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Statistical Murder

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Robert Zubrin writes in “How Much Is an Astronaut’s Life Worth?” (Reason, Feb 2012):

…policy analyst John D. Graham and his colleagues at the Harvard Center for Risk Analysis found in 1997 that the median cost for lifesaving expenditures and regulations by the U.S. government in the health care, residential, transportation, and occupational areas ranges from about $1 million to $3 million spent per life saved in today’s dollars. The only marked exception to this pattern occurs in the area of environmental health protection (such as the Superfund program) which costs about $200 million per life saved.

Graham and his colleagues call the latter kind of inefficiency “statistical murder,” since thousands of additional lives could be saved each year if the money were used more cost-effectively. To avoid such deadly waste, the Department of Transportation has a policy of rejecting any proposed safety expenditure that costs more than $3 million per life saved. That ceiling therefore may be taken as a high-end estimate for the value of an American’s life as defined by the U.S. government.

This reminds me of my old article on Value of Life – where the hidden cost of the Iraq war for the US comes to 720,000 lives lost (based on the huge cost).

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20 Comments

  1. revo11 says:

    This term and these arguments are utterly bizarre.

    Rejecting a proposal which spends more than$3 million per life is only warranted if the counterfactual is that the money IS allocated towards a plan that is more efficient. If they reject the proposal and the money goes, say, to tax breaks which a rich person spends on a yacht, you could take the same argument and say _that_ is statistical murder compared to whatever the >3million$ per life proposal was.

    There seems to be a bizarre linearity assumption that’s unlikely to hold in the real world. For instance, research funding has very non-linear returns. You could have situations where 3 million dollars a person isn’t enough to achieve the breakthrough, but 4 million dollars achieves a breakthrough. Then by the same argument, the 3 million dollar investment is “statistical murder” relative to the 4 million dollar investment.

    All this is to say, I’m all for allocating money wisely and modeling outcomes. But don’t use a term as loaded as murder for what amounts to guesswork.

    • seppo says:

      “Rejecting a proposal which spends more than$3 million per life is only warranted if the counterfactual is that the money IS allocated towards a plan that is more efficient.”

      Not necessarily. It depends on how we got to the number of $3 million. If people tend to (statistically) behave in a way that values some small reduction of risk to die by some amount which will statistically add up to $3 million per one life saved, then no, we do not want to pay anything more than 3 million to save one life. We rather take the risk. Think about it, you yourself clearly have the upper bound you are willing to invest in reducing the risk to your life.

      • revo11 says:

        That’s going down the libertarian argument that decentralized allocation is always optimal for a population. That’s a separate point than the one that’s being made here – the basis for rejecting grants is that the money could be allocated to their known programs which have a predicted ROI that’s “better”. You’re probably arguing that the “best” counterfactual is to give people their money back, but that has nothing to do with the 3$ million dollar figure they’re throwing around (which is based on their other programs). My point is that’s not always the counterfactual, and by their definition the actual counterfactual (to accepting the grant) could sometimes be called “statistical murder”. Secondly, that underlying that argument are not only faulty counterfactual assumptions, but faulty linearity assumptions. I don’t have a problem with making these rough calculations, just that the term murder should be nowhere near them – it’s a sign one has mistaken their model for reality.

        Now as for the libertarian argument, this could go on forever. But consider that two people may have the same set of preferences, however, only one of them is able to exercise those preferences. This gets back to the previous post – imo too much inequality becomes a threat to individual liberties.

        • Jonathan (a different one) says:

          I think the general context from this argument is that agency X has a budget which they allocate to various projects. In that context, these calculations make perfect sense, although you are roughly correct in that threshhold effects are being ignored. There is another sense in which, even in the presence of threshhold effects, these sorts of effects help prioritize.

          The term murder is a bit over the top, perhaps, but it helps focus the mind that real choices are involved here.

        • seppo says:

          Jonathan is right indeed – there was absolutely nothing libertarian in my logic, nor had it anything to do with decentralized allocation.

          I even think, I know what you mean, revo11, but I think you may overlook important point in this context. Let me try to write it down (and pardon for my English): let there be a nice little family who like bananas and let there be a chance to buy them for $3 per kg. Now the spouses know, that in another supermarket the bananas would cost $2 per kg, but they also know that they will not go to the other supermarket. If they value bananas for more than $3 per kg, they will buy them. They will buy the bananas. But let the bananas now cost $22 per kilogram. Not only are they cheaper in another place, but the spouses really do not value the bananas as highly. If they happen to have some rationality inside, they will not buy them even if the money will not be spent on bananas.

          This is what I argued for – it may really not be worth it to invest $4 million for decreasing everyones chance to die a little bit.

          This $3 million for a statistical life saved is actually not the most effective alternative (this would be the neonatal hospitals in developed world as much as I know), it is exactly the maximum that is thought to be worth it. The calculations behind it are of course very rough and at the end some assumptions are just made and agreed upon, but the rationale behind the number is this.

          • Andrew says:

            Funny to see someone named Seppo who’s not an American.

          • seppo says:

            Oh, thanks for destroying my blissful ignorance :) The name is very common in Finland as a first name (I am from neighboring Estonia though). Will have to start orienting towards Chinese-speaking audience now :)

  2. John says:

    Suppose 9/11 inaugurated a state of the world where every year, with probability 0<p<=1 a terrorist event took place, and that the number of victims increase every year as some function of previous victims.

    That is, assume it announced a "terrorist threat regime" whereby victims increased every year nothing was done about it. Success breed success.

    3 trillion cost of war / 307 million US citizens = 9,800US$ per capita.

    Not a crazy amount if you think of it as payment for a reversal to the status quo ante. Certainly not far off from some life insurance options.

  3. Anon says:

    According to http://www.feb.se/EMFguru/conflicts/money-science.html , “Graham said that reducing dioxin levels too far might “do more harm . . . than good.” Incredibly, he argued that dioxin might prevent cancer in some cases …”

    Just pointing out he’s made some strange arguments in the past.

  4. John Mashey says:

    For calibration of risk and lives lost, I recommend Stanford Prof. Robert Proctor’s fine (if horrifying) book Golden Holocaust: Origins of the Cigarette Catastrophe and the Case for Abolition.

    “Tobacco killed only about a hundred million people in the twentieth century, compared with the billion we can anticipate in the twenty-first-if things continue as they have in the past. Tobacco now kills about six million people per year.” p.2.

    “The companies make about a penny from every cigarette sold, and since one tobacco death results from every million smoked, that means that a human life is worth about $10,000 to your average cigarette maker.” p.9 (Six trillion are smoked per year.)

    There also interesting demographic statistics to be explored, for example in China, India and Indonesia.

  5. Turadg says:

    Regarding the Superfund program, isn’t *quality* of live part of the outcome sought? People suffering from pollution doesn’t make it into the cost/benefit analysis?

  6. Eli says:

    One would have to be careful about only applying this standard to expenditures that are solely interested in “lives saved” without concern for other positive externalities like health, quality of life, justice, or future prosperity.
    If environmental health regulation has other benefits, it might be worth it. More than $90million have been spent on Pink Floyd’s “Dark Side of the Moon”, but it’s hard to think of it as having killed 30 people.

  7. Brett Keller says:

    Mary Roach’s “Stiff” (on what happens to humans once we die, and to a lesser extent how we achieve that state) has an interesting section that outlines various valuations of human life used (I believe mostly implicitly) in regulatory decisions re: how much airlines are required to invest in safety precautions.

  8. A. Zarkov says:

    How much is a life worth? Which life? And to who? I can think of some people who have negative worth (to me), and most likely to most everyone else. For example, Charles Manson. I don’t think this is a well posed question.

    • I’ve come across papers that actually studied how people’s lives are worth differently (at different times). For a specific project or policy decision, the estimates might be different.

    • seppo says:

      There are a number of papers for these calculations and they are heavily used in every kind of cost-benefit analysis. It is better to imagine it not as “the value of someone’s life”, but the value of reduction of everyone’s probability to die by some small amount. If a project is able to reduce the probability much enough for a large enough group, that this becomes noticeable, then these kind of benefits can be accounted by using the statistical value of life.

  9. Counterfactual... says:

    Yeah- that value of a statistical life re the Iraq ear is total bogus. Andrew, as you know, you can’t just look at the costs endured in the current state of the world and presume that they would be the same in any other state of the world wherein we spent less money on war and more on other things. Your back of the envelope calculation (or at least the one you cite) is misleading.

  10. Phil says:

    I think revo11 got it right in the very first post on this thread. Is the money people spend on internet service “statistical murder” because it could be used to save lives instead? If so, hey, I’m murdering someone right now!