[Paleopsych] Economist: Modelling conflict: Rules of engagement

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Modelling conflict: Rules of engagement

    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

    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
    [63]Colombia's wars
    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.]


   55. http://economist.com/science/displayStory.cfm?Story_id=4198496
   56. http://economist.com/science/displayStory.cfm?Story_id=4198920
   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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