Modeling conflict, with examples from terrorism Kristian Skrede Gleditsch Based on joint work with Aaron Clauset (SFI), Lindsay Heger (UCSD), and Maxwell Young (Waterloo) Department of Government, University of Essex & Centre for the Study of Civil War, PRIO http://privatewww.essex.ac.uk/ ∼ ksg/ 20 November 2007 CABDyN Seminar, Said Business School, Oxford University K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 1 / 18
Introduction Scale invariance in conflict data Frequency and severity of terrorism (CYG JCR 2007) Implications for study of terrorism Frequency and severity in Israel-Palestine conflict (CHYG 2007) K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 2 / 18
Scale invariance in conflict data L.F. Richardson 1948 demonstrated the scale invariant distribution of war magnitude/severity However, almost all subsequent research considers conflict as incidence or binary events Some debate on general vs. separate theories for larger or smaller conflicts ( International Interactions 1990) Specific work on war size: Cioffi-Revilla 1991 JCR forecast of Gulf War magnitude; Lacina 2006 JCR on civil wars Cederman 2003 APSR: computer simulation of geopolitical system that reproduces a scale invariant war distribution Johnson et al. 2006: scale invariance for a large range of conflicts, including events within conflict; Spirling ND for democide K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 3 / 18
Scale invariance in terrorism Most studies of terrorism focus on incidence, or accounting for location where and when attacks occur CYG in J. Conflict Resolution 51 (2007): frequency-severity in MIPT data on terrorist events since 1968 0 10 Deaths Injuries Total −1 10 P(X ≥ x) −2 10 −3 10 −4 10 1 10 100 1000 10000 severity of event, x K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 4 / 18
Summary of distributions Distribution N � x � x max N tail x min p KS ≥ σ std α Injuries 7456 12.77 94.45 5000 259 2.46(9) 55 0.41 Deaths 9101 4.35 31.58 2749 547 2.38(6) 12 0.94 Total 10878 11.80 93.46 5213 478 2.48(7) 47 0.99 A summary of the distributions with power -law fits from the maximum likelihood method. N ( N tail ) depicts the number of events in the full (tail) distribution. The parenthetical value depicts the standard error of the last digit of the estimated scaling exponent. K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 5 / 18
Why is this interesting? Terrorist events vary dramatically in their severity Terrorist seek media attention and spectacular attacks More severe attacks can provide signals of resolve to governments Political and economic impact of terrorism a function of severity 11 Sept attack on WTC/Pentagon vs. previous 1993 WTC bombings 7 July London bombings vs. 21 July copy -cat attack Suggested predictors in work on terrorist incidence (e.g., Li JCR 2005) unable to account for variation in severity Severity offers a complimentary perspective to incidence K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 6 / 18
Trends in average log -severity 4 mean log 2 ( severity ) mean + σ 3 2 1 0 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 1 auto−correlation 0.5 0 −0.5 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 separation time, τ (years) (upper) average log-severity (deaths), 24 months sliding window (lower) ACF of average log-severity K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 7 / 18
Trends in scaling parameter 3.00 1 mean 0.75 ± σ p KS 0.5 2.75 0.25 0 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2.50 scaling exponent α 10 x min 2.25 5 1 2.00 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 21 interval (days) 14 1.75 7 1 1.50 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 year year (L) Average scaling exponent α for two -year periods (R top) significance, one-sided KS test (R middle) estimated x min (R bottom) average inter-event interval for events in tail K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 8 / 18
Disaggregating by locus and weapon type 0 0 10 10 Events inside OECD Events outside OECD −2 10 Chem/Bio −1 Explosives 10 −4 10 0 10 P( X ≥ x ) Firearms P(X ≥ x) −2 −2 10 10 Fire −4 10 0 −3 10 10 Knives Other −2 10 −4 −4 10 10 1 10 100 1000 10000 0 2 4 0 2 4 10 10 10 10 10 10 severity of event, x (total) severity, x (total) severity, x (total) (L) Frequency -severity distributions for OECD and non-OECD nations (R) Frequency-severity distributions by weapon types K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 9 / 18
Generative models for scale invariance Many generative models can generate scale invariant distributions Sel f-organized criticality model applied to forms of conflict such as interstate wars, strikes Limitations Terrorism is not inherently spatial phenomenon Severity not only function of size of explosion Substitution between targets/weapons Johnson et al. fragmentation and coalescence model of insurgency CYG JCR: Toy model for scale invariance through competitive forces K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 10 / 18
Toy model for scale invariance Competition non -state actor (terrorist) and government Severity function of planning and time invested Selection mechanism where probability event executed inversely related to planning required Payoff of additional planning proportional to time already invested Potential severity: p ( t ) ∝ e κ t Severity of real event to planning time of a potential event: x ∝ e λ t After selection of realized events: p ( t ) d t → p ( x ) ∝ x − α where α = 1 − κ/λ p ( x ) d x = � � If slight advantage to state | κ | � | λ | , then we get a power law with exponent α � 2 K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 11 / 18
Counterterrorism and beyond Standard approach considers substitution of targets (Enders and Sandler 1993, 2002): Countermeasures make alternative targets relatively more attractive But, calculus of terrorism much more complicated, e.g.: inter -group competition, political support violence vs. non-violence, severe vs. non-severe Data allow evaluating these influences in Israel-Palestine conflict Focus on main players: Fatah, Hamas, PFLP , PIJ Plus, data on Israeli countermeasures and Palestinian support K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 12 / 18
Israeli countermeasures 140 Suicide attacks Non−suicide attacks 15 Israeli counter attacks Israeli counter attacks 120 13 100 11 Number of incidents Number of incidents 80 9 7 60 5 40 3 20 1 0 2000 2001 2002 2003 2004 2005 2006 2000 2001 2002 2003 2004 2005 2006 Year Year (L) Counts for suicide attacks and Israeli counter -terrorism events (R) Counts for non-suicide and Israeli counter-terrorism events K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 13 / 18
Competition, imitation, and public opinion 225 60 225 60 Severity Data Severity Data Fatah Percentage Hamas Percentage 200 200 99% Confidence Interval 99% Confidence Interval 50 50 175 175 Public Opinion Percentage Public Opinion Percentage 150 40 150 40 Severity 125 Severity 125 30 30 100 100 75 20 75 20 50 50 10 10 25 25 0 0 0 0 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Year Year (L) Fatah suicide attack severity (left axis) and public approval (right) (L) Hamas suicide attack severity (left axis) and public approval (right) K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 14 / 18
No evidence of coordination Fatah−PLO to Hamas Hamas to Fatah−PLO 10 5 0 0 −5 Conflict−Cooperation −10 Conflict−Cooperation −10 −20 −15 −30 −20 −25 −40 −30 2001 2002 2003 2004 2005 2001 2002 2003 2004 2005 (L) Fatah to Hamas conflict cooperation score, by week (R) Hamas to Fatah conflict cooperation score, by week K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 15 / 18
Change in share of claimed attacks 1 claimed / attributed unknown fraction of events per 6 months 0.8 0.6 0.4 0.2 0 2000 2001 2002 2003 2004 2005 K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 16 / 18
Attack modes and elections 4 150 Hamas suicide attacks Hamas non−suicide attacks 3 Palestinian elections event count event count 100 2 50 1 0 0 ave. casualties per event ave. casualties per event 200 200 150 150 100 100 50 50 0 0 2000 2001 2002 2003 2004 2005 2006 2000 2001 2002 2003 2004 2005 2006 (L) Incident frequency (upper pane) and average casualties per attack (lower), suicides (R) Incident frequency (upper pane) and average casualties per attack (lower), non -suicides K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 17 / 18
Summary Frequency -severity distributions in conflict data Thinking about event severity offers important new insights Calculus of terrorism is highly complex Many possible strategies Many possible targets and modes Many possible interpretations of data In Israel-Palestine conflict evidence of inter-group competition: innovation, imitation interaction with political processes: public support, elections K.S. Gleditsch (Essex) Modeling conflict Oxford CABDyN 18 / 18
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