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

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Dominance Principles in Social Network Dynamics
and TerrorismDIMACS 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

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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
  7447-76.

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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.

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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)
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MASON 4a war onset
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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 gt s?.
• For first-order (parallel) disjunction, if Y 1
  ? (1 ? p)?, where ? is the number of sufficient
  modes, then p dominates ?. Formally, sp gt 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. 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.
2. 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.)
3. Strategies to prevent, combat, and respond to
   terrorism must be cognizant of these differential
   sensitivities.
4. Intuitions and common perceptions about these
   phenomena are often misleading, erroneous, or
   outright dangerous.