Dominance Principles in Social
Network Dynamics and Terrorism
DIMACS Working Group on Modeling Social Responses to
Bio-terrorism Involving Infectious Agents, DIMACS Center,
Rutgers University, May 29-30, 2003
Claudio Cioffi-Revilla
Director, Center for Social Complexity
George Mason University
http://socialcomplexity.gmu.edu
Reference
• Claudio Cioffi-Revilla (1998) Politics and
Uncertainty: Theory, Models and Applications
(Cambridge University Press), Part III
(Micropolitics): Chapters 5-7.
• Claudio Cioffi-Revilla & Harvey Starr (1995)
“Opportunity, willigness and political uncertainty:
theoretical foundations of politics,” Journal of
Theoretical Politics 7:447-76.
2
Dominance Principles
• A dominance principle is a formal theorem
that states the relative sensitivity (elasticity)
of the probability Pr(Y) = Y of a compound
event Y to variation in (i) the number of
elementary events N that cause Y and (ii)
the component causal probabilities {pi}.
3
Compound events & terrorism
• All interesting terrorism-related events are arguably
compound events:
–
–
–
–
–
–
The success (or failure) of a warning system (Quarantelli)
The success of a terrorist strike (Shubik)
The detection of impending terrorist action (Kvach)
The success of a counterterrorism operation
The success of first-responders or mitigation measures (Sorensen)
Reaching any state in Glasser et al.’s model (CDC). Each arrow!
• Key: each of these events, and others, is composed of more
basic, elementary events that are causally linked by
elementary conjunction and disjunction operations (often
highly complex) defined on the complete set of causal
events.
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The structure function (Y)
• Formally, each event occurrence Y is given by a structure function
(Y) that specifies the causal conjunctions and disjunctions of the
elementary events {X} that produce Y.
• E.g., (Y)  A  [(B C)(D E)],
[1]
so Y occurs whenever A and either B and not C or D and E occur.
• Remark: The s.f. (Y) is obtained through finite event analysis, by
decomposing processes and parsing compound events (CC-R, 1998).
• Thus, the probability of a compound event Y(pi) is derived from the
corresponding s.f. (Y) associated with the causal occurrence of event
Y.
• For [1], the s.f. yields
Y = a[(b - bc) + (d + e - de)].
[2]
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MASON “M 3”: GeniPol)
2. Poli tical crisi s
(PC) aris es P
PC orig inates
internal ly I
Increas ed
agri cul tural
output occurs
A
Group of L oca ls
attempts to
sei ze power G
EU(G)  EU(G)
Agri cul tural
increas e occu rs
as state of
Nature A 1
PC orig inates
extern ally X
Other inte rnal
PC occurs I *
Fore igne rs
thre aten
locals T
Physical
enviro nmen tal
stre ss (PES)
occurs M
Other externa l
PC occurs X *
EU(T )  EU(T )
Agri cul tural
increas e occu rs
purp osivel y
A2
Drough t occu rs
H
EU(A )  EU(A )
Flo od o ccurs
O
Other PES
occurs M *
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MASON “4a”: war onset
R
Peace
Y1
P
I
Y2
Y 31
R
E
Y 33
P
Y 32
E
T
N
OI
WI


OR
WR
SP



Ms
Mo
SR
Mo
W1
W2
W3 
U1
U2
U3
Wm
Q
VR
W1
W2
W3 
U1
U2
U3
Wm
I'
VP
War
Z
DI
DA
OI'
WI'
ODI
WDI
ODA
WDA







Ms
Mo
Mo
W1
W2
W3 
U1
U2
U3
Wm
Mo
W1
W2
W3 
U1
U2
U3
Wm
W1
W2
W3 
U1
U2
7U3
Wm
Sensitivity sx(Y)
• Let Y = ƒ(X). The sensitivity of Y (e.g. probability
of a compound event) with respect to X (e.g., p or
N) is defined by the relative first-order derivative
(economists’ “elasticity”):
(i) continuous case: sx(Y) = (∂Y/∂X)(X/Y)
(ii) discrete case: sx(Y) = (YX + 1  YX)(X/Y)
• Remark: Sensitivities are always directly
comparable because they are expressed in pure
numbers (dimensionless).
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First-order dominance
• For first-order (serial) conjunction, if Y = p, where  is
the number of necessary conditions, then p dominates .
Formally, sp > s.
• For first-order (parallel) disjunction, if Y = 1  (1  p),
where  is the number of sufficient modes, then p
dominates . Formally, sp > s.
• Remark: In both cases variations in component
probabilities p dominate variations in causal complexity (
or ) in terms of the effect on Y, so p is the preferred target
of intervention (control variable) to increase or decrease Y
assuming equal costs in percent changes.
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So what? Applications
• Given an anti-terrorist strategy based on 
operations with individual probabilities p, is it
more effective to increase p or to increase  (add
redundancy)?
• Given a terrorist attack based on  requisites each
with probability p, is it easier to prevent attack by
lowering p or by increasing ?
• Given a response plan based on  requirements
each with success probability p, is it better to
decrease  or to increase p?
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Nth-order dominance
• Similar results can be derived for compound
events of unlimited causal complexity, so long as
the s.f. can be specified (modeled).
• Examples:
– second-order conjunctive-disjunctive compound events,
causally based on AND (conjunction) with ORs
(disjunctions) at each requirement
– second-order disjunctive compound events, causally
based on OR (disjunction) modes with ANDs
(conjunctions) for each mode.
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Extensions
• Distribution models
E.g., E(T) = (/)1 [1 + 1/( + 1)], for
Weibull-distributed onset attacks.
• Probability kinematics
when p, ,  and other parameters vary over time
• Vector fields (role of dynamics):
Y  Pp p  PN n
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Conclusions
1.
2.
3.
4.
The probability of compound events (arguably all terrorism events of
interest) is affected in qualitatively and quantitatively different ways
(differentiated impacts) by changes in the underlying causal
probabilities and in their causal connections.
In general, changes in component probabilities have a greater effect
on the overall probability of a compound event than do changes in
the number of causal events (whether conjunctive or disjunctive).
(“Causal uncertainty is more important than causal complexity.”)
Strategies to prevent, combat, and respond to terrorism must be
cognizant of these differential sensitivities.
Intuitions and common perceptions about these phenomena are often
misleading, erroneous, or outright dangerous.
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