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Thread: Power laws and Interstate War

  1. #1 Power laws and Interstate War 
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    Does anyone have any thoughts on why war casualties are related to war frequency
    by a power law?

    Here is a link for some background: http://netwar.wordpress.com/2007/08/...r-laws-of-war/

    A power law means that war frequency vs. war casualties (as a percent of population)
    for all wars form a straight line in a logarithmic graph.

    This was first discovered by a guy named Lewis Richardson (physicist) and so this is called: "Richardson's Law".

    Why does this matter?

    Well if wars follow a power law then you can have frequent small wars, or rare large wars eg. world wars, or something in between.

    At least one author has speculated that the presence of a power law means that all wars have one underlying cause.

    I don't have the references handy but a couple people have done some computer simulations of some power law systems to see what happens if you change some things.

    I think one guy used a "forest fire/percolation" model and sharply reduced the frequency of "ignitions" or lightning strikes. Eventually, the power law failed and the forest burned right down to the ground when the rare ignition finally occurred. This would be an "extinction scenario".

    Another guy, I think his name was Brunk, did some simulations where he used a "sand pile/avalanche" model and reduced the input to the system. Brunk found when he started to "turn off the sand" then "large avalanches" never occurred at a point where the input was reduced to about 60% of a baseline level. (The baseline was a level at which large avalanches did occur.)

    An avalanche or a forest fire would be analogous to a war. A large avalanche would be a world war. Brunk showed that if you knew what the "underlying process" was and could reduce it, then world wars would never occur.

    On the other hand, the forest fire scenario seems to suggest that if you do nothing to "turn off the sand" and only work to prevent ignitions, then you risk an "extinction scenario" eg. A very very bad world war.

    What would be the effect of nuclear weapons? Unfortunately, the most likely effect of nukes is to stop ignitions. Thus, "turning off the sand" could be important.

    Unfortunately, if there is one underlying process/cause for all wars then no one knows what it is.


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  3. #2  
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    Isn't the underlying cause/process pretty much always economics?


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  4. #3  
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    Quote Originally Posted by kojax
    Isn't the underlying cause/process pretty much always economics?
    I agree that economics is probably the best candidate for an "underlying process", if in fact such a process exists.

    However, I don't think it is accepted that there is an underlying process common to all wars. Most theories of "the cause of war" do not address Richardson's Law.

    One of the references in the article cited (Cederman, "Modeling the Size of Wars...")
    suggested that advances in "technology" could explain Richardson's Law.

    I think your suggestion is better. Countries could start a war because of lack, perceived lack, or desire for control of resources.

    One other interesting mechanism that an animal rights activist named Tuttle (World Peace Diet) suggested as "the cause of war", is "reductionism", or treating living beings as if they were objects. Tuttle does not talk about Richardson's Law.
    Tuttle argues that cruelty to animals is transferable to humans. There is some support for this in criminal violence literature. However, you cannot apply literature on individuals, to countries.

    Tuttle's hypothesis is interesting to me because it reminds me of the forest fire model. There are numerous plants in the forest. However, when the plants dry, all the plants become "fuel in the forest" or one process. Several behaviors could contribute to "reductionism", including cruelty to animals.

    I am only a foreign policy interested bystander, not an expert. However, the "cause of war" theories I have read about such as "Balance of Power" seem to focus on the period temporal to the onset of war. They do not really look at some ongoing process such as tension building up over time.

    However, not all power law processes involve tension, or potential energy, building up
    in a system over time. City sizes also follow a power law. I think article citations might also work this way.
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  5. #4  
    Forum Ph.D. Leszek Luchowski's Avatar
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    I am puzzled because I cannot see either the formula or the log-normal plot you folks are discussing. Could some kind soul please enlighten me?

    Also, what exactly are the variables?

    Do you count the total number of casualties in "one war"? Or per month of war? Do you divide that by the total population of the fighting countries?

    How do you count the frequency of wars? So and so many wars per century between some two countries? Or on a continent? Or in the world? If there is a short truce (how short is short?) and then fighting breaks out again, is it a second war or just a continuation of the same one? Was Vietnam and Korea two separate wars, or were they just "hot episodes" in the long standoff between the USSR and the West known as the Cold War?

    In 1943, Italy changed sides and turned against their German allies - does this mean Italy fought two different wars during WWII?
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
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  6. #5  
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    Quote Originally Posted by Leszek Luchowski
    I am puzzled because I cannot see either the formula or the log-normal plot you folks are discussing. Could some kind soul please enlighten me?

    Also, what exactly are the variables?

    Do you count the total number of casualties in "one war"? Or per month of war? Do you divide that by the total population of the fighting countries?

    How do you count the frequency of wars? So and so many wars per century between some two countries? Or on a continent? Or in the world? If there is a short truce (how short is short?) and then fighting breaks out again, is it a second war or just a continuation of the same one? Was Vietnam and Korea two separate wars, or were they just "hot episodes" in the long standoff between the USSR and the West known as the Cold War?

    In 1943, Italy changed sides and turned against their German allies - does this mean Italy fought two different wars during WWII?
    In the Cederman article:
    http://www.econ.iastate.edu/.../Lars...SizeOfWars.pdf

    In the appendix on page 35 or 36 there is a logarithmic graph of war frequency vs. war intensity. The graph is a straight line. Apparently, this relationship holds for wars as far back as 1495.

    I think that to qualify as a war, there must be at least 1000 casualties. I believe that conflicts involve at least two states. Casualties are defined as a percent of population killed. Thus, as population increases, absolute numbers of casualties also increase.
    I think all the conflicts in WW II are considered to be part of one war. Vietnam and Korea are separate wars.

    The variables? The power law describes war frequency vs. intensity.

    Cederman says that the presence of a power law implies that there is both a self-reinforcing effect, and some sort of "braking/inhibitory effect in the system. There should also be some sort of "trigger variable".

    For example, in the forest fire model model, there is "fuel in the forest" that makes fires more likely and helps fire spread. Moisture or rain inhibits fire.
    Lightning is a trigger.

    In the sand pile model, a computer drops sand on a table and measures avalanches.
    Avalanches can be small or huge. When avalanches are huge, frequency of avalanches falls, and vice versa. However, the relationship between frequency and size of avalanches is described by a power law.
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  7. #6  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Thank you Dedo for your reply;

    Quote Originally Posted by dedo
    In the Cederman article:
    http://www.econ.iastate.edu/.../Lars...SizeOfWars.pdf

    In the appendix on page 35 or 36 there is a logarithmic graph
    (...)

    I think that to qualify as a war, there must be at least 1000 casualties. I believe that conflicts involve at least two states.

    (...)

    I think all the conflicts in WW II are considered to be part of one war. Vietnam and Korea are separate wars.
    The link doesn't work, you put an ellipsis in the URL.

    And could you please state a clear rule as to what constitutes "one war" or "many wars", at times where conflicts break out on several fronts, at slightly different times? Only a definition will allow us to really know what we are talking about; your answer about WWII, Korea and Vietnam may be right, but it does not solve scores of similar dubious situations throughout history.

    In the last decades of the 18th century, the French revolutionaries and the Americans may have seen themselves as fighting for a common cause, against the old system of monarchies. Today we seem to think of the two events as separate revolutions.

    When Mussolini invaded Ethiopia (then Abyssinia) in 1936, he probably didn't think of himself as an ally of the Japanese invading China (1931). Today both events are considered preludes to WWII.

    Also, your notion that a war involves at least two states leaves out civil wars and revolutions, which also cause lots of casualties.

    But I will (partly at least) answer my own question by hypothesizing that the frequency of war should be measured locally: how often the inhabitants of a given place are involved in a conflict, either by having it run over their heads or by being citizens of a warring nation. Then plot this against the death toll among the same population. Is this right, according to the premises of that power law?

    Cheers, Leszek.
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  8. #7  
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    Maybe they should be divided by treaty and/or final resolution. The Cold war ended with the disolving of the USSR. The Vietnam war ended with US withdrawl. The Korean war ended in an actual treaty.

    These sub-wars in WW2.... did any of them actually end in separate treaties?
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  9. #8  
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    Sorry about the missed link. Searching google for the Cederman article brings up a pdf file of the article with the search terms: Cederman modeling the size of wars

    I don't know all the criteria for which conflict/subconflict is used as the start of WW II. The references linked to in the first link, or the Cederman article, should give more details. It has been a while since I went through these so I can't say which one is best off hand.

    However, I am pretty sure that "frequency" is more global than local. For example, I believe it was Jack Levy that determined that Richardson's Law holds for wars as far back as 1495. Levy looked at European wars.

    I doubt that it matters how a war ends (eg. truce vs. treaty). It seems that the important thing is that hostilities stop.
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