[Paleopsych] Economist: Modelling conflict: Rules of engagement
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Modelling conflict: Rules of engagement
http://economist.com/science/displayStory.cfm?story_id=4197737&CFID=60149428&CFTOKEN=122d592-080ff44f-c382-402f-bbdb-c7f42ed6965f
5.7.21
Scientists find surprising regularities in war and terrorism
ON JULY 19th, IraqBodyCount, a group of academics who are attempting
to monitor the casualties of the conflict in that country, published a
report suggesting that almost 25,000 civilians have been killed in it
so far. In other words, 34 a day. But that is an average. On some days
the total is lower, and on some higher--occasionally much higher.
It is this variation around the mean that interests Neil Johnson of
the University of Oxford and Michael Spagat of Royal Holloway College,
London. They think it is possible to trace and model the development
of wars from the patterns of casualties they throw up. In particular,
by analysing IraqBodyCount's data and comparing them with equivalent
numbers from the conflict in Colombia, they have concluded that, from
very different beginnings, these conflicts are evolving into something
rather similar to one another.
The groundwork for this sort of study was laid by Lewis Fry
Richardson, a British physicist, with a paper on the mathematics of
war that was published in 1948. Using data from conflicts that took
place between 1820 and 1945, Fry Richardson made a graph displaying
the number of wars that had death tolls in various ranges. The outcome
was startling: rather than varying wildly or chaotically, the
probability of individual wars having particular numbers of casualties
followed a mathematical relationship known as a power law.
Power-law relationships crop up in many fields of science and are
often a characteristic of complex and highly interacting systems
(which war certainly is). Earthquake frequencies and stockmarket
fluctuations are both described by power laws, for example. Power laws
also have properties that make them different from statistical
distributions such as the normal curve (or bell curve, as it is
familiarly known). Unlike a bell curve, a power-law distribution has
only one tail and no peak. Small tremors occur frequently, but over a
few decades enormously large earthquakes will also occur with
reasonable frequency. As will deadly wars and attacks.
In May, Aaron Clauset and Maxwell Young, of the University of New
Mexico, modified Fry Richardson's method to look at terrorist attacks.
Instead of total casualties in a conflict, they plotted the deaths
from individual incidents. Again, they got a power law. Actually, they
got two. Power-law relationships are characterised by a number called
an index. For each ten-fold increase in the death toll, the
probability of such an event occurring decreases by a factor of ten
raised to the power of this index, which is how the distributions get
their name. Terrorist attacks within G7 countries could be
distinguished from those inside non-G7 countries by their different
indices. G7 countries were more likely to suffer large attacks.
Indeed, in an article published earlier this year by Britain's
Institute of Physics, Mr Clauset and Mr Maxwell said that "if we
assume that the scaling relationship and the frequency of events do
not change in the future, we can expect to see another attack at least
as severe as September 11th within the next seven years."
Dr Johnson and Dr Spagat took the method a couple of steps further.
They extended Mr Clauset's and Mr Maxwell's idea of looking at the
sizes of individual incidents within a campaign to other sorts of
conflict, and also looked at how those conflicts have changed over
time. As they report in a paper published recently in arXiv, an online
archive, they found, yet again, that the data follow power laws. And
for both of the wars they studied, the indices of those power laws
have been approaching the value Mr Clauset and Mr Maxwell found for
non-G7 terrorism, though from different directions. In other words,
for the war in Iraq, the data indicate a transition from an index
characteristic of more lethal, conventional war between armies to one
closer to terrorism. No real surprise there, perhaps, though it is
interesting to see perceptions on the ground reflected in the maths.
For the Colombian conflict, though, the data show the opposite, a
transition from a war characterised by smaller, less cohesive forces
to a more unified rebel front--something that ought to worry
Colombia's government.
Dr Johnson and Dr Spagat put forward as an explanation a mathematical
model they have developed. It consists of a group of self-contained
"attack units", each of a particular strength. Such units can join
together or fragment into smaller pieces. Over time, an equilibrium of
joining and breaking is reached, but where that equilibrium lies
depends on the strength of any central organisation. The model
explains the power-law behaviour seen in both conventional wars and
terrorist attacks. Different rates of fragmentation lead to different
indices--conventional war is fought with robust armies that are
unlikely to fragment, while terrorists are more likely to have
shifting alliances.
Dr Spagat points out that, if their model is correct, it makes
casualty data useful in a situation where intelligence about the enemy
is hard to come by--as seems to be the case in Iraq at the moment. For
instance, it should be possible to distinguish an insurgency with a
rigid command structure from a group of smaller, randomly linked
units. Learning about the distribution of earthquakes may not prevent
the Big One, but for war and terrorism, power-law statistics may teach
governments something about how to defeat the enemy, and make war less
deadly.
From The Economist
[55]Colombia's paramilitary demobilisations
Jul 21st 2005
[56]A wave of bombings in Iraq
Jul 21st 2005
[57]The uncertainty principle and codes
Jun 21st 2001
Country Briefing: [58]Colombia, [59]Iraq
More articles about...
[60]War in Iraq
[61]Jargon and statistics
[62]Wars
[63]Colombia's wars
[64]Terrorism
Websites
The [65]report from IraqBodyCount is available online. [66]ArXiv posts
a [67]paper by [68]Mr Johnson and [69]Mr Spagat, and a [70]study by
[71]Mr Clauset and Mr Young. Royal Holloway College provides
[72]conflict analysis resources. Wikipedia gives details and links
about [73]Fry Richardson and [74]power-law relations. See also the
[75]Institute of Physics.
[I own a copy of Richardson's classic Statistics of Deadly Quarrels. It's a
scarce book. Copies at http://bookfinder.com range from $50 to $100.]
References
55. http://economist.com/science/displayStory.cfm?Story_id=4198496
56. http://economist.com/science/displayStory.cfm?Story_id=4198920
57.
http://economist.com/science/displayStory.cfm?Story_id=S%26%2884%28QA%3B%2B%0A
58. http://economist.com/countries/Colombia/index.cfm
59. http://economist.com/countries/Iraq/index.cfm
60. http://economist.com/research/articlesBySubject/display.cfm?id=348966
61. http://economist.com/research/articlesBySubject/display.cfm?id=348972
62. http://economist.com/research/articlesBySubject/display.cfm?id=540162
63. http://economist.com/research/articlesBySubject/display.cfm?id=1223026
64. http://economist.com/research/articlesBySubject/display.cfm?id=1604388
65. http://www.iraqbodycount.net/press/pr12.php
66. http://arxiv.org/
67. http://arxiv.org/pdf/physics/0506213
68. http://www.lincoln.ox.ac.uk/fellows/johnson/
69. http://www.rhul.ac.uk/Economics/About-Us/spagat.html
70. http://arxiv.org/pdf/physics/0502014
71. http://www.cs.unm.edu/~aaron/
72. http://personal.rhul.ac.uk/pkte/126/Pages/ccar.htm
73. http://en.wikipedia.org/wiki/Lewis_Fry_Richardson
74. http://en.wikipedia.org/wiki/Power_law
75. http://www.iop.org/
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