Modeling Small Network Dynamics
Whitman Richards M. I. T.
Computer Science and Artificial Intelligence Laboratory
MURI: Computational Models for Belief Revision, Group Decisions and Cultural Shifts
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28 Feb 07
Sageman & Chen, 2005
A Complex Network Structure
Clumps
Central Staff
Core Arab
Southeast Asian
Maghreb Arab
Node Size
Leader
Lieutenant
Other people
Fate
Dead
Captured
Militant Core => a small social network
Leaders < 3
Soldiers < 12 +/-
Supporters 10 - 50+
Itza
Church
Start-up
Street Gang
Sports Team
Activist Group
Mafia
Militia
Terrorist Cell
Three Aspects of Small Groups
Goals, beliefs: sacred vs secular values
Model for Core (i.e leader-soldier relations): a network
Model for Recruitment: conformity vs consistency
Part I: Recruitment
Conformity - Consistency Model (Page et al.)
Conformity: want to be like “one of the BIG guys”
Consistency: want your beliefs to be in harmony
A Surprise: Time to Equilibrium (mean field)
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Sacred Beliefs:
1
Consanguineous Marriages (Bittles et al.)
Part II
Small Network Models
Leaders < 3
Soldiers < 12 +/-
Small Graphs
Supporters 10 - 50+
1. Impossibility “Theorem”:
think small !
2. New Representation: leader dominance vs bonding
2004 Australian Bombing (Militant Minority) [Atran, Magourik et al]
Ring Banten Group
An-Nur Group
Kompak Group
Accommodations
Group
Core Bombing Group
= Lukmanul Group
= Ngruki Ties
= an-Nur Group
= Ring Banten Group
= Kompak Group
= Afghan Ties
= Misc Other
+ = Dead
= Arrest
Descriptive Parameters: graphs: {# nodes, #edges}
Model Abstraction: Dominance of Leader vs Coherence of Network
Two Measures of Social Network Structure
Leadership Dominance: {max. vtx. deg,}
Coherence: {cluster coeff.}
(Freeman, 1978)
Watts & Strogatz (1998), Newman(2004)
2004 Australian Bombing (Militant Minority) [Atran et al]
Ring Banten Group
Max. Vtx. Deg = 3
An-Nur Group
# Triangles = 1
n=4
Kompak Group
Coherence, C:
Leadership, L:
Accommodations
Group
= Lukmanul Group
#triangles / nC3
= Ngruki Ties
= an-Nur Group
= Ring Banten Group
∑(MaxDeg - VtxDeg.)/(n-1)*(n-2)
= Kompak Group
Core Bombing Group
= Afghan Ties
= Misc Other
+ = Dead
= Arrest
Key observation: as bonding increases, dominance of leader decreases
Lacunae: Data lacking on…..
• Street Gang Evolution
Hmong, Haitian, Yakusa, Somali…
• Street Gang Recruitment
What’s sacred? Why join?
Buddy vs friend of friend
Roles of contact, video, email
• Mergers: from Small to Global
More Lacunae
Mergers: Physical vs Virtual links; given 2 gangs,
which member of each is most likely to build bridge?
Web networking: friends of friends (myspace, etc.);
likely candidates for militant acts (eg High School)
How to evaluate trust in a network?
Disenchantment (return to earlier beliefs)
Email analysis: text style -> tag for hidden content (analog to
voice analysis.)
Violent vs non-violent spectrum: what are key parameters?
Long term supporters (requires different model.)
Extent of strategizing; at what level? Emotional factors.
Y-factor: propaganda, secular vs sacred.
MURI Scope
Network
Complexity
WWII
Society
Community
Jihad
Itza
Street Gang
Contextual
Complexity
Football
Family
chess
Individual
Morra,
Chicken
Colored Trails
Strategic
Complexity
The Team
Belief Structures:
Scott Atran, Univ. of Michigan & John Jay, CUNY, Anthropology
Doug Medin, Northwestern University,
Psychology
Ken Forbus,
Northwestern Univ.,
Computer Science and Education
Mark Finlayson & P. H. Winston, MIT,
Computer Science and AI
Network Structure & Evolution
Joshua Tenenbaum,
MIT,
Computation and Cognitive Science
Jenna Bednar, Univ. of Michigan, Political Science & Public Policy
Scott Page, University of Michigan, Political Science & Complexity
Whitman Richards, MIT,
Cognition and Artificial Intelligence
Decision-Making & Strategic Planning:
Brian Stankiewicz, Univ. of Texas, Austin, Expt’l Psychology
Avi Pfeffer,
Harvard,
Computer Science
Consultants:
Robert Axelrod, University of Michigan, Political Science
Marc Sageman, University of Penna., M.D., PhD.