small group evolution

MURI Continuing Review @ MIT 17 Dec 07 (Location: Stata Center; 32 Vassar St. (Bldg 32-4th floor) Room 32D-463)

8:30 – 9:00 assemble; coffee & pastries

9:00 W. Richards & T. Lyons: Introductions & Objectives

Experimental & Network Analysis Results

9:15 M. Sageman: Militant Networks studies (with S. Atran)

9:45 comment by R. Axelrod: Reframing Sacred Values

10:00 D. Medin: Sacred & Secular results

10:30 Coffee & Soda break

Model Development and Applications

11:00 J. Tenenbaum: Infinite Block Model for Beliefs Categories

11:30 K. Forbus: Causal Models

12:00 comment by P. Winston on Story Workbench

12:15 Lunch: 4th Floor of Stata (a bargain for $6.00 !!!)

1:30 W. Richards: Small Group Network Evolution

2:00 A, Pfeffer: Multi-agent Models & Patterns of Reasoning

2:30 S. Page: Belief Revision Models

3:00 Coffee & Soda Break

3:30 General discussion & Future directions

4:00 T. Lyons (closed session)

5:30 Adjourn

Small Group Evolution

Whitman Richards

Scott Atran et al, Marc Sageman

Rajesh Kasturirangan, Kobi Gal

AFOSR MURI Review 17 Dec 07

The Problem

Typical Group Representation:

Number of Graphical Forms:

n=6: 110

n=8: 850

n=10: 10 million

n=12: 150 billion

A Picture is NOT worth 1000 words !!

Leadership:

Bonding:

Diversity:

L = 1.0

B = 1.0

D = 0.92

Proposed Solution: Three subgraphs that capture key properties of group formation

L ~ normalized sum of diff in vertex degrees

B ~ avg. number of among vertex & neighbors

D ~ num. K2 separated by at least two edge steps (Non-adjacent clusters of Kn increase diversity.)

L, B, D parameters are not independent

Leadership:

Bonding:

Diversity:

L = 0.67 (1.0)

B = 0.875 (1.0)

D = 0.33 (0.92)

Question

Can only three parameters (L,B,D) adequately describe a group during its evolution (i.e, is this compression of pictorial information sufficient) ?

Ans: Yes ! but …….

modeling the evolutionary dynamics will require the application of theories for strategic play….

An Example of Group Formation & Evolution

(to illustrate strategic aspects and model form)

Note: adding a cluster reduces overall bonding

Equilibrium? What’s Next?

Small Group Evolution: example

CASE STUDIES

1. Start-up Company

2. Madrid Militant Group

Start-up Evolution

Madrid Group Evolution

Summary

1. L, B, D parameters describe Small Group evolution(pictures are not always worth 1000 words)

2. Evolution entails strategic play (game theoretic)

Future

3. Is there an optimal evolutionary path ? (e.g. context, internal vs external forces on group, objectives )

=> analysis of patterns of strategic reasoning

= 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

(Non-adjacent clusters of Kn which increase diversity.)

Definitions

n = number of vertices; di = degree of vertex vi

L = (dmax −di ) / ((n−1)(n−2))i=1

n∑

B=3* #Δ 's / #connected_ triples_of _v's

D=#disjoin_dipoles(K2* ) / #K2

* for _Rn

Disjoint dipoles are separated by at least two edge steps K2*