William M. Briggs

Statistician to the Stars!

Are Wars And Violence Decreasing? Taleb’s New Paper Reviewed


The vale of tears

I’ve been asked by several people to comment on Pasquale Cirillo and Nassim Nicholas Taleb’s paper (thankfully, not peer-reviewed, unless you count this) “On the tail risk of violent conflict and its underestimation“. That paper was written partly in response to Steven Pinker’s contention that people (us, we) have been growing less violent thanks (mainly) to progressivism and democracy (a redundancy).

We met Pinker’s book before (link) so I won’t spend any time with it, except to say that I didn’t buy his argument.

So then. What is violence? Used to be, in days of yore, people fought constantly—men, anyway, or mainly men—and with fewer deaths than our sophisticated weaponry today provides. For proof, read any ethnology, or for a decent summary Constant Battles: Why We Fight by Steve LeBlanc. Men have always conked each other upside the head. LeBlanc gives too much weight to environmental causes for wars, when status and sex are are as influential.

But that’s neither here nor anywhere: fact is, men are violent. Wars for honor are still fought, though in the West we don’t call them “wars”—but we do call them battles. Mexican drug gangs are slicing and dicing each other. Citizens here are often unhappy. ISIS is chewing up the Mideast. Truly progressive governments are discovering they could do without certain citizens (for just one example). And this unpleasantness is only a small sample in a small piece of time.

Body counts are hard to come by. Do we include old-fashioned crime? Or only bloodlettings from officially declared wars? Seems to me any natural reading of violence would include those acts which purposely end somebody’s life. That would include abortion—the violent killing of a life—euthanasia and executions. Yet those killings make some squeamish, so as a favor to delicate readers I’ll skip over them.

Don’t skip by too lightly, though. If we’re going to quantify violence—which Pinker, Cirillo and Taleb all do—we need to have a rigorous definition of what counts. Another point: including only deaths is difficult. For instance, emergency medicine (battlefield and civilian) has improved dramatically these past decades. Many who would have died now live. Point is: much depends on what we’re quantifying.

Enter Cirillo and Taleb

Cirillo and Taleb looked for historian-defined “wars” and “conflicts” and not what we today call crime. These wars were classed as “events”, except when they lasted more than 25 years when the single event was cut up into multiple “events.” This makes the data more amenable to their model, but at the cost of changing reality. There are difficulties in counting the dead in named wars. Why not a year-by-year tally of violently killed regardless under what flag? Focusing on concrete historian-generated boundaries makes for better stories, but it hinders counting. And there is other fuzziness:

Further, in the absence of a clearly defined protocol in historical studies, it has been hard to disentangle direct death from wars and those from less direct effects on populations (say blocades [sic], famine). For instance the First Jewish War has confused historians as an estimated 30K death came from the war, and a considerably higher (between 350K and the number 1M according to Josephus) from the famine or civilian casualties.

Excellent points. Famine does not kill as many (I did not say none) today after a war because food production and distribution are more robust. The authors also say, “We can assume that there are numerous wars that are not part of our sample, even if we doubt that such events are in the ‘tails’ of the distribution, given that large conflicts are more likely to be reported by historians.” More likely does not imply certainly. And they say, “events are more likely to be recorded in modern times than in the past”

Measurement error, as admitted by the authors, and is by now obvious, is a tremendous and incurable problem. What that means is that any formal model of violence is going to be too sure of itself and in a way that we can’t quantify. This is not surprising: not all uncertainty is quantifiable.

Lastly, the authors “rescaled” the event death tolls by world population estimates (more unaccounted for uncertainty). This makes some sense, but it has its limits. When Cain whacked Abel, he reduced the world’s population by a quarter, but today when Boko Haram rapes a woman to death the effect on the tax rolls is minuscule. The figure above “Rescaled death toll of armed conflict and regimes over time” in their final dataset.

An Lushan? Led a revolt against the Tang dynasty and was so nasty his own son had to take him out. Is Zhang Xianzhong isn’t on the list? His motto was “Kill. Kill. Kill. Kill. Kill. Kill. Kill.” Reports are that he enthusiastically implemented it. And where’s Mao, Stalin? Caused the death of tens of millions. Here’s a problem: it isn’t “war” or “conflict” if you kill your own subjects. More uncertainty.

Are killings unusual?

Anyway, let’s assume the picture is in the ballpark (the rescaling technique suffers in smaller populations, as with Cain and Abel) but that it represents an error-prone way of counting violence (older events are more likely to have been missed). Including our knowledge of recent history, then ask yourself: is violence going down?

Yes and No. We haven’t, as observed, had a large scale (International-Socialism, WW2, etc.) kill-off this last half century, but that in no way implies we won’t have one in the next half century, or indeed at any time. We lasted some 50 years with only (only!) small-scale slaughter, if you except abortion. But there have been plenty of similarly lengthed periods “in-between” mass killings in history. Armageddons don’t happen yearly; they are sparse, but not unusual.

And we’re done. We don’t need a model or any other form of quantification to tell us the obvious. We never need a model to tell us what we’ve seen—unless we’re using that model to tell us what happened in the presence of measurement error, like exists here. But that’s not the use to which Cirillo and Taleb put their model. They use it to tell what happened. Or, rather, not what happened, but what happened to their model.

Now in their favor, everybody does this. Nobody is content to let the data speak for itself. People will build models and say, “Here’s what happened” when what they really mean is, “Here is a replacement of reality that pleases me and has these mathematical properties.”

The only reason to build a model of violence—and it’s a darn good reason—is to predict how many dead bodies we expect to create in the future (so we know where not to be). But given all the unquantifiable uncertainties mentioned, I would have very little confidence in that model.

Causes of war

Before I discuss (briefly) Cirillo and Taleb’s model, understand this: something caused each war. There are surely similarities in causes across wars (“I want to kill,” says somebody in each), but there are always causes for each death. There is thus no “mean rate” of violence that is “natural”, a rate which propels men toward slaughter. (This summary of the paper makes this error repeatedly,) There is no such thing as a “background violence rate”: there are only causes which we may or may not fully understand. If we understood them, we’d never need statistical models.

There are mean numbers of dead bodies, of course, measured over whatever arbitrary time points we pick, but that kind of summary gains us nothing over plots like that above. That picture—how it was created, the vagaries of the data included and unseen, and the like—is the entire analysis. Cirillo and Taleb are to be congratulated for the hard work in collecting this data (they credit one Captain Mark Weisenborn). Yet putting math to the data can only produce over-certainty unless we use the math to predict what will happen. But then we have to wait and see if the model made the correct predictions (put high probability on what happened and low on what didn’t).

Obviously, we haven’t waited and so can’t say whether the model Cirillo and Taleb posit is any good. The pair present some measures of model fit, and these are of modest interest, but they are far (as in far) from proof of the model’s goodness. Don’t forget climate and sociological models also show good fit but poor predictive skill.

We must avoid the Deadly Sin of Reification. This is the false belief that, somehow, mathematics is superior to reality, that the model is good because it makes reality cleaner. Cirillo and Taleb talk about the “stochasticity of under inter-arrival times” as if wars arrive or are guided by some mathematical process. This is the sin. Wars are caused by men. Our understanding of the uncertainty of when wars start might usefully be encapsulated by a model, but that’s as far as we can go (and we haven’t yet demonstrated that that is true for Cirillo and Taleb’s model).

Wars and rumors of wars

One thing that is obvious in the plot, and from any serious reading of (non-Howard Zinn-like) history, is that large kill-offs are not especially rare. Cirillo and Taleb’s model agrees (as it must). Why are they not rare? This is key. We know wars are caused by humans, and if we accept the premise that human nature is flawed, it is rational to conclude more wars will occur and that some will cause the creation of copious coffins.

Cirillo and Taleb appear (they don’t explicitly mention it) to accept this premise. Pinker does not. That premise is the real and substantial difference between the prediction of future wars. If you believe people are perfectible through education and enlightenment, then it follows wars will decrease in number and intensity. But if you believe men will always disappoint, and given the data in plots like Cirillo and Taleb’s, then it’s only a matter of time until the next full-scale war hits.

Good thing about both of these models is that they are testable. We just have to wait and see which is true.

Update I saw in other discussions of this paper (and of my discussion) words about how times between wars are or aren’t “random.” These are all wrong-headed. Just as something caused each war, something caused each peace. Random only means unknown. Data are not random: it is only that our knowledge of their causes is incomplete. No MODELS ARE NEEDED HERE.


  1. >If you believe people are perfectible through education and enlightenment, then it follows wars will decrease in number and intensity.

    Logic error, because of uncertainty in the definitions, especially of “perfectible.” (“Perfectible” to someone might mean people becoming more prone to fight — I don’t know: people becoming “more able to stand up for their rights”, something like that?)

    But your turn of phrase also does touch on the eerie vacancy of Dr. Pinker’s logic — there’s too much assuming that such giant ideas are already well-defined by all Sensitive Clever Modern people.

    I don’t know if Dr. Pinker tells us this in his book, but certainly one impetus for his train of thought would seem to be the ethnographic finding that pretty consistently, about one-third of men in primitive societies died in warfare/raids/duels of various kinds. And then noticing that “one-third” is not the proportion one sees today, even across all of Maoist China history, or Leninist-Stalinist history. This difference, if real, also has a cause.

    I’m guessing that big States don’t ‘need’ as much violence, having gradually found more efficient ways to seduce and control large populations for access to power and resources. But if such Big Machines fight, then we have Transformer Wars.

    Thanks for bring this other study to my attention, and for your analysis, which demonstrates again that you have better tools in your toolset to think about such things.

    And also, thanks for: “… to progressivism and democracy (a redundancy). ” You slipped that in there. But I noticed.

  2. In the second to last line, is “(and plots like Cirillo and Taleb’s)” missing something?

    I unconsciously completed it: …plots like Cirillo and Taleb’s seem to confirm that point)….

    But I may be off base.

  3. Briggs

    May 20, 2015 at 10:15 am


    Good catch; lousy writing on my part. I fixed it. Thanks.

  4. “I fixed it” – um, no.


  5. Well, there’s some unwarranted precision from WB, as well. If Cain’s killing of Abel reduced the population by 25%, we’ll be hard-pressed to account for his finding a wife (unless it was mom, of course), or for his or God’s concern that “anyone” might slay him (unless, of course, we’re gonna go with the parental units in this instance, too).

  6. Briggs

    May 20, 2015 at 11:34 am


    Unless the humans could breed with the other homo species, which seems to be the case.

    Anyway, you get the point of the example.

  7. Interesting stuff. Reminds me of an article on a similar topic I read last year, but I can’t recall who it was penned by.

    Where do they get the figures for the An Lushan rebellion? I would guess that is a lot more murky than something like WWII.

  8. A quick scan of the paper, it seem that the focus of the paper is exactly on the difficulty of attempting to capture and classify the data. And that is it unlikely that the historical sample mean has value as a predictive variable.

  9. It looks like the unkewed poll of the2012 election

  10. If you include abortion women are doing a good job at catching men up in the violence stakes. But it doesn’t appear to concern too many of them.

  11. Sander van der Wal

    May 20, 2015 at 2:28 pm

    How about doing the counts by region? Or are people too afraid to find that people in and around China are much better at killing people than everybody else?

  12. In addition to any kind of basic human desire to go to war, there are additional potential causal factors. Strategy, tactics, and technology will, regardless of the motivation for war, play a big role in how many people die. WW1 is a good example of this. To run an army before trains and advanced supply lines and before your lands could support a standing army, it was advisable to kill and pillage a lot.

    Another one is the ability to print money to pay your armies.

  13. Briggs

    May 20, 2015 at 3:13 pm

    Doug M,

    Just so. The model of the “journalistic” mean is likely to be poor predictor for future data. To tell for sure, we’ll have to wait and see. But we don’t need models to tell us how rare (or how common) things that already happened were: we can just look. Their model should not be used to tell us what happened, though it may make a good candidate to say how many bodies we can expect in some specified time period. It’s very likely to be better than a mean, but I don’t think anybody was seriously arguing for the mean. Well, Pinker might have been, but he has many other flaws.


    Wikipedia. Or so they said. They also said that, eventually, they’ll release the data.

  14. Ye Olde Statistician

    May 20, 2015 at 5:39 pm

    That great big An Lu Shan bubble is from Matthew White’s Great Big Book of Horrible Things (Norton, 2011), which Pinker cited as if it were actual historical research. (White self-describes as a librarian with “a few years of college.”)

    He obtained the figure is by comparing the Chinese census of AD 753 (52,880,488) to the census of AD 764 (16,900,000). Holy moley! Where’d 36,000,000 Chinese go? They must be casualties of the revolt!

    But historians of China tell us it is due to the collapse of Tang administration and their failure to secure an accurate census.

    After the An Lushan rebellion, the Tang court lost the ability to enroll, enumerate, and impose taxes directly upon the majority of China’s peasant households. This development is dramatically illustrated by the decline of the registered population from approximately nine million households in 755 to less than two million in 760. (Graff, Medieval Chinese Warfare, p. 240)

    So the comments about the difficulty of defining terms and securing accurate data are apropos when dealing with such amorphous objects of study. They lack (as Richardson noted) “thinginess.”
    The grand-daddy of them all was Lewis Fry Richardson and his “Statistics of Deadly Quarrels” (1960) in which he did include murders and the like. He broke up complex wars (Napoleonic, Great War) into theaters of conflict. e.g.: Western Front, Eastern Front, Italian Front, etc.

    Later, J. David Singer and Melvin Small wrote a book — The Wages of War, 1816-1965: a Statistical Handbook — in which they made an effort to define their objects operationally. (At least one combatant an organized state; at least a specified number of casualties, etc.)

  15. One other big question is whether the data set is complete. For example, (although I don’t know that exact numbers, so maybe I’m wrong and have overimagined the death count and these are some of those smaller bubbles) I would have expected the Islamic conquests to feature heavily in the period 650-1000AD.

  16. BB,

    The Islamic conquest didn’t create much massacre. Of course, if town or region didn’t surrender there would be combat that would create casualties but must of the time they surrendered. The Islamic ruler authorized other religion as long as the special tax was paid and people were free to convert but not forced.

  17. Ah, good ol’ ‘throw up yer hands’ conservatism. Nothing to see here folks, just genetically programed machismo.

    Humans are social primates. Our closest relatives are relatively peaceful sorts of chimps. It is society that created mankind as we know him now. We didn’t show up this way. Manly Man World is pretend.


  18. Briggs

    May 21, 2015 at 6:18 am


    Actually and of course it is primarily, or rather only, progressives who push the idea of genetic determinism. Humans are primates, all right, nasty animals—chimps also have war—and because humans are smarter, they do war more effectively.

    Somehow this is apropos: http://thefederalist.com/2015/05/20/lgbt-activists-arm-for-further-war-on-free-speech/

  19. Sometimes it takes great wisdom to do nothing. The progressive mindset is to always do something, even if the something makes matters worse.

  20. I really enjoyed this. I’d make a narrower point, probably less insightful and wise. If you are going use statistics to show that someone else is wrong, it seems to me that you should:

    1. State precisely what view you question.
    2. Provide examples of your opponent espousing this view.
    3. Run statistical tests specified to test the view.

    As far as I can see Cirillo and Taleb do none of these things. They seem to be challenging the notion of a “long peace”?—?lack of war among great powers since 1945, and more precisely the idea that the long peace is here to stay. But they never say this in so many words. And they never show that Pinker believes the long peace is a portent of the future (though he may well). They never focus on great powers. And they never run a statistical test of whether, say, a post-1945 dummy improves their model more than would be expected by chance.

    The argument therefore seems fundamentally flawed.

    My fuller take is at http://davidroodman.com/blog/2015/05/19/little-greek-letters-become-weapons-in-war-of-words-over-trend-in-violence/.

  21. William (Bill?),
    On your update: I ‘get’ that little in life is truly random, but stochastic models often provide a good fit to the data, and have some predictive utility, such as how many body-bags to order. It may be less important to know what the detailed ’causes’ are.

    Life gets interesting in conflict and economics, for example, when one suddenly has a run of ‘1 in 100 year’ events. The common approach seems to be to regard this as bad luck and carry on using the established stochastic model. An alternative is to think that there may have been some causal change, and to go and look for it. So I think the issue is not the use of stochastic models, but how they used.

  22. Ye Olde Statistician

    June 2, 2015 at 6:48 pm

    I ‘get’ that little in life is truly random, but stochastic models often provide a good fit to the data,

    Heck, Ptolemaic models provided a good fit to the data for a couple of millennia. But that didn’t make them causally true. Gravitational models in which the Earth is considered as a point source also provide a good fit to the data, but that doesn’t mean the Earth a mathematical point. Models like F=GMm/d² can be fruitful, but the model is not the physics any more than the map is the territory.

  23. It seems to me that if you want to predict eclipses then a model is needed. While you can never know that the model corresponds to reality, and can often be sure that it does not, a model can sometimes be fit for purpose. The problem that I see with the use of stochastic models is not that they are intrinsically bad or useless but that they are habitually used well beyond reason.

    By the way, I try to avoid the use of words like ’cause’ outside of specific models, as they seem unhelpful and often confusing. I wonder what you mean by the term?

  24. Thanks for the link. She is always worth reading, but I find always a challenge to interpret. From “We make our best causal inferences in very special situations—situations where our general view of the world makes us insist that a known phenomenon has a cause; where
    the cause we cite is the kind of thing that could bring about the effect and there is an appropriate process connecting the cause and the effect; and where the likelihood of other is ruled out.”

    So weren’t Ptolemaic models causally true ‘for them’? Currently, it seems causally true for some that austerity causes promotes recovery while for others its seems causally true that austerity holds back recovery. My own experience is that in many conflicts and confrontations there are conflicts over causality, and that attempts to rationalise can be fruitful. (Maybe the same would be true in economics?)

    Surely the key point is that whatever theory/model we have, and no matter how strongly we believe in it, and no matter on how strong an ‘evidence base’, we should always recognize that there is some residual uncertainty, and seek to ‘prove’ the model in the good sense of the term. Maybe then wars and violence would decrease?

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