small group evolution
DESCRIPTION
Scott Atran et al, Marc Sageman. Rajesh Kasturirangan, Kobi Gal. Small Group Evolution. Whitman Richards. AFOSR MURI Review 17 Dec 07. The Problem. Number of Graphical Forms:. Typical Group Representation:. n=6: 110 n=8: 850 - PowerPoint PPT PresentationTRANSCRIPT
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*