Numbers Games

I’m not going to go over the existing disputes about the methodology or findings of the Lancet study on civilian casualties in Iraq. That’s been done at a great many other blogs.

I’d like to instead talk about how I tend to approach quantitative debates in history in general.

I’m not much of a quantitative thinker myself: I lack the expertise to do really fine work myself along these lines, and numbers rarely seem to me to meaningfully adjudicate a lot of the questions and issues that draw me as a historian. But there are plenty of discussions among historians where the importance of numbers is indisputable, debates which I read appreciatively.

The thing is, numbers don’t have a self-evident significance. It’s largely a matter of whether there is a question on the table within which numbers play a decisive role.

Let me take the example of one of the great “numbers games” in historiography: the Atlantic slave trade. Philip D. Curtin’s important census of the Atlantic slave trade, first published in 1969, kicked off a long-running discussion of the numbers of Africans who were taken into slavery across the Atlantic. Curtin observed that the numbers which had previously been offered rested on little more than random conjecture, on “common sense” of various kinds, on casual repetition of claims across a long series of texts. He was right: his book was the first truly systematic account. It was followed by various systematic corrections, objections, amendations and observations by other historians, and sometimes also by sharp debate about whether or not Curtin’s figure underestimated the magnitude of the trade.

The tone and character of that debate sometimes puzzles me, but then so to does the sheer amount of labor invested by some in methodically updating or testing Curtin’s numbers. Having a figure that was meaningfully systematic mattered, a lot. But for many of the questions and interpretations surrounding the trade, it really is only important to know a rough order of magnitude. In particular, the moral and ethical questions raised by the Atlantic slave trade are not necessarily transformed much by whether the final magnitude is 8 million, 12 million or 20 million over four centuries.

The nitty-gritty of the numbers–and the methods used to generate them–matter intensely only in relation to very specific discussions or problems, some of which are themselves quantitative in nature. For example, evaluating the demographic impact of the slave trade on West and Equatorial Africa requires both the best numbers of slaves taken and the best numbers of people living within those regions that we can generate. But it doesn’t really matter how hard you try: the second set of numbers are never going to be anything more than a good guess. More importantly, the numbers alone don’t resolve the discussion, or speak for themselves. That really comes down to deeper theoretical arguments about population dynamics, economic production, kinship structures and the like. Having one number of people taken and one number of people remaining really is not self-explanatory at all: common sense can lead us badly astray. We might think that if the numbers taken are a very large proportion of the total population numbers, that is self-evidently a catastrophe. It might well be, but the case for that lies well beyond the numbers.

This, I suppose, is one reason I find the discussion over the Lancet findings a bit frustrating. Almost everyone is acting as if the significance of that number, large or small, is obvious. From my perspective, even a small number is something that supporters of the war should take seriously, but that’s got nothing to do with how we count civilian casualties in methodological terms. It has to do with the (supposed) aims of the war. If you’re fighting a conventional war to take territorial or geographic objectives, civilian casualties of any magnitude may or may not be morally worrisome, depending on your own moral system. But they do not, in most cases, directly impact your success in achieving your objective. Whether or not you capture a bridge, a strong point, a key resource site: the magnitude of civilian casualties are a side issue if the question is, “Did we win?” in this instance. In some cases, of course, killing civilians IS the objective. I can well imagine that some of the insurgent factions care very much about how accurate the Lancet figures are, as these are direct measures of the magnitude of their success.

But as I understand the declared objectives of the American effort in Iraq, the exact number of civilian casualties is not altogether that important, save perhaps for the symbolically important question of whether more would have died under Hussein’s rule than under occupation. Even that can be well sidestepped with a certain amount of cliched rhetoric about omelettes and eggs. The problem here is that the civilians ARE the objective: not killing them, but protecting them. Not just protecting their lives, but their well-being, their ability to live freely and securely under the rule of law. If that’s the objective, 50,000 or 300,000 or 600,000 all strike me as deeply worrisome numbers, just as once you cross the threshold of “many millions”, the moral gravity of the Atlantic slave trade is forever established. More millions doesn’t do anything more than put a few more weights on a scale that is already firmly crushed to earth. So there is one sense in which the sturm und drang of the last week seems to me another “numbers game”, and not a terribly illuminating one in terms of defending the case for the war.

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19 Responses to Numbers Games

  1. hestal says:

    The number of casualties in Iraq, of all types, is important for the future. And it should have been important for those who invaded Iraq. A humane government would take into account the level of casualties a new war would cause the invaded state versus the number of casualties that would occur in the invading state should the invasion never take place. In this analysis one would want good data including probabilities on both sides of the body count.

    I know it sounds naïve to think that states will one day act this way, but I think it will happen well before the end of this century. I think the West is coming to that conclusion rapidly. How many casualties will it require in Islamic states to eliminate the possibility of casualties in the West? The ratios are already unacceptable. We have to live with risk on this side of the pond if we are to be honorable.

    These numbers, unattractive as they are, will lead to new approaches in trying to minimize our risk, and that will include not killing others willy-nilly. We just need to know how big willy and nilly might be.

    But another important number in this world is the number that measures time. So much of our public institutions take no notice of the threads of individual lives and how they are affected by the time of life. The needs and powers that distinguish each stage have a measurable characteristic that weighs the value society places on the individual as well as the value the individual places on his own life – especially in the context of weighing where he is and where he wants to go. The very first question to ask is, “Do I have enough time to get where I want to go?” The second question is am I moving at the right speed or must I, can I, make a change? The third question is what are the costs and the risks, expressed in terms of other choices.

    The basic understanding of how important time is to our individual lives is so important and it is not intuitive. It must be taught and society needs to do so. Society also needs to provide routine tools for individuals to use as needed to measure their time status just as they measure their health status.

  2. withywindle says:

    I don’t actually object to adducing numbers in support of political arguments, per se. Like Tim, I’m often dubious about accuracy, significance, etc., but I think they do express truths with real moral weight. So while I may reject the Lancet’s numbers as spurious, I don’t think it’s illegitimate to use such a quantitative study as one means by which to judge the Iraq War. This is me being a bit contrarian–I’m in many ways in agreement with Tim’s points and point of view.

    So, Tim, when you teach *Beloved*, will you discuss the dedication “To 60 million”?

  3. Timothy Burke says:

    Sure, I would. One of the things I get into in my Africa in the Era of the Slave Trade is the way in which the numbers game in that context is driven partially by a need to establish the comparable gravity of the Holocaust and the Atlantic slave trade; that is surely also a bit of what is going on in the dedication to Beloved. (Though the number there is, I think, about the total number of Africans in the diaspora in slavery, right? Not people taken across the Atlantic.)

  4. withywindle says:

    I believe that it was indeed supposed to be people embarked from African parts–that being the canonical (and spurious) position of the relevant numbers-inflators. (I fancy that if you Google “60 million” and “slave trade” you will find some relevant hits.) Morrison was tying her novel about slavery to a specific, and false position on the statistics of the slave trade. Worth noting.

  5. jim says:

    I think there is some point to the numbers game as applied to Iraq. Norm Geras said, in part as a response to Burnham et al., that had he known the war would have such consequence, he wouldn’t have backed it. He wouldn’t have opposed it either, though, since removing the Baath regime was important. It seems to me that he can’t quite have it both ways. The deaths are a consequence of removing the Baath regime. Either the good (removing the regime) outweighs the bad (at least 400,000 deaths according to Burnham et al.) or it doesn’t. There is some sort of utilitarian calculus at work. And there’s some level of deaths which presumably would be acceptable in light of the benefit to the world of removing Saddam Hussein from power. No-one believed at the outset there would be no deaths whatsoever. So the question really does become How many is too many? To say that the actual number doesn’t matter is to say that the “too many” threshold is small, so small that we long ago by any measure exceeded it. That, I take it, is the purpose of the slavery analogy: once you get into the millions, it doesn’t really matter, morally, how many millions. The problem with Iraq is that there isn’t agreement on how many is too many. Which is why there’s heated argument over Burnham et al.’s estimate.

  6. Tim, I wonder what you make of the orders of magnitude issue with respect to the post-Columbus New World die-off versus the pre-Columbus New World population figures. Like the slave trade, the obvious politics associated with it are that lower ones look not so bad for old Europe, larger ones look very bad. (Percentages of population lost in specific regions already make it far worse than the Plague in Europe.) So it is very important to try to get it as close to right as possible, as dispassionately as possible. Not just to avoid being a witness for the defense or prosecution on old Europe’s crimes and complicities, but to get a more accurate sense of what was lost during the die-off, a clearer sense of the range of cultures and civilizations in the Americas (before they were ever called the Americas, that is). I’ve read Horace Mann’s 1491 which tries to bring some of the recent debates and discoveries in academia to a wider audience, but I was wondering if you or others who read this blog know of an attempt by an academic historian to provide an overview of the field….

    doubledubya, it seems to me that artistic licence covers an author’s dedication to a novel along with the novel itself, but that’s probably just me. A more serious response would point to the novel’s subtle insistence on giving testimony to the deaths of African slaves during the Middle Passage (see especially the increasingly fragmented series of monologues near the end) and ask: how reliable are the standard numbers on this particular way of dying under slavery? Caryl Phillips’s novel Crossing the River suggests that as a simple business practice, captains of slave ships or their subordinates kept careful count of those who died in transit, so ships’ logs should provide fertile and reliable evidence, if read well, of both death and resistance during the Middle Passage. Is it possible that enough went uncounted to affect the total slave trade numbers by a significant order of magnitude? What are (IYO) the best numbers nowadays on the slave trade? And who sez?

    That asked, since Morrison’s novel focuses as much on the Reconstruction period (and its end) if not more than on slavery, I think Tim’s interpretation that the 60 million and more line references all those, living, and dead, who were taken from Africa, and their descendants, living and dead, is more plausible. I also agree that there’s a Holocaust allusion, there, too. I’m working on a book chapter in which I argue that there’s a Salem witch trial thing going on in the novel itself. W/o giving too much away, think “specter evidence,” “Young Goodman Brown,” The Scarlet Letter, and Stamp Paid….

  7. Sdorn says:

    About 10 years ago, I had the pleasure of having this both ways, talking both about the demography of graduation and also about the social meaning of it (and the creation of “dropout” as a social problem).

    And, yikes!, but the price of that has gone up since it first came out 10 years ago. Folks, get it from your local library if you’re interested and don’t want to pay that.

  8. Walt says:

    Tim – You’re right about the importance of numbers in history. While it’s good to work from the most accurate facts you can get, they’re just pieces of the puzzle.

    You’re right, too, that supporters of the war need to take seriously the moral issue of civilian casualties. In this case, though, it makes a big difference whether the toll is, say, 60 thousand or less, vs. 600 thousand. The former can be compared to the damage that would have resulted from various alternative policies; the latter, not so much. And, whether the war has caused net good or net harm in this respect is more than just symbolically important.

    So I’m sorry that you began your story by, apparently, taking seriously the Lancet study, and then by refusing to address its credibility. I accept that you want to leave detailed discussions of the methodology to others. But where are your critical skills as a historian, or as an ordinary reader? This report wasn’t produced by neutral historians or statisticians. It was produced just before an election by people who are passionately against the war. It is greatly at variance with any previous estimate. Isn’t that enough to reject it out of hand?

    You wouldn’t read past the first paragraph of a report by, say, Douglas Feith’s old office that put the civilian death toll at one tenth of previous estimates. (Neither would I.) How is the Lancet study any different? It isn’t that partisans can’t produce good research — they can, but you need some reason to pay attention. Have these authors described their methodology in detail? Have they attempted to reconcile their results with any other source? Has their work been supported by any impartial reviewer? You don’t need to be a statistician to apply those tests, but you do need to apply those tests to be a serious commentator.

  9. Doug says:

    Walt, you’ve read Daniel Davies’ posts over at Crooked Timber, right?

    Also, just to reiterate, Lancet is peer-reviewed and not driven by US electoral cycles.

  10. withywindle says:

    Constructivist –

    Not having my books on me right now, I recollect a figure that ca. 11-12 million slaves actually arrived in the New World (the majority of whom probably died of overwork within 7 years of landing) between 1500 and 1900; that some millions more died in transit from Africa, and some millions more in transit within Africa; ca. 20 million, therefore, is the extraordinarily rough figure for the number of people initially taken captive for the Atlantic slave trade. High enough! — but not 60 million. I think the Adas et al World Civ textbook uses similar figures, and I trust Michael Adas is not taken as a Europhilic minimizer? Although for impact of daily life, I once made a seat-of-the-pants calculation that at the height of the slave trade, a few hundred slave ships each year came to the continent–which translates to remarkably little actual interaction between Europeans and Africans for such enormous consequences.

    As for the New World die-off: I think you need to be more precise. A large die-off due to disease is taken as exculpatory of Europeans, on the theory that no matter how they behaved, 95% of Indians would have died anyway. If you discount disease, the effects of European conquest and slavery are magnified. I rather buy the disease theory, surprise surprise, though I do think that if you posit European conquest and slavery as making the difference between 90% and 95% death ratios, that has very great historic impact and moral weight. I found an estimate of 54M for the Americas in 1492 quite convincing, 3M north of the Rio Grande, the rest heavily concentrated in Mesoamerica (25M?) and the Andean heartland (20M?). Higher estimates I gather include 100M total, 10M north of the Rio Grande.

  11. Timothy Burke says:

    Walt: my point about the Lancet study is that the methodology, and the precise numerical findings, only matter from certain kinds of prior premises, and that most of the people involved in the debate about are not actually that engaged by those premises. For example, if you wanted to know about what precise social impact the war is having on families or households in Iraq, then the precise numbers of deaths (and injuries) might be far more important.

    This is why I’d agree that relative precision about numbers is often quite desirable, as long as the question on the table is one which meaningfully turns on those numbers. As, for example, in the discussion of the demographic impact of smallpox and other diseases on New World populations, or in evaluating just what percentage of existing West and Equatorial African populations were taken into slavery over particular periods of time.

    Withywindle: my thought on Beloved is that she is referring to ALL peoples of African descent who were enslaved within the Atlantic world between 1500 and 1900, and the point here is that there were far more people who were slaves than those taken into slavery because slave populations in the Americas reproduced themselves; e.g., 60 million includes people born into slavery in the Americas. I don’t think anyone, even Inikori, has claimed 60 million taken directly from Africa.

    The problem of the impact on daily life is that it was highly uneven: in some places, at some moments, extremely intense, at other places over longer periods of time, slow and diffuse. This is where “Europe” and “Africa” are very bad units for talking about the Atlantic slave trade in the first place: it makes much more sense to talk about “Liverpool” and “Nantes” and “Ouidah”.

  12. withywindle says:

    Morrison apparently has explicitly contradicted herself, making the claim that 60M refers to the slave trade, and also the claim that it includes all people in slavery (which, given the horrendous death rates and failure of most slave populations to reproduce, may also be an overstatement):

    Naomi Mandel, “I made the ink”: Identity, Complicity, 60 Million, and More,” Modern Fiction Studies – Volume 48, Number 3, Fall 2002, pp. 581-613, available on Project Muse.

    A google search finds “thirty to sixty million” in the slave trade rather commonly used (by non-academics)–most “sixty million and up” references seem to refer back to Toni Morrison, who may have started that trope.

    “Taken directly from Africa” is a little confusing–I do take as valid the contention that the numbers ought to include people taken as slaves within Africa, who died before they reached the ports, and also the contention that this number can never be more than an informed guess. Do Inikori’s numbers refer to shipment from African ports, or total caught up in the slave trade? I see (google-searching) that he used the number 15M at one point, but I don’t know to which that refers.

  13. Walt says:

    Doug, I hadn’t read Daniel Davies’s posts, but on your suggestion I found his essay at the Guardian’s blog (
    /2006/10/how_to_not_lie_with_statistics.html – you’ll have to cut an paste; I’m not good at inserted links). (I couldn’t find anything by him on the Crooked Timber front page.)

    He doesn’t present himself as a neutral reviewer, does he? Part of his essay is partisan and combative, much like some statements by Lancet’s editor. Davies answers the objection (which I wouldn’t have made) that one can’t extrapolate from a 1849-household sample, and the objection (which I reject out of hand) that the numbers don’t matter. He doesn’t address the issue of fraud except to dare anyone to allege it. (It’s alleged by many on the right, but neither they nor Davies have any basis to know). He seems to take the political timing in stride, saying that the issue is important enough to justify it.

    But of course we all know that there are countless ways to influence the results of a study that fall just short of fraud. (Among many ways, the easiest would be to allow respondents to report deaths of persons who might not otherwise have been considered part of the surveyed households.) If you doubt the possibility, think of the standards you would apply to an industry-funded pollution-damage study. Are you applying the same standards, or do you think that the issue is so important that you should suspend your normal skepticism?

    Tim, I apologize for hijacking your comment section for this rant; I’m assuming that you don’t have to pay for the extra bytes. I’ll stop now unless somebody wants to suggest a better forum.

  14. michael says:

    The Lancet article is an example of the idolatry of the question’ which characterizes Liberalism. The basic syllogism in symbolic Logic is ‘If A ] B,’if A then B.’ Liberalism seeks to gain a desired ground, B, by finding a single proposition A which drives the conclusion B. Naturally such arguments often come in moral terms as they must drive an entire proposition in one hit. The Lancet article derives from the proposition excess death (A) means immoral activity. It claims that it has found this proposition A; therefore the conclusion B that the Iraq War is an immoral activity is established. At best the opponents of the argument are left to define for those making the proposition what level of A would qualify for a truth quotient. No syncretism involving other propositions is allowed. Having asked the ‘tough question’ ennobles the asker and makes any syncretism or finding of methodological flaws pusilanimous. In the current discussion here, this single question is accepted as normative. The American effort is to be judged entirely by one stipulated outcome among a range of effects. One might turn this method of argument onto the other topic brought up by the poster, the impact of the slave trade. By the same method of argument just employed for Iraq, one could say that the slave trade was a glorious success. The economic and intellectual status of blacks in this country is gloriously better than of those in Africa. Somehow, that ‘if A ] B’ was not employed. Overall I prefer my liberals to be more like the communist Chou-en-Lai, who, when asked if the French Revolution was a success, said ‘it was too early to tell.’

  15. hestal says:


    So which is it: there were no “excess deaths?” — there were “excess deaths” but they were moral? — there were “excess deaths” that were immoral and some that were moral and the difference doesn’t matter? — there were “excess deaths” and they were immoral? Are liberals not worth the powder it takes to blow them up?

    Is your single proposition, “that liberals always seek to gain a desired ground by finding a single proposition,” a conscious, clever way of showing the weakness of liberalism or simply an unconscious revelation that critics of liberalism fall prey to the same methods? Could it be that these liberals have stumbled on the truth, even though they shouldn’t have because their methodology was faulty?

    Is this kind of bitter castigation (mine and yours) of other’s points of view a Lesson of History?

    Why can’t we all just get along?

    Is Symbolic Logic really any use in the real world? Is it more a tool of those who enjoy the construction of superior, even perfect, world systems over a drink or a smoke?

    Did those who launched the war in Iraq determine a level of acceptable deaths, using their own definition of acceptability? If they did, what should they do or say if the acceptable level is exceeded? Should we consider casualty levels or should we follow the philosophy of the Texas Conservatives who say, “let the rough end drag,” when dealing with casualties, or job losses, or votes that don’t get counted, or golf junkets, or health care rationing by bank account size, or… Oh, wait, I have done it again. I have found found a desired ground driven by a single proposition. Well, actually several grounds driven by that single proposition.

    So long as you have your Symbolic Logic textbook open, please parse, “Stay the Course,” “You are either with us or against us,” “Dead or Alive,” “Mission Accomplished,” “No child left behind,” “the Death Tax,” “WMD,” “God told me to run for President,” “Democracy is on the march in the Middle East,” “Cut and Run” There are more, but I suspect they will all fall into only one or two logic patterns.

  16. michael says:

    Hestal, Slogan or Die!

  17. (second try; much briefer) “If that’s the objective, 50,000 or 300,000 or 600,000 all strike me as deeply worrisome numbers, “

    Wouldn’t 6000 also be deeply worrisome, and even 700, and even 80, and even 9, or 1? I’m pretty sure Cindy Sheehan would be upset if the 1 was her son.

    Many good things have a cost, even a cost in lives. Sometimes, in retrospect, the cost in lives was much higher than expected. This doesn’t reduce the benefit of the good thing, but it does reduce the NET value, the benefits minus the cost.

    There surely is SOME amount of civilian Iraqi deaths which a majority of voters would say is “too high” — that the benefits aren’t worth the cost. Of course, US voters count American deaths as of much more voting concern than Iraqi deaths.

    Because of this, Lancet inaccuracies are deplorable, but the meaning of the numbers is still in the mind of those thinking about it.

    Was the D-day invasion worth the price? (If the June 44 alternative is to wait one more year, let the Germans and Russians fight more)

    Was Lincoln’s war to save the Union worth it? How many Americans would have had to die before you would say the US Civil War was NOT worth it?

    Was it good to run away from Vietnam in ’73, after signing the Peace Accords? Was it good to cut funding in ’75 after the ’74 elections, thereby almost guaranteeing the collapse of a corrupt, incompetent, cowardly, but human rights protecting S. Viet government?
    How many Vietnamese and Cambodians would have to be murdered before you would claim that the “cut and run” which the Democratic Party supported was a mistake?

  18. Doug says:

    WW, Davies presents himself as, I quote from memory, “a fat young man without a good word for anybody.” Neutrality is not his schtick, but he’s good on sociology and good on statistics and got Iraq basically right with a three-point test, one that Brad DeLong often quotes.

    I’m basically with Tim on this one, that the order of mangitude, or even one order lower, reflect very badly on what the Bush administration is trying to do in Iraq. Whether the right figure is 300,000 or 600,000 does not change that reflection.

    On the other hand, I don’t expect to convince you at all. You’ve said that whatever the Bush administration is trying to do in Iraq is worth 500,000 American lives, so presumably an approximately equivalent number of Iraqi lives is no great shakes in your view.

  19. hestal says:

    If the ratio of killed to wounded is the same for Iraqis as it is for our military there, what does this mean in terms of the number of maimed and wounded?

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