are tension free

by modifying their profiles of sentiments to reduce their exposure to intransitivity. Individuals

vary in the extent to which they are exposed to a bundle of intransitive triads. Thus, exposure to

intransitivity is based on the subset of nchoose 3 ijktriads that contain a particular individual

i. Individuals also vary in the extent to which their n-1bundle of sentiments toward others in the

group are perceived as tense relations. Our hypotheses deal with temporal relationships between


16/48

14

these two individual-level bundles of intransitive triads and relational tensions. We use the term

total to refer to these bundles. Two researchable hypotheses, theoretically central to balance

theory, are formulated at the individual-level. Individual-level reductions of exposure to

intransitivity should be associated with prior relational tensions, and individual-level reductions

of relational tension should be associated with reductions of exposure to intransitivity.

H3a: (Temporal Reductions of Intransitivity) Individual-level change of total exposure to

intransitivity is a function of prior total levels of relational tension, such that greater

prior total levels of relational tension are associated with greater total reductions of

exposure to intransitivity.

H3b: (Temporal Reductions of Tension) Individual-level reduction of total relational

tensions is a function of reduction in individuals total exposure to intransitivity, such

that greater reductions of exposure of intransitivity are associated with greater

reductions of relational tension.

DATA AND METHODS

Communes and Sentiments

We test these hypotheses using the Urban Communes Data Set (UCDS) a unique,

multiwave, multimethod study of relatively small, voluntary communities in the United States,

beginning in the 1970s and continuing with additional waves over a period of several years (for

full description, see Zablocki 1980; also, Martin, Yeung, & Zablocki 2001). These data provide a

number of conceptual and methodological advantages over prior studies of balance theory. First,

the data are longitudinalso that, adjusting for individual turnover and a number of communes

that dissolved prior to the first follow up, it is possible to directly assess shifts toward or away


17/48

15

from balance. We make use of this temporal structure with observations at two time points (1974

and 1975). Second, these data contain measures of directed positive sentiments among commune

membersthat is, all commune members were explicitly asked to indicate the tenor of their

relationship with every other member, using numerous relational indicators, including whether or

not a particular relationship was loving and/or tense (with an 80% response rate for the

communes completing the questionnaire). Third, even after omitting communes that disbanded

or lost too many of their initial members to provide triadic analyses (for our purposes, we omit

any of those with fewer than 4 stable members), twenty groups remain suitable for study,

affording greater reliability than previous longitudinal studies of single groups. Finally, because

these groups explicitly formed around a collective identity and the explicit goal of fostering

community, they have the characteristics of Gemeinschaftthat are likely to elicit the proposed

structural dynamics of balance (Davis 1963).

We focus on those loving and tense reported relationships that were present in both

the first and second waves of the UCDS (1974 and 1975), among those members of these groups

who responded to the network questionnaires for both waves. The analysis is based on 135

individuals distributed in twenty communes. The communes we analyze are geographically

diverse, and represent new religious movements, some with charismatic leaders, as well as non-

religious groups. We make no claims concerning the generalizability of findings from these

groups. Rather, we are particularly interested in these groups because if the proposed dynamics

of structural alignment and tensions are likely to manifest clearly in any real world situation, it is

among these surviving communes and their stable members. If they do not present support for

balance theory dynamics, and support for its relational tension assumption, then some greater

level of scrutiny of the theory is warranted. Future research may seek to move away from these


18/48

16

unusual settings in order to address the scope conditions of our emphasis on relational tensions

(see our discussion).

Triadic ModelsHypothesis 1

To test Hypothesis 1, we obtain triad censuses for loving ties within each commune for

each year, and examine aggregated changes in triads across all communes. We examine only

strongly positive sentiments, recoding responses of sometimes loving as non-positive.7

Because we use only stable commune members between the two years, the total number of triads

within each group remains constant over the period, while the distribution of these triads across

the sixteen types may shift. A test of the hypothesis that groups reduce intransitivity is therefore

a straightforward matter of inspecting the total shift in the number of intransitive triads between

the first and second wave compared to transitive and vacuously transitive triads (recall that a

vacuously transitive triad is one that does not violate transitivity because the condition necessary

for a violation does not exist in it; i.e., a sequence ikj of positive sentiments). We compare

the observed triad censuses to a bootstrapped distribution of triad censuses. To do so, for each

year we simulate 1,000 random worlds of sentiment each of which has twenty communes of

the same size and density of ties as those we observe, but where these ties are distributed

according to an Erds-Renyi random distribution (see Newman, Strogatz, and Watts 2001).8 We

7We estimated models that included the sometimes loving as a positive tie, and most significant results

became more pronounced. Because there is no clear guidance for what should be considered a positivesentiment in terms of sometimes responses, we present the more conservative of the two sets of results.8We estimated models using random graphs that conditioned distributions of the triad censuses on the

number of mutual, asymmetric, and null dyads in each network-year. This is commonly referred to as theU|MAN distribution and has been a theoretical baseline for comparison in other triadic approaches. Thisdid not change the direction or substance of our results (figures available on request). Indeed, these

findings were more pronounced when conditioning on these dyadic features, primarily because doing sodecreased the standard deviations of the triad frequencies while having little effect on their means. The

results we present are once again the more conservative of equally plausible approaches.


19/48

17

then compare the distribution of triads of each type in these random worlds to the number we

actually observe. One-tailed tests (using the conventional 5% cutoff for significance) are then

performed on each type of triad in order to assess whether or not in a given year this triad

appears more/less than chance as balance theory would predict, and the extent to which these

departures from random expectations increase or decrease over time.9

Dyadic ModelsHypotheses 2a-2c

To test Hypotheses 2a-2c, we shift our analyses to the dyad levelthat is, each ijordered

pairing of individuals within each commune. We begin by assessing whether or not an

individuals time t designation of a particular relation as tense depends on the extent to which

that relation is embedded in intransitive configurations of sentiment at time t. We then proceed to

assess the extent to which relational tensions motivate sentiment conversions in general, and

specifically conversions that result in larger reductions in intransitive triadic configurations.

Given that the average size of the twenty groups we study has between seven and eight stable

members, this creates between 41 and 48 dyads ([n n]- n) per group, and thereby produces a

dyad dataset of 860 ij observations for each of the two years in the time period.

Dependent Variables. For Hypothesis 2a, the dependent variable is a binary variable

indicating the presence/absence of an i to jtension at time t. A tension is present when a

respondent reports the relationship to be tense or sometimes tense. This is a measure of

directed tension, and eachjobject of tension is also a person ithe dataset. For both Hypothesis

2b and 2c, we estimate three separate models: the probability of a conversion event, the

9We prefer this bootstrap technique to the taustatistic (see Wasserman & Faust 1995: 594), which relieson distributional assumptions. This statistic has long been the subject of debates concerning validity (see

Hallinan 1974: 31-6), and was developed prior to advances in computational power that allow for relativeease in simulating conditional distributions of ties in random networks.


20/48

18

probability of a positive to non-positive conversion event, and the probability of a non-positive

to positive conversion event. The latter two conversion models are estimated on the subset of

dyads in which positive sentiment relations either existed or did not exist, respectively, in the

previous year.

Independent Variables. For Hypothesis 2a, the hypothesized predictor is the ij exposure

to intransitivity based on the subset of n choose 3 ijktriads that contain a particular ijordered

pair. It is the number of the n-2 configurations in this subset at time tthat are intransitive with

respect to i(either +Sij, +Sjk, andSik, orSij, +Sjk, and +Sik).10 For Hypothesis 2b, the focal

predictor is this exposure to intransitivity measure for the first year. For Hypothesis 2c, we

construct a variable that gauges the payoff resulting from converting sentiments with respect to

projected changes in intransitivity based on the configuration of relations at time t=1. This payoff

variable is the number of the intransitive triads in which dyad ij is located that would become

transitive or vacuously transitive if iwere to convert the i toj sentiment (positive to non-positive,

or viceversa). We include the total numberofdyadsas a group-level control in order to account

for inherent differences in the overall probability of selecting or retaining any given member as

an object of tension based on group size.11 We also include an indicator of a directedji

positive sentiment to control for the effects of being the object of positive sentiments on the

likelihood of itensions and sentiment conversions (especially reciprocity in positive sentiments).

10We estimated models using the proportion of intransitive triads and found substantively identicalresults. We also estimated models using an alternate specification of intransitivity that counted triads asintransitive configurations without respect to a focal individual ii.e. those in which iis the object of one

or more misaligned sentiments betweenjand kwere considered identical to those in which theintransitivity exists within i's ego-centered sentiments. Results were largely consistent with those we

present here. We briefly discuss these and other robustness checks in our discussion.11We tested for possible non-linear effects for group size. In some models, we found a significantcurvilinear effect; but this altered neither the direction nor magnitude of predicted effects. Consequently,

we omit such effects from the final models.


21/48

19

Estimation.Dyadic data contain inherent interdependencies in observations, and this has

given rise to various modeling strategies suited to different research goals (e.g. Kenny, Kashy, &

Cook 2006). Because our primary concern is the possibility that such dependencies bias

downward standard errors, we follow the strategy of using multi-way clustering in order to

estimate standard errors, using the estimation procedures outlined in Cameron, Gelbach, and

Miller (2011). A variety of models are amenable to multi-way clustering and can be estimated

with available statistical software. Consequently, this approach is being employed in a growing

number of network analytic studies of dyads (Dahlander and McFarland 2013; Kleinbaum,

Stuart, and Tushman 2013; Rawlings et al. 2014). For Hypothesis 2a, we estimate a logistic

regression predicting the probability of an i toj tension ( 1):

(=)(=) ++ + , (1)

where is abaseline logit of tension when predictors are zero,Iijis the number of intransitive

triads in which the dyad ij is located, Zis a set of controls, and is an error term that is multi-

way clustered for each ijdyad.

For each of Hypotheses 2b and 2c, we estimate three logistic regression models

predicting the conversion of sentiments (any conversion, positive to non-positive, and non-

positive to positive) between t=1 and t=2 as follows:

(=)(=0) + + + , (2)

where is a baseline logit of an ij sentiment persistence into time t=2when predictors are zero.

For Hypothesis 2b,Iij1is the time t=1 number of intransitive triads in which the dyad ij is

located. For Hypothesis 2c,Iij1gauges the projected payoff in reducing the number of intransitive

triads in which dyad ijis embedded through a sentiment conversion. Controls are contained inZ,


22/48

20

including the lagged time t=1 indicator of a positive sentiment of itowardjfor models predicting

any conversion; and is an error term that is multi-way clustered for each ijdyad.

Individual-level ModelsHypotheses 3a and 3b

Hypotheses 3a and 3b deal with changes in an individuals levels of exposure to

intransitive triads and changes in relational tensions, respectively. The unit of analysis for these

models is the individual (N=135) over the entire period.

Dependent Variables. The outcomes of interest are changes for each individual over the

period. For Hypothesis 3a, we examine changes in i's total exposure to intransitivity. We

examine the same triads at times t=1 and t=2 and then calculate a change score gauging the

difference in i's total exposure to intransitivity, such that higher scores indicate greater

reductionsinintransitivity (Ij1- Ij2).12 Here, and henceforth, all summations are overj. For

Hypothesis 3b, we examine changes in the size of each individualsbundle of tensionsthat is,

changes in the number of individuals with whom ihas directed tensions, such that higher scores

indicate greater reductions in tensions(Tj1- Tj2).

Independent Variables. For H3a, the key predictor of change in exposure to intransitivity

is an individuals prior exposure to relational tensions. We therefore include each individual i's

total number of ijtensions. For H3b, the key predictor of a change of relational tensions is the

change in individual is exposure to intransitivity. We therefore use the reductions in

intransitivity variable that is the dependent variable for H3a as the focal predictor in H3b.

12As with the dyad-level models, we calculate exposure to intransitivity using only triads that areintransitive from the standpoint of each focal individual. We estimated the same models using the

alternate specification of intransitivity that included any ijk triad presenting an intransitive sequence,regardless of i's position in that sequence, and found the direction and significance of results to be

unchanged.


23/48

21

Estimation. The dependent variables are normally distributed change scores nested in

communes, and we estimate OLS regression models with standard errors clustered within the

twenty communes. Written at the level of individual i within commune c, the model for H3a

takes the form:

2 + + + , (3)

where is a baseline average i's change in the total number of intransitive triads when other

predictors are at zero,is the number of directed tensions at time t=1, and Zcontains controls.

The model assumption is that relational tensions are conditional independent within communes.

For H3b, the model takes the form:

2 + 2 + + , (4)

where notation is consistent with that described in equation (3).

Table 1 shows descriptive statistics for variables used in the above statistical models.

--Insert Table 1 Here--

RESULTS

Group-level Results

Hypothesis 1. We begin with results bearing on the general structural transformation

hypothesis of balance theory, which asserts that intransitive configurations of positive sentiments

within groups are reduced over time. Figure 3 presents results from the triad censuses for 1974

and 1975. The figure plots the observed frequencies of transitive, vacuously transitive, and

intransitive triads in a given year alongside the bootstrapped random distributions of ties in

groups of the same size and network density as those we observed. The boxes in the figure

present the median and the interquartile range of the random distributions, while the whiskers


24/48

22

present the 95% reference range of the distribution. The single point that is plotted in relation to

this distribution is the observed frequency for that class of triad in the twenty communes. Results

are consistent with prior cross-sectional studies of networks in showing a strong structural

disinclination for intransitivity and a tendency for transitive and vacuously transitive ties.

--Insert Figure 3 Here--

A comparison of triad frequencies in 1974 to 1975 provides support for Hypothesis 1.

Keeping in mind that the total number of triads remains the same over time, there is a clear shift

away from intransitive triads. The proportion of intransitive triads decreases from 24.5% to

14.7% of the total (from 212 to 127 triads) and the departure from the random networks becomes

more pronounced (zdecreases from -7.66 to -7.83). The structure of positive sentiments within

the communes becomes more balanced, even as the overall group density of positive sentiments

decreases. The average number of positive sentiments per individual deceases from 3 to 2.5. The

changing density of positive ties accounts for the different distributions in the randomly

generated networks for the two years. This also helps explain the decrease in the number of

transitive ties and the increase in vacuously transitive ties. While the structure of sentiments is

clearly shifting away from intransitive ties, it is not in absolute numbers moving towardgreater

transitivity. Rather, on average, there is a greater movement away from both intransitive and

transitive ties toward more vacuously transitive triads. When compared to random networks of

the same size and density, the departure from random networks increases for transitive triads (the

z-score increases from 4.31 to 5.15). Although the observed number of vacuously transitive ties

increases considerably, thez-score actually decreases somewhat from 3.57 to 3.33. This points to

the somewhat counter-intuitive overall decrease in positive sentiments in these groups that is

associated with the structural redistribution of these ties toward greater balance.


25/48

23

--Insert Figure 4 Here--

Figure 4 disaggregates the triad census results from Figure 3 into each of the sixteen

isomorphic types of triads. The seven triad types at the top of the graph are intransitive. Here, we

see that, despite the general disinclination for intransitivity, there are significant differences at

the triad level in terms of how much triads depart from random expectations. For example,

within the class of intransitive triads, we find one intransitive triad type (111U) that (contrary to

our prediction) occurs more frequently than predicted by chance. Triads of the 111 type have

also been found to occur more frequently than expected by other investigators (Holland &

Leinhardt 1971; Srenson & Hallinan 1976). Srenson & Hallinan (1976) attribute the anomaly

to the high probability that triads often must transition through this type of triad on their way to

greater transitivity.

However, looking across all triads, the pattern of frequencies suggests something more

than transition probabilities at work. This something moreis illustrated in the differences

between types of triads that have the same transition probabilities but different observed

frequencies. While the 021D and 021U triad have the same likelihood of appearing with respect

to transition rates, one appears more likely than chance while the other appears less likely than

chance. These differences become more pronounced over the period. A similar difference can be

found between the 111U and the 111D triads, which once again share the same transition

probability, but differ markedly in terms of frequency. The third comparison between the 120D

and 120U triads shows a similar difference. We suspect that such differences have to do with a

tendency among these individuals to experience tension where there is a more unequal

distribution of positive ties, a tendency that may be specific to communal settings with an ethos

of universal love. If we measure inequality as the concentration of received loving ties (for


26/48

24

example, using a Herfindahl index, such that H= [Indegreei/N]2 + [Indegreej/N]

2 +[Indegreek/N]

2), then each of the paired triads differ with respect to this concentration with one having a

greater amount of concentration/inequality (e.g. H[111U] = .327; H[111D] = .546). In each case,

the triad type with more unequal distribution of positive sentiments occurs less frequently and

the type with more equality appears more frequently than in random distributions. The greater

frequency of these more equal triads is also inconsistent with interpretations of the prevalence of

transitive social structures as derivative of contexts that generate and promote unequal

popularity.13

Dyad-Level Results

Hypothesis 2a. We begin our dyad-level analyses by evaluating the cross-sectional

prediction that exposure to intransitivity is positively associated with relational tension. Table 2

shows results from logit models predicting the likelihood of relational tensions among commune

members as a function of exposures to intransitive configurations of sentiments in a given year.

Results support Hypothesis 2a. For both 1974 and 1975, the greater the number of intransitive

triads in which a sentiment relation is embedded, the greater the likelihood that ireports the

relationship withjas tense. For each additional intransitive triad in which a sentiment is

embedded in 1974, we would expect to see a 52% increase in the odds of there being a relational

tension (exp[.419]=1.52). The magnitude of the effect of intransitive triads on tensions decreases

somewhat over time.14

13The difference here is also likely due to different operationalizations of positive ties. While we includeall stated ties, Feld and Elmore (1982) use a fixed small number of friendships per individual.14This may be a random fluctuation, or it may indicate that interpersonal tensions tend to become less

structural and more personal in nature as groups shift toward greater balance. Without at least anadditional data point, we are unable to infer such a trend.


27/48

25


Hypotheses 2b & 2c. Structural transformations of sentiment structures are motivated by

relational tensions that arise from intransitive triadic configurations. Having established the

cross-sectional association of intransitivity and tension, we evaluate whether the extent to which

a dyad is located within intransitive triads predicts the likelihood of converting the i toj

sentiment. Table 3 presents results from logistic regression models predicting conversions of

sentiments based on prior levels of intransitivity. There is support for Hypothesis 2b, which

posits that the likelihood of a sentiment conversion (both non-positive to positive and viceversa)

increases as exposure to intransitivity increases. Model 1 shows a significant effect of

intransitivity on the overall likelihood of either type of conversion. For each additional

intransitive triad contextualizing a given sentiment, we would expect to see a 40% increase in the

odds of sentiment conversion (exp[.34]=1.405). Models 2 and 3 distinguish conversions by type

and show that intransitivity is somewhat more likely to trigger non-positive to positive

sentiments conversions than viceversa. These results also indicate that interpersonal tensions

reinforce the negative sentiment relation, making conversions to positive sentiments less likely

than in equally intransitive relationships without tensions. We also find a significant effect for

reciprocity in the conversion of non-positive sentiments.

Table 4 presents results supporting Hypothesis 2c. The models predict sentiment

conversions based on the projected payoff in reductions of intransitivity resulting from a given

conversion. The model 1 results support our hypothesis that the greater the intransitivity-

reduction payoff of a conversion, the more probable the conversion. Results are consistent with

those in Table 3. However, comparing the magnitude of effects across these two tables shows

that the payoff specification is a stronger predictor of conversions than prior levels of


28/48

26

intransitivity, especially for conversions from positive to non-positive sentiments.15 For each

unit of intransitivity-reduction payoff of a particular conversion, we would expect to see an 83%

increase in the odds of converting that sentiment (exp[.603]=1.83).

--Insert Tables 3 & 4 Here--

Individual-Level Results

Hypothesis 3a. Table 5 presents results from regressions at the individual level,

predicting changes in total number of intransitive triads over the period. Results support

Hypothesis 3a. Larger reductions of intransitivity are instigated by higher levels of tensions. For

each additional relational tension toward another commune member in the base year, there is a

predicted individual-level reduction of 1.62 intransitive triads over the period.


Hypothesis 3b. Table 6 shows results from models predicting changes in the total number

of an individuals relationaltensions toward commune members as a function of changes in an

individuals total number ofintransitive triads. Results support Hypothesis 3b. Individuals with

larger reductions in total exposures to intransitivity experienced greater reductions in the number

of relational tensions. For each unit reduction in the number of intransitive triads, there is a

predicted reduction of .085 felt tensions. In other words, for approximately every 12 fewer

intransitive triads per individual, we would expect a reduction of one relational tension over the

same period.


15We estimated models including both variablesi.e. the time t=1 level of intransitivity and the projected

payoff for making a sentiment conversion. Due to the high level of correlation among these variables(r=.8), it was not possible to partial out their unique contributions on sentiment conversions in these data,

net of other effects, and both variables were rendered non-significant.


29/48

27

DISCUSSION

The balance theory of sentiment relations seeks to explain the structural dynamics of sentiment

networks in groups of acquainted individuals. It presents a fascinating set of structural

propositions on how sentiment networks alter over time as each individual seeks to find or retain

a tension-free position within the network. The postulated dynamics present predictions of the

evolution of a group toward particular generic forms of macrostructure. While there has been

considerable support for the theorys emphasis on theimportance of intransitivity reductions, the

key tension-reduction basis of the theory has remained largely untested, and based on inferences

in cross-sectional studies of single groups. Our findings broaden and deepen the empirical

supports for the balance-theoretic approach to sentiment change.

In addition to providing stronger confirmation of the predicted group-level structural

dynamics of balance than in previous studies, we were able to explicitly link group-level flights

from intransitivity to dyad and individual dynamics of relational tension reductions and

sentiment conversions. Our findings trace a causal sequence in which the more intransitive triads

contextualizing a given dyad the more likely the existence of a directed tension; thus, greater

intransitivity increases the likelihood of sentiment conversions, especially when the payoffs of

such conversions would produce greater reductions in levels of individual exposure to

intransitivity. Balance theory posits an intimate relationship between individual-level bundles

of total tension and total intransitivity, such that more tensions precipitate larger temporal

reductions in intransitivity, and larger temporal reductions in intransitivity produce greater

reductions in total interpersonal tensions. We do not assert that interpersonal tension is the only

factor generating such structural dynamics, or that all tensions arise from intransitive relations.


30/48

28

Balance theory posits an intimate relationship among these two individual-level quantities, which

should be manifested in the communes that we have studied; the absence of such a relationship

would strongly contradict balance theorysclaims. Our findings offer a consistent set of

confirmations of the core postulates of balance theory at the levels of groups, dyads, and

individuals.

We performed a number of robustness checks on the sensitivity of the findings to our

methodological decisions. As we have noted throughout the text, our modeling choices have

been geared toward generating conservative lower-bounds for the point estimates of

hypothesized effects. We have re-estimated models using an alternative measure of positive

sentiments, given the possibility that the reported loving ties in the context of communes were

different than other positive sentiments, or that different understandings of what love means in

different communes skewed our results (see Yeung 2005; also Swidler 2001). In this check on

robustness, instead of defining positive ties as loving ties, we defined them as the absence of

negative emotions, re-estimating models using non-hateful ties that is, positive sentiments

are inferred when individuals report that they didnt hateone another. This alternate specification

produced very similar results. We also examined overall shifts toward transitivity that allowed

for group turnover; these analyses presented altered estimates, but maintained the pattern of

hypothesis test conclusions. Finally, we re-estimated all dyad- and individual-level models using

a more relaxed measure of intransitivity that counted any ijktriad as intransitive if it presented at

least one intransitive sequence, regardless as to whether or not i had any directed positive

sentiment toward eitherjor k. The overall modest weakening of findings from these models

suggests that individuals are more attentive to their own proximate relations than others

relations within their triads.


31/48

29

Future research may choose to move beyond the scope of this somewhat unusual setting

in order to see the extent to which these findings hold, as well as to better identify results that

might be distinct to communal settings. The communes we studied show a pronounced structural

disinclination toward hierarchy in the structure of loving ties that cuts across classes of

transitivity. The observed resistance to hierarchical sentiment structures may be related to the

universal loving ethos of many of these intentional communities, which is in contrast to those

groups studied by others. For example, friendships in the context of schools would seem to be

precisely the kind of context that is likely to manifest status orders due to various popularity

tournaments (see Martin 2009: 64-7), and may therefore require some modified understanding of

the links between tensions and triads that takes into account the institutional context.

A number of our empirical findings merit further examination and, in particular, our

finding that the payoffs of particular sentiment conversions are stronger predictors than the prior

levels of intransitivity. If such a finding holds in contexts where the measure of payoffs is not as

strongly correlated with levels of intransitivity, then this would bear on arguments concerning

the automaticity vs. the deliberative cognitive underpinnings of sentiment network dynamics.

Results suggested that such deliberative processes may be especially important in the conversion

of positive sentiments to negative sentiments; while conversions of negative to positive may be

more automatic in nature. Such future refinements and additional analyses may provide

important elaborations of the scope conditions and social psychological mechanisms for social

network theory as sentiments undergird various relations that are the bases of influence (Friedkin

& Johnsen 2011) and information flows (Granovetter 1979).

We have investigated the dynamics of sentiment structures using the general definition of

structural balance as the absence of intransitivity. More restrictive definitions of balance are


32/48

30

special cases of this definition. They are restrictive with respect to the number of triad types that

they forbid. Having found support for this general definition, averaged across the twenty

communes, future work could proceed by looking at variation among communes with respect to

more restrictive definitions of balance. These communes differ markedly in terms of their power

and authority relations, and these differences have been linked to the different belief systems of

these groups (Bradley 1999; Martin 2001). Based on this variation between communes,

researchers may be able to determine which groups are more likely to resemble Heiders original

notion of balanceperhaps due to a strongly Manichean worldview (i.e. a cult-like us vs. them

belief system)and which are more likely to resemble Davis (1967) clustered hierarchies

(perhaps due to charismatic leaders, formal ranks, and clearer status hierarchies within the

group). We would strongly expect that the types of triads that are most tension-laden will differ

according to such group-level differences in culture and authority, because such cultural contexts

impact what love is for these groups (see Yeung 2005), and consequently what the absence of

a loving tie implies in terms of balance.

Finally, we examined only surviving communes, because these allowed us to create the

longitudinal networks that are so rare in testing models of structural dynamics. However, a large

number of the roughly 60 communes in the original survey were disbanded between 1974 and

1976. Zablocki (1980) has already shown that these disbanded communes actually tended to be

more densely loving. Our approach suggests that the more consequential differences between

these disbanded groups and those that survived may have more to do with the structural features

of interpersonal sentiments in these communes than their volume of positive sentiments (see

Bradley 1999). Some of these groups may form balanced sentiment structures based on a

connected network of positive sentiments composed of ranked clusters and asymmetric


33/48

31

(unreciprocated) positive sentiments. The emergence of such hierarchical structures are

consistent with balance theory, but so are disconnected (clustered ) structures composed of

multiple subgroups with all positive within-group sentiments and all non-positive between-group

sentiments. In avoiding tension, some groups may fall into greater fragmentation, while others

achieve a more integrated state.


34/48

32

REFERENCES

Abell, Peter. 1968. Structural Balance in Dynamic Structures. Sociology2: 333-52.

Abell, Peter, and M. Ludwig. 2007. An Evolutionary Model of Social Networks.European

Physical Journal B, 58: 97-105.

Aderman, David. 1969. Effects of Anticipating Future Interaction on the Preference for

Balanced States.Journal of Personality and Social Psychology11: 214-19.

Antal, T., P.L. Krapivsky, and S. Redner. 2005. Dynamics of Social Balance on Networks.

Physical Review E 72 036121

Bradley, Raymond T. 1999. Charisma and Social Structure: A Study of Love and Power,

Wholeness and Transformation.New York: toExcel

Cameron, A. Colin, Jonah Gelbach, and Douglas L. Miller. 2011. Robust Inference with

Multiway Clustering.Journal of Business and Economic Statistics29: 238-49.

Cartwright, Dorwin, and Frank Harary. 1956. Structural Balance: A Generalization of Heiders

Theory.Psychological Review63: 277-93.

Crano, William D., and Ralph E. Cooper. 1973. Examination of Newcombs Extension of

Structural Balance Theory.Journal of Personality and Social Psychology27: 344-53.

Dahlander, Linus, and Daniel McFarland. 2013. Ties that Last: Tie Formation and Persistence

in Research Collaborations over Time.Administrative Science Quarterly58: 69-110.

Davis, James A. 1963. Structural Balance, Mechanical Solidarity, and Interpersonal Relations.

American Journal of Sociology68: 444-62.

Davis, James A. 1967. Clustering and Structural Balance in Graphs.Human Relations 20: 181-

87.

Davis, James A. 1970. Clustering and Hierarchy in Interpersonal Relations: Testing Two


35/48

33

Theoretical Models on 742 Sociograms.American Sociological Review 35:843-52.

Davis, James A. 1979. The Davis/Holland/Leinhardt Studies: An Overview. Pp. 51-62 in Paul

Holland and Samuel Leinhardt (eds.)Perspectives on Social Network Research. New

York: Academic Press.

Davis, James A., and Samuel Leinhardt. 1972. The Structure of Positive Interpersonal Relations

in Small Groups. Pp. 218-51 in Sociological Theories in Progress(Joseph Berger,

Morris Zelditch, and Bo Anderson, eds.). Boston: Houghton Mifflin.

Doreian, Patrick, and David Krackhardt. 2001. Pre-Transitive Balance Mechanisms for Signed

Networks.Journal of Mathematical Sociology25: 43-67.

Doreian, Patrick, Roman Kapuscinski, David Krackhardt, and Janusz Szczypula. 1996. A Brief

History of Balance through Time.Journal of Mathematical Sociology21: 113-131.

Durkheim, Emile. 1933 [1893]. The Division of Labor in Society(George Simpson, trans.).

Glencoe, IL: Free Press.

Feld, Scott L. 1981. The Focused Organization of Social Ties.American Journal of Sociology

86: 1015-35.

Feld, Scott L., and Richard Elmore. 1982. Patterns of Sociometric Choices: Transitivity

Reconsidered. Social Psychology Quarterly45: 77-85.

Festinger, Leon. 1957.A Theory of Cognitive Dissonance. Stanford, CA: Stanford University

Press.

Friedkin, Noah E. 1998.A Structural Theory of Social Influence.New York: Cambridge

University Press.

Friedkin, Noah E., and Eugene C. Johnsen. 2011. Social Network Influence Theory: A

Sociological Examination of Small Group Dynamics. New York: Cambridge University


36/48

34

Press.

Fuller, Carol H. 1974. Comparison of Two Experimental Paradigms as Tests of Heiders

Balance Theory.Journal of Personality and Social Psychology30: 802-6.

Granovetter, Mark. 1973. The Strength of Weak Ties.American Journal of Sociology78:

1360-80.

Granovetter, Mark. 1979. The Theory Gap in Social Network Analysis. Pp. 501-18 in

Perspectives on Social Network Research (P.W. Holland & S. Leinhardt, eds.). New

York: Academic Press.

Greenwald, Anthony, Mahzarin R. Banaji, Laurie A. Rudman, Shelly D. Farnham, Brian A.

Nosek, Deborah S. Mellott. 2002. A Unified Theory of Implicit Attitudes, Stereotypes,

Self-Esteem, and Self-Concept.Psychological Review 109:3-25.

Hage, Per. 1976. Structural Balance and Clustering in Bushmen Kinship Relations.Behavioral

Science 21: 36-47.

Hallinan, Maureen T. 1974. The Structure of Positive Sentiment. New York: Elsevier.

Hallinan, Maureen T., and Edwin E. Hutchins. 1980. Structural Effects on Dyadic Change.

Social Forces59: 225-45.

Heider, Fritz. 1946. Attitudes and Cognitive Orientation.Journal of Psychology 21: 107-12.

Holland Paul W., and Samuel Leinhardt. 1971. Transitivity in Structural Models of Small

Groups. Comparative Group Studies2: 107-24.

Homans, George. 1950. The Human Group. New York: Harcourt, Brace

Hummell, Hans, and Wolfgang Sodeur. 1987. Strukturbeschreibung von Positionen in Socialen

Beziehungsnetzen. In Pappi, F.U. (ed.) Methoden der Netzwerkanalyse. Munich:

Oldenbourg.


37/48

35

Hummon, Norman P., and Patrick Doreian. 2003. Some Dynamics of Social Balance Processes:

Bringing Heider Back into Balance Theory. Social Networks25: 17-49.

Johnsen, Eugene. 1985. Network Macrostructure Models for the Davis-Leinhardt Set of

Empirical Sociomatrices. Social Networks7: 203-24.

Kahneman, Daniel. 2003. A perspective on judgment and choice: Mapping bounded

rationality. American Psychologist 58: 697-720.

Kenny, David A., Deborah A. Kashy, William L. Cook. 2006.Dyadic Data Analysis. New York:

Guildford Press.

Kleinbaum, Adam M., Toby Stuart, Michael L. Tushman. 2013. Discretion within Constraint:

Homophily and Structure within a Formal Organization. Organization Science 24:1313-

1336.

Kossinets, Gueorgi, and Duncan Watts. 2009. Originsof Homophily in an Evolving Social

Network.American Journal of Sociology115: 405-50.

Krackhardt, David. 1992. The Strength of Strong Ties. Pp. 216-38 inNetworks and

Organizations: Structure, Form, and Action (N. Nohria and R. Eccles, Eds.). Boston,

MA: Harvard Business School Press.

Kulakowski, Krzysztof, Przemyslaw Gawronski, and Piotr Gronek. 2005. The Heider Balance:

A Continuous Approach.International Journal of Modern Physics C16: 707-16.

Lawler, Edward J. 2001. An Affect Theory of Social Exchange.American Journal of

Sociology107: 321-52.

Macy, Michael, and Robb Willer. 2002. From Factors to Actors. Annual Review of Sociology

28:143-66.

Martin, John Levi. 2002. Power, Authority, and the Constraint of Belief Systems. American


38/48

36

Journal of Sociology107: 861-904.

Martin, John Levi. 2009. Social Structures.Princeton, NJ: Princeton University Press.

Martin, John Levi, King-To Yeung, and Benjamin Zablocki. 2001. The Urban Communes Data

Set: A Gold Mine for Secondary Analysis. Connections 24:54-8.

Marvel, Seth A., Jon Kleinberg, Robert D. Kleinberg, and Steven H. Strogatz. 2011. Continuous

Time Model of Structural Balance.Proceedings of the National Academy of the

Sciences108 (5): 1771-1776.

Montgomery, James. 2009. Balance Theory with Incomplete Awareness.Journal of

Mathematical Sociology33:69-96.

Newcomb, Theodore M. 1961. The Acquaintance Process. New York: Holt, Rinehart, and

Winston.

Newcomb, Theodore M. 1968. Interpersonal Balance. In Newcomb, T.M., Turner, R.H., and

Converse, P.E. (eds.) Social Psychology. New York: Holt, Rinehart, and Winston.

Newman, M.E.J., Steven Strogatz, and Duncan Watts. 2001. Random Graphs with Arbitrary

Degree Distributions and Their Application.Physical Review E64:1-17.

Opp, Karl-Dieter. 1984. Balance Theory: Progress and Stagnation of a Social Psychological

Theory.Philosophy of the Social Sciences 1984: 27-49.

Osgood, Charles, and Percy Tannenbaum. 1955. The Principal of Congruity in the Prediction of

Attitude Change.Psychological Review62: 42-55.

Press, Allan N., Walter H. Crockett, Paul S. Rosenkrantz. 1969. Cognitive Complexity and the

Learning of Balanced and Unbalanced Social Structures.Journal of Personality37: 541-

553.

Rawlings, Craig M., Daniel McFarland, Linus Dahlander, and Dan Wang. 2014. Streams of


39/48

37

Thought: Research Collaborations and Knowledge Flows. Working Paper, Dept. of

Sociology, UC-Santa Barbara.

Simmel, Georg. 1950. The Sociology of Georg Simmel(Kurt Wolff, trans.). Glencoe, IL: Free

Press.

Simmel, Georg. 1955. Conflict and the Web of Group Affiliations(Reinhard Bendix, trans.).

Glencoe, IL: Free Press.

Snijders, Tom, Gerhard G. van de Bunt, and Christian E.G. Steglich. 2010. Introduction to

Stochastic Actor-Based Models for Network Dynamics. Social Networks32: 44-60.

Srenson, Aage, and Maureen T. Hallinan. 1976. A Stochastic Model for Change in Group

Structure. Social Science Research 5: 43-61.

Swidler, Ann. 2001. Talk of Love: How Culture Matters. Chicago: University of Chicago Press.

van Rijt, Arnout. 2011. The Micro-Macro Link for the Theory of Structural Balance. The

Journal of Mathematical Sociology35: 94-113.

Wang, Zhigang, and Warren Thorngate. 2003. Sentiment and Social Mitosis: Implications of

Heiders Balance Theory.Journal of Artificial Societies and Social Simulations6 (3).

Yeung, King-To. 2005. What Does Love Mean? Exploring Network Culture in Two Network

Settings. Social Forces84: 391-420.

Zablocki, Benjamin. 1980.Alienation and Charisma: A Study of Contemporary American

Communes. New York: The Free Press.


40/48

38

TABLE 1

Descriptive Statistics for Variables Used in Regression Models

Variable N Mean/Proportion Std. Dev. Min Max

Dyad-level Models: Hypotheses 2a-2cRelational i jTension Time t=1 860 0.215 0.411 0 1Relational i jTension Time t=2 860 0.203 0.403 0 1Exposure to Intransitivity Time t=1 860 0.591 1.123 0 7Exposure to Intransitivity Time t=2 860 0.340 0.819 0 8

Positive i jSentiment Time t=1 860 0.501 0.500 0 1Positive i jSentimentTime t=2 860 0.409 0.492 0 1

Payoff of a Conversion 860 0.284 0.908 0 7Sentiment Conversion 860 0.292 0.455 0 1Positive to Non-Positive Sentiment Conversion 860 0.192 0.394 0 1

Non-Positive to Positive Sentiment Conversion 860 0.100 0.300 0 1Positivej iPositive Sentiment Time t=1 860 0.501 0.500 0 1

N Dyads in the Commune 860 63.033 36.280 12 132

Individual-level Models: Hypotheses 3a-3bChange in Total Individual Intransitivity 135 1.600 6.286 -24 18

Change in Total Relational Tensions 135 0.074 1.847 -8 7Total Individual Tensions Time t=1 135 1.370 1.520 0 7Total Individual Positive Sentiments Time t=1 135 3.193 2.604 0 8

N Dyads in the Commune 135 51.763 33.301 12 132


41/48

39

TABLE 2.

Hypothesis 2a: Logit Models Predicting the Likelihood of ijTensions

among Commune Members by Year

Variable 1974 1975

Exposure to Intransitivity Time t 0.419*** 0.276*

(0.084) (0.120)

Positive i jSentiment Time t 0.283 0.484

(0.243) (0.263)

Number of Dyads in the Commune -0.032*** -0.018***

(0.005) (0.005)

Constant -0.073 -0.693*

(0.324) (0.347)

Number of observations 860 860Degrees of freedom 3 3

* p


42/48

40

TABLE 3

Hypothesis 2b: Logit Models Predicting Conversions of Sentiments

Based on Prior Levels of Intransitivity

Variable Any Conversion Positive toNon-Positive Non-Positive toPositive

Exposure to Intransitivity at Time t=1 0.340*** 0.287* 0.428**

(0.087) (0.127) (0.145)

PositiveijSentiment at Time t=1 0.906*

(0.377)

Relational ijTension at Time t=1 0.012 0.159 -0.403*

(0.094) (0.130) (0.179)

PositivejiSentiment at Time t=1 0.269 -0.177 0.942**

(0.217) (0.250) (0.362)

Number of Dyads in the Commune 0.004 0.019* -0.006

(0.005) (0.008) (0.009)

Constant -2.010*** -1.818*** -1.210*

(0.415) (0.543) (0.549)

Number of observations 860 431 429

Degrees of freedom 5 4 4

* p


43/48

41

TABLE 4

Hypothesis 2c: Logit Models Predicting Conversions of Sentiments

Based on the Payoffs of Reductions of Intransitivity

VariableAny

ConversionPositive to Non-

PositiveNon-Positive to

Positive

Payoff of a Conversion 0.424*** 0.603** 0.478***

(0.126) (0.209) (0.138)

PositiveijSentiment at Time t=1 0.950*

(0.377)

Relational ijTension at Time t=1 0.055 0.198 -0.352*

(0.090) (0.128) (0.164)

PositivejiSentiment at Time t=1 0.359 -0.13 1.094**

(0.211) (0.243) (0.352)Number of Dyads in the Commune 0.005 0.022** -0.006

(0.005) (0.008) (0.009)

Constant -2.126*** -1.964*** -1.262*

(0.424) (0.563) (0.543)

Number of observations 860 431 429

Degrees of freedom 5 4 4

* p


44/48

1

TABLE 5

Hypothesis 3a: OLS Regression Models

Predicting Changes in Total Individual Intransitivity

Note: Standard errors are clustered at the commune level.

Variable (1)

Total Individual Tensions Time t=1 1.619** (0.426)

Total Individual Positive Sentiments Time t=1 -0.157 (0.259)

Number of Dyads in the Commune 0.026 (0.016)

Constant -1.436 (0.953)

Number of observations 135

Degrees of freedom 3

* p


45/48

2

TABLE 6

Hypothesis 3b: OLS Regression Models

Predicting Changes in Total Individual Tensions

Variable (1)Change in Total Individual Intransitivity 0.085* (0.033)

Total Individual Positive Sentiments Time t=1 -0.009 (0.074)

Number of Dyads in the Commune -0.007 (0.006)

Constant 0.317 (0.476)

Number of observations 135

Degrees of freedom 3

* p


46/48

1

FIGURE 1. Sixteen Isomorphic Triad Types by Transitivity Class

Transitive

Vacuously Transitive

Intransitive

030T 120D 120U 300

003 012 021U 021D 102

021C 111U 111D 030C 201 120C 210


47/48

2

FIGURE 2. Triads of Positive Sentiments Ties in 20 Communes (Observed Frequencies

and Distributions from Random Networks of the Same Size and Density)

Transitive


Intransitive

100 200 300 400 500 600Count

Triad Census 1974

Transitive


Intransitive

100 200 300 400 500 600Count

Triad Census 1975


48/48

FIGURE 3. Triads of Positive Sentiments in 20 Communes by Triad Type (Observed

Frequencies and Predicted Distributions)

003

012

102

021D

021U

021C

111D

111U

030T

030C

201

120D

120U

120C

210

300

0 50 100 150 200 250

Count

Triad Census 1974

003

012

102

021D

021U

021C111D

111U

030T

030C

201

120D

120U

120C

210

300

0 50 100 150 200 250

Count

Triad Census 1975

rawlings friedkin balance

Documents