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Abstract
In the spirit of Lewis Richardson’s original study of the statistics of deadly conflicts, we study the frequency and severity of terrorist attacks worldwide since 1968. We show that these events are uniformly characterized by the phenomenon of “scale invariance,” that is, the frequency scales as an inverse power of the severity, P(x) Αx-α. We find that this property is a robust feature of terrorism, persisting when we control for economic development of the target country, the type of weapon used, and even for short time scales. Further, we show that the center of the distribution oscillates slightly with a period of roughly τ≈ 13 years, that there exist significant temporal correlations in the frequency of severe events, and that current models of event incidence cannot account for these variations or the scale invariance property of global terrorism. Finally, we describe a simple toy model for the generation of these statistics and briefly discuss its implications.
|
Arce, M. , Daniel G. , and Todd Sandler . 2005. Counterterrorism: A game-theoretic analysis. Journal of Conflict Resolution 49 (1): 138-200. Google Scholar | |
|
Bak, Per , and Chao Tang . 1989. Earthquakes as a self-organized critical phenomena. Journal of Geophysical Research 94 (B11): 15635-15637. Google Scholar | Crossref | ISI | |
|
Bak, Per , Chao Tang , and Kurt Wiesenfeld . 1987. Self-organized criticality: An explanation of 1/f noise. Physical Review Letters 59 (4): 381-384 Google Scholar | Crossref | Medline | ISI | |
|
Biggs, Michael . 2005. Strikes as forest fires: Chicago and Paris in the late 19th century. American Journal of Sociology 111 (1): 1684-1714. Google Scholar | Crossref | ISI | |
|
Bogen, Kenneth T. , and Edwin D. Jones . 2006. Risks of mortality and morbidity from worldwide terrorism: 1968-2004. Risk Analysis 26 (1): 45-59. Google Scholar | Crossref | Medline | ISI | |
|
Cederman, Lars-Erik . 2003. Modeling the size of wars: From billiard balls to sandpiles. American Political Science Review 97 (1): 135-150. Google Scholar | Crossref | ISI | |
|
Cioffi-Revilla, Claudio . 1991. On the likely magnitude, extent, and duration of the Iraq-UN war. Journal of Conflict Resolution 35 (3): 387-411. Google Scholar | SAGE Journals | ISI | |
|
Clauset, Aaron , and Maxwell Young . 2005. Scale invariance in global terrorism. Preprint. http://arxiv.org/abs/physics/0502014 (accessed on February 3, 2005). Google Scholar | |
|
Congleton, Roger D. 2002. Terrorism, interest-group politics, and public policy. Independent Review 7 (1): 47-67. Google Scholar | |
|
Crook, Clive . 2006. The height of inequality. The Atlantic Monthly 298 (2): 36-37. Google Scholar | |
|
Enders, Walter E. , and Todd Sandler . 2006. The political economy of terrorism. Cambridge, UK: Cambridge University Press. Google Scholar | |
|
Farmer, J. Doyne , and John Geanakoplos . 2006. Power laws in economics and elsewhere. Unpublished manuscript. Santa Fe Institute, NM/Yale University, New Haven CT. Google Scholar | |
|
Federal Bureau of Investigation , Counterterrorism Threat Assessment and Warning Unit , Counterterrorism Division . 1999. Terrorism in the United States, 1999. US Department of Justice, Washington, DC. http://www.fbi.gov/publications/terror/terror99.pdf (accessed on January 22, 2005). Google Scholar | |
|
Gartner, Scott S. 2004. Making the international local: The terrorist attack on the USS Cole, local casualties, and media coverage. Political Communication 21 (1): 139-159. Google Scholar | Crossref | ISI | |
|
Goldstein, Michel L. , Steven A. Morris , and Gary G. Yen . 2004. Problems with fitting to the power-law distribution. European Physical Journal B: Condensed Matter and Complex Systems 41 (2): 255-258. Google Scholar | Crossref | ISI | |
|
Hoffman, Bruce . 1999. Terrorism trends and prospects. In Countering the new terrorism, edited by Ian O. Lesser , Bruce Hoffman , John Arquilla , David Ronfeldt , Michele Zanini , and Brian Michael Jenkins , 7-38. Santa Monica, CA: RAND. Google Scholar | |
|
Johnson, Neil F. , Michael Spagat , Jorge Restrepo , Juan Bohorquez , Nicholás Suarez , Elvira Restrepo , and Roberto Zarama . 2005. From old wars to new wars and global terrorism. Preprint. http://arxiv.org/abs/physics/0506213 (accessed on June 29, 2005). Google Scholar | |
|
Johnson, Neil F. , Michael Spagat , Jorge A. Restrepo , Oscar Becerra , Juan C. Bohorquez , Nicholás Suarez , Elvira M. Restrepo , and Roberto Zarama . 2006. Universal patterns underlying ongoing wars and terrorism. Preprint. http://arxiv.org/abs/physics/0605035 (accessed on May 3, 2006). Google Scholar | |
|
Kleiber, Christian , and Samuel Kotz . 2003. Statistical size distributions in economics and actuarial sciences. Hoboken, NJ: John Wiley. Google Scholar | Crossref | |
|
Lacina, Bethany A. 2006. Explaining the severity of civil wars. Journal of Conflict Resolution 50 (2): 276-289. Google Scholar | SAGE Journals | ISI | |
|
Li, Lun , David Alderson , John C. Doyle , and Walter Willinger . 2005. Towards a theory of scale-free graphs: Definition, properties, and implications. Internet Mathematics 2 (4): 431-523. Google Scholar | Crossref | |
|
Li, Quan . 2005. Does democracy promote or reduce transnational terrorist incidents? Journal of Conflict Resolution 49 (2): 278-297. Google Scholar | SAGE Journals | ISI | |
|
Malamud, Bruce D. , Gleb Morein , and Donald L. Turcotte . 1998. Forest fires: An example of self-organized critical behavior. Science 281: 1840-1841. Google Scholar | Crossref | Medline | ISI | |
|
Mickolus, Edward F. , Todd Sandler , Jean M. Murdock , and Peter A. Flemming . 2004. International terrorism: Attributes of terrorist events, 1968-2003 (ITERATE 3-4). Dunn Loring, VA: Vinyard Software. Google Scholar | |
|
Mitzenmacher, Michael . 2004. A brief history of generative models for power law and lognormal distributions. Internet Mathematics 1 (2): 226-251. Google Scholar | Crossref | |
|
National Memorial Institute for the Prevention of Terrorism . 2006. Terrorism knowledge base. http://www.tkb.org (access on June 18, 2006). Google Scholar | |
|
Navarro, Peter , and Aaron Spencer . 2001. September 11, 2001: Assessing the costs of terrorism. Milken Institute Review (Fourth Quarter): 16-31. Google Scholar | |
|
Newman, Mark. E. J. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46 (5): 323-351. Google Scholar | Crossref | ISI | |
|
Overgaard, Per B. 1994. The scale of terrorist attacks as a signal of resources. Journal of Conflict Resolution 38 (3): 452-478. Google Scholar | SAGE Journals | ISI | |
|
Pape, Robert A. 2003. The strategic logic of suicide terrorism. American Political Science Review 97 (3): 343-361. Google Scholar | ISI | |
|
Press, William H. , Brian P. Flannery , Saul A. Teukolsky , and William T. Vetterling . 1992. Numerical recipes in C: The art of scientific computing. Cambridge, UK: Cambridge University Press. Google Scholar | |
|
Reed, William J. , and Barry D. Hughes . 2002. From gene families and genera to income and Internet file sizes: Why power laws are so common in nature. Physical Review E 66 (6): 67103-67107. Google Scholar | Crossref | ISI | |
|
Reich, Walter . 1990. Origins of terrorism. Cambridge, UK: Cambridge University Press. Google Scholar | |
|
Richardson, Lewis F. 1948. Variation of the frequency of fatal quarrels with magnitude. Journal of the American Statistical Association 43 (244): 523-546. Google Scholar | Crossref | ISI | |
|
Rosendorff, B. Peter , and Todd Sandler . 2005. The political economy of transnational terrorism. Journal of Conflict Resolution 49 (2): 171-182. Google Scholar | SAGE Journals | ISI | |
|
Sandler, Todd , and Daniel G. Arce M. 2003. Terrorism and game theory. Simulation & Gaming 34 (3): 319-337. Google Scholar | SAGE Journals | |
|
Sandler, Todd , and Harvey E. Lapan . 1988. The calculus of dissent: An analysis of terrorists’ choice of targets. Synthese 76 (2): 245-261. Google Scholar | Crossref | ISI | |
|
Serfling, Robert . 2002. Efficient and robust fitting of lognormal distributions. North American Actuarial Journal 6 (1): 95-109. Google Scholar | Crossref | |
|
Shubik, Martin . 1997. Terrorism, technology, and the socioeconomics of death. Comparative Strategy 16 (4): 399-414. Google Scholar | Crossref | |
|
Simon, Herbert. A. 1955. On a class of skew distribution functions. Biometrika 42 (3/4): 425-440. Google Scholar | Crossref | ISI | |
|
United States Bureau of the Census . Census 2000. Washington, DC: Government Printing Office. http://www.census.gov/main/www/cen2000.html (accessed on September 18, 2006). Google Scholar | |
|
United States Department of State . 2004. Patterns of global terrorism, 2003. Washington, DC, U.S. Department of State, April. http://www.state.gov/documents/organization/31912.pdf (accessed on January 22, 2005). Google Scholar | |
|
Wilkinson, Paul . 1997. The media and terrorism: A reassessment. Terrorism and Political Violence 9 (2): 51-64. Google Scholar | Crossref | ISI | |
|
Zipf, George K. 1949. Human behavior and the principle of least effort. Cambridge, MA: Addison-Wesley. Google Scholar |
