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Whitman Richards M. I. T. Computer Science and Artificial Intelligence Laboratory

MURI: Computational Models for Belief Revision, Group Decisions and Cultural Shifts

28 Feb 07

Modeling Small Network Dynamics

A Complex Network Structure

Central Staff

Core Arab

Southeast Asian

Maghreb Arab

Clumps

Node Size

Leader

Lieutenant

Other people

FateDead

Captured

Sageman & Chen, 2005

Militant Core => a small social network

ItzaChurchStart-up

Street GangSports TeamActivist Group

MafiaMilitiaTerrorist Cell

Leaders < 3Soldiers < 12 +/-

Supporters 10 - 50+

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)

<- Group Conformity Individual Consistency ->

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1

Sacred Beliefs:

Consanguineous Marriages (Bittles et al.)

Small Network Models

1. Impossibility “Theorem”: think small !

2. New Representation: leader dominance vs bonding

Part II

Leaders < 3Soldiers < 12 +/-

Supporters 10 - 50+

Small Graphs

= Lukmanul Group

= Kompak Group = Afghan Ties

= Ngruki Ties

+ = Dead = Arrest

= Misc Other

= an-Nur Group = Ring Banten Group

An-Nur Group

Accommodations Group

Ring Banten Group

Kompak Group

Core Bombing Group

2004 Australian Bombing (Militant Minority) [Atran, Magourik et al]

Descriptive Parameters: graphs: {# nodes, #edges}

Model Abstraction: Dominance of Leader vs Coherence of Network

Two Measures of Social Network Structure

Leadership Dominance: (Freeman, 1978)

Coherence: Watts & Strogatz (1998), Newman(2004)

{max. vtx. deg,}

{cluster coeff.}

2004 Australian Bombing (Militant Minority) [Atran et al]

= Lukmanul Group

= Kompak Group = Afghan Ties

= Ngruki Ties

+ = Dead = Arrest

= Misc Other

= an-Nur Group = Ring Banten Group

An-Nur Group

Accommodations Group

Ring Banten Group

Kompak Group

Core Bombing Group

Max. Vtx. Deg = 3

# Triangles = 1

Leadership, L: ∑(MaxDeg - VtxDeg.)/(n-1)*(n-2)Coherence, C: #triangles / nC3

n = 4

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.

-factor: propaganda, secular vs sacred.

MURI Scope

Society

Community

Individual

ContextualComplexity

Strategic Complexity

Network Complexity

Family

chess

WWII

Football

Morra, Chicken

Itza

Jihad

Street Gang

Colored Trails

Decision-Making & Strategic Planning:Brian Stankiewicz, Univ. of Texas, Austin, Expt’l PsychologyAvi Pfeffer, Harvard, Computer Science

Consultants: Robert Axelrod, University of Michigan, Political Science

Marc Sageman, University of Penna., M.D., PhD.

Joshua Tenenbaum, MIT, Computation and Cognitive Science

Jenna Bednar, Univ. of Michigan, Political Science & Public PolicyScott Page, University of Michigan, Political Science & ComplexityWhitman Richards, MIT, Cognition and Artificial Intelligence

Network Structure & Evolution

The Team

Belief Structures:Scott Atran, Univ. of Michigan & John Jay, CUNY, AnthropologyDoug Medin, Northwestern University, PsychologyKen Forbus, Northwestern Univ., Computer Science and EducationMark Finlayson & P. H. Winston, MIT, Computer Science and AI