Modeling social processes
with network analysis
Emmanuel Lazega
Institute of sociology
University of Lille 1
European Science Foundation
QMSS Workshop
Ljubljana, July 2005
1
Basic neo-structural sociology I
• The main concept: resource interdependencies between actors
(individual or collective).
• Relationships as resources and commitments. Resources can be
economic and social. Structures as regularities in flows of
resources and stable commitments.
• Relational structures as one determinant, out of many, of
individual behaviour and of collective behaviour.
• Managing interdependencies in power relationships (for
example to escape situation of open competition for resources,
to put others in situations of open competition, etc.).
• Actors who manage their interdependencies are also capable of
observing them. They can endogenize the structure and
politicize their exchanges, i.e. invest in relationships with
particularistic interests in mind (social niches, status
competition, etc.), but also general interests and derived
satisfactions. Hence endogenous change.
2
Basic neo-structural sociology II
• This management of interdependencies leads to a complex
social discipline (that is recognized as legitimate by the
members).
• Social discipline can be approached as a set of social
processes or social mechanisms traditionnally studied by
sociologists: solidarity, social control, regulation, learning,
etc. [See Hedström and Swedberg (1988) for a review].
• Social processes have a relational dimension and can thus be
examined by network analysis.
• Network analysis is a method that helps in modeling these
processes and in looking at this complex social discipline.
[There is no « network theory » per se]. It can be used by
institutional, structuralist, or RC theorists alike.
• We are at the beginning of a period of our discipline which
will mainly improve modeling and analyses of such
processes. And perhaps derive new theory from this work.
3
A case study
• Deconstructing and modeling social processes at Sue,
Grabbit & Run, a corporate law partnership. Dataset
available for reanalyses or further analyses.
• The Collegial phenomenon, OUP, 2001.
Background:
• What do corporate lawyers do? Litigation and corporate work.
• Division of work and resource interdependencies.
• Three offices, no departments, built-in pressures to grow, intake and
assignment rules.
• Partners and associates: hierarchy, up or out rule, billing targets.
• Partnership agreement (sharing benefits equally, 90% exclusion rule,
governance structure, elusive committee system) and incompleteness
of the contract.
• Informal, unwritten rules (ex: no moonlighting, no investment in
buildings, no nepotism, no borrowing to pay partners, etc.).
• Huge incentives to behave opportunistically and social processes that
makecooperation among rival partners possible.
4
71 attorneys
5
Three social processes at SG&R
• Social processes have a relational
dimension that can be used to characterize,
model and compare them
-Solidarity
-Control
-Regulation
6
Sociometric name generators used
to elicit coworkers, advice, and ‘friendship’ ties at SG&R
"Here is the list of all the members of your Firm.
Strong coworkers network: "Because most firms like yours are also organized very informally,
it is difficult to get a clear idea of how the members really work together. Think back over the
past year, consider all the lawyers in your Firm. Would you go through this list and check the
names of those with whom you have worked with. [By "worked with" I mean that you have spent
time together on at least one case, that you have been assigned to the same case, that they read or
used your work product or that you have read or used their work product; this includes
professional work done within the Firm like Bar association work, administration, etc.]"
Basic advice network: "Think back over the past year, consider all the lawyers in your Firm. To
whom did you go for basic professional advice? For instance, you want to make sure that you are
handling a case right, making a proper decision, and you want to consult someone whose
professional opinions are in general of great value to you. By advice I do not mean simply
technical advice."
‘Friendship’ network: "Would you go through this list, and check the names of those you
socialize with outside work. You know their family, they know yours, for instance. I do not mean
all the people you are simply on a friendly level with, or people you happen to meet at Firm
functions."
7
Day 1. Solidarity
• Measuring the relational dimension of
solidarity:
- Cohesion
- Direct and indirect reciprocity
8
Cohesion in general
9
Cohesion in the firm: relational stitches
10
Solidarity via structural equivalence
• Burt’s solution for structural
equivalence in Structure (4.2)
• Detector: Euclidean distance
• Social distance, Katz’s (1954)
transformation:
N is the number of
individuals that i can reach
regardless of the number of
steps. F is the number of
individuals that i can reach
by doing the minimum
number of steps that are
necessary to reach j.
z  1 ( f N )
ij
ij
i
11
Solidarity via structural equivalence : welfare
and patronage in access to clients and work
• Intake and assignment rule.
• Analysis of strong
coworkers network.
• RED sets.
• Access to pools of associate
manpower.
• Schedulers vs. rainmakers.
• Competing forms of
solidarity (‘welfare’ and
clientelism) and firm
integration.
12
Another example:
Structure 4.2. blocks in advice network at SG&R
13
Social Niches
• Multiplex, multifunctional blocks
• Dense blocks are called
social niches (see
diagonal values in
density tables)
14
Density tables
15
Assigning people to blocks via Pajek
16
17
18
19
Structural equivalence in advice network at SG&R
Pajek solution (Ward
clustering, hierarchical
indirect approach) and
Structure solution are
identical (modulo
Katz’s transformation,
use of Euclidean
distance, and
assignments in the
residual category in
Structure).
20
Comparing Pajek-Structure solutions
• Anuska’s comment:
The fact that the hierarchical indirect approach of
blockmodeling that is run on Pajek is so similar to the
Structure approach is due to the fact that both approaches have
the same 'greedy' effect. When two units are merged together
they stay together in the later stage regardless of the fact that it
could be better if they could be assigned to another cluster. See
about this effect the chapter on cluster analysis in the
Blockmodeling book or on the indirect aproach to
blockmodeling.
21
Pajek pictures of the decomposition of
the three networks into social niches ?
22
Structure 4.2. blocks in advice network at SG&R
23
Solidarity at the local level
• p2 models for statistical analyses at the dyadic
level (Van Duijn and Snijders)
• p* models higher order (especially triadic
level) statistical analysis (Pattison, Robbins,
Wasserman, et al.)
24
p2 models and solidarity
25
Reciprocity and economic performance:
Example of Blau ties
• Dyadic decomposition
of a network can be
useful for all sorts of
purposes.
• Blau’s exchange of
advice for recognition
of status
26
Confirmation: variables explaining performance
27
Using p* models and their nomenclature for detection of
solidarity (especially indirect reciprocity)
 15 _ a
 14 _ a, b
 13 _ a, b
 12 _ a, b
 11_ a, b
j
j
j
j
j
i
a
i
a
i
b
k
a
i
b
k
a
i
a
b
 10 _ a, b,c
 9 _ a, b,c
 8 _ a, b,c
 7 _ a, b,c
 6 _ a,b,c,d
j
j
j
j
j
a
i
b
a
k
c
j
c
b
k
c
b
i
a
k
c
b
i
a
k
i
k
a b
d
k
c
 5 _ a,b,c,d
 4 _ a,b,c,d
 3 _ a,b,c,d
 2 _ a, b,c,d,e
 1_ a,b,c,d,e,f
j
j
j
j
j
a
i
k
b
k
c
d
b
a
k
i
c
d
b
k
a
i
c
d
a b
b
k
i
c
d
e
k
a b c d
e k
i
f
Symbols a, b, c, d, e and f refer to any uniplex or multiplex tie.
Symbols i, j and k represent any three actors, with i  j  k.
28
Example: the coworkers’ network at SG&R
29
Some substructures from the univariate
model for the cowork relation
(extracted from Table 3.4)
W
W
W
(Restricted exchange
in Levi-Strauss’ terms)
4.45 (.47)
-3.49 (.25)
W
W
W
(Generalized exchange
in Levi-Strauss’ terms)
.30 (.06)
30
More complex forms of reciprocity:
Configurations corresponding to multivariate p* parameters
W (cowork), A (advice), F (friendship), WA (cowork and advice), WF (cowork and friendship),
AF (advice and friendship), WAF (cowork, advice and friendship)
Cowork and Advice:
Advice and Friendship: Cowork and Friendship:
Strong interdependence Strong interdependence Weak interdependence
WA
AF
2.44 (.13)
WF
2.42 (.22)
.56 (.17)
A
W
W
F
F
A
.61 (.21)
AF
W
AF
W
W
.13 (.02)
A
FW
F
A
-1.13 (.23)
31
A
Summary of p* results on solidarity
• Solidarity is partly based on the possibility of
multiplex exchanges (which take different forms in
different contexts).
• The interplay of relationships among members helps
in cultivating and mitigating status competition
among peers.
32
Back to the specific example of
advice network at SG&R
Blockmodels, p2 and p* models show that solidarity
exists in transfers of advice and that it takes
several forms.
Advice relationships have special characteristics:
• Flows are very centralized (status games) and one rarely
seeks advice from people « below » in the pecking order.
• There are ‘lateral’ exchanges of advice and reciprocity (but
no generalized exchange).
• Advice, collaboration, and friendship : complex
interdependencies showing role and embeddedness of
advice ties in other kinds of ties.
33
p* decomposititon in Pajek?
34
Triads counts for pattern search
35
Vlado’s solutions for direct and
indirect reciprocity
Representing the number of cycles each relation
belongs to and the people who are most active in
generalized exchange.
36
Day 2. Social control
• Social control as a generic process: dealing with
opportunistic behaviour, a decisive dimension of
collective action.
• Partners locked themselves in a cooperative situation.
This creates enormous incentives for opportunistic
behaviour, and a need for self-policing.
• Opportunistic behaviour at SG&R: shirking,
grabbing, leaving (anything that is perceived by
members as betraying the definiton of relationships as
commitments).
• Control in a bureaucracy (Bentham’s panopticon) vs.
among control among peers among whom direct
command is considered inappropriate.
37
Recall general principles
• Actors who manage their interdependencies are
also capable of observing them. They can
endogenize the structure and politicize their
exchanges, i.e. invest in relationships with
particularistic interests in mind (social niches,
status competition, etc.), but also general interests
and derived satisfactions.
• This management of interdependencies leads to a
complex social discipline (that is recognized as
legitimate by the members).
• The social mechanism observed here is an
illustration of this complexity.
38
Second-order free rider problem
• Main insight: control among peers is based on this
management and use of interdependencies.
• But then, who will bear the costs of control (see the literature
on the second order free-rider issue (Coleman, Ostrom,
Wittek)) ?
• My hypothesis: there is a « lateral control regime » (a form of
indirect control) at SG&R that spreads and shifts the costs of
control among partners. It helps them pressure each other back
to good order.
• My goal : describe this lateral control regime as a social
mechanism.
• Theoretical hypothesis: driving the process are individual
actors spending their own relational capital for the protection
of the common good.
39
A structural approach to social control among
collectively responsible partners at SG&R
(or what happens when we are at the same time the victim,
the deviant, the police agent, and the judge?)
Triplets representing lateral pressure :
Lever
Respondent
Target
At each step we know what the relationship is:
between respondent and lever,
respondent and target,
and lever and target
40
Methodology:
Name generator for eliciting choices of levers for each target
[20% of corporate lawyers in the U.S. have an alcohol and/or drugs problem]
41
Individual conceptions of how social control
operates among partners
(partner 32’s view)
42
Individual conceptions of how social control
operates among partners
(partner 35’s view)
43
Individual conceptions of how social control
operates among partners
(partner 18’s view)
44
Individual conceptions of how social control
operates among partners
(partner 20’s view)
45
Combining sociometric data and leverage data
Typology of pathways of lateral control
46
Analysis of the typology of paths
• The vast majority of paths are partly personalized
paths, a sort of privatization of social control.
• There are nevertheless many completely impersonal
paths (13.5 %).
• There are some completely personalized and
saturated paths (3.3 %).
• Question: Do partners spend their own relational
capital or do they borrow others’ connections?
• To answer this question: an analysis of the ways in
which partners manage their ties and
interdependencies for the collective good.
47
This is where the
identification of
social niches (dense,
multiplex, multifunctional blocks)
becomes very useful.
48
Combining sociometric data and leverage data
49
Lateral control occurs in social niches:
Their existence reduces the costs of control
50
Lateral control occurs in social niches:
Their existence reduces the costs of control
51
Lateral control occurs in social niches
52
Problem with reduction of cost of
control via social niches
• Reduction of costs of control via personalized ties
and social niches raises the issue of ‘oppositional
solidarity’ (Wittek). Infractors may be too close to
pressure, and may be reserved preferential treatment.
• How does the firm deal with the niche-induced risk of
personal loyalty of the lever to the target?
• Answer: by legitimizing paths of lateral control that
do not use personal ties, i.e. creating a specialized and
more impersonal form of status.
• The ‘protector of the common good’.
53
Lateral control also depends on a specific form of status:
The ‘protectors of the common good’
54
Who are the ‘multi-target’ levers or
‘protectors of the common good’?
Answer: Uncontroversial partners
55
Who are these uncontroversial partners?
A specific form of status
56
Who guards the guardians at SG&R?
Using strucural equivalence on leverage data
57
The social structure of collective responsibility
• Quasi-voluntary compliance depends on lateral control which
itself depends on social niches (its is ‘privatized’) and on
status inconsisency (the existence of ‘protectors of the
common good’ who are uncontroversial partners avoiding
conflict escalation).
• Counter-intuitive complementarity between status competition
and niche-seeking for social control.
• We thought that the process was driven by individual actors
spending their own relational capital for the protection of the
common good.
• We realize that they also borrow other people’s relational
capital for that purpose, then find partners with a special kind
of status to finish the job.
58
What would happen in less collegial settings?
• Hypotheses:
– Social control would be shared between hierarchy
and peers?
– Use of relationships would become more brutal?
– Multi-target levers (if they exist) would have more
threatening power?
– The organization would move to court proceedings
more quickly?
59
Analyses of leverage data on Pajek
60
Day 3. Regulation
• Solidarity, control and redefining the rules of
the game (regulatory activity).
• Contribution of neo-structural sociology to the
study of regulatory activity.
• Recall that strategic actors politicize their
exchanges.
• For the study of the regulatory process, it is
useful to look at a specific dimension of this
politicization : status competition (Festinger,
Frank).
• Actors as status competitors and social
discipline.
61
Status
• Relative position in the group (formal
hierarchy and networks of exchange).
• Extensive mandate to participate in regulation
of community.
• This mandate provides legitimacy for speaking
on behalf of general interests in the regulatory
process.
• ‘Multi-dimensionality of status’ or ‘status
heterogeneity’.
• Now you see it, now you don’t.
• Importance of multiplexity.
• The concept of status inconsistency (Lenski)
and its network indicators.
62
Finders, minders and grinders:
status heterogeneity at SG&R
63
Finders, minders, and grinders
(associates included)
64
Regulatory process among
heterogeneous peers
• Policy issues underlying controversies at SG&R:
– Workflow
– Compensation
– Markering
– Peer review.
• Position in the structure and policy preferences.
• Two useful concepts:
– Precarious values (Selznick).
– ‘Multi-status oligarchs’.
• Polarization of policy preferences and the reasons for the
absence of change.
65
Polarization of policy preferences among partners
66
Status inconsistency and policy preferences
The majority of partners with inconsistent
forms of status favor the status quo.
67
Multi-status ‘oligarchs’
• Multi-status oligarchs framing deliberation on
precarious values.
• Status inconsistency and the special influence of
‘improbable’ actors.
• Partners with several and inconsistent forms of status
carry a special weight: they can ‘sacrifice’ one
dimension of status (for the common good) without
losing other dimensions of status.
• They tend to be radical conservatives at SG&R.
• Explanation of inertia in collegial organizations?
68
Summary of neo-structural approach
to regulation
• Change as betrayed promises.
• A complex structural basis of normative order.
• Relational structures, especially status
heterogeneity / inconsistency, are invisible
ingredients of regulatory processes -the
reformulation and interpretation of rules.
• All this with simple correlation tables.
69
Representing status inconsistency
with Pajek?
70
Difficulties related to sociological
knowledge on social processes
• Limits with ou capacity to observe and
reconstitute interactions and social networks:
exploring simulation ?
• Better probabilistic reasoning for social
networks in small populations ?
71
Questions to students
• How does one approach forms of solidarity
using network analysis?
• How can social control depend on relational
structures?
• How can regulation (in the sense of
(re)definition of the rules of the game) depend
on relational structures?
• How can economic performance depend on
relational structures?
72