Kip Viscusi was kind enough to email me his estimates of the risks of terrorism, and gave me permission to share them.

To be more precise, Viscusi told me that, in his judgment, the *median* number of deaths from domestic terrorism in the coming year will be *zero*, and the *mean* number of deaths in the coming year will be 50 - "or about half the number of motor-vehicle related deaths per day."

If Viscusi is right, it's safe to say that we're annually spending more than a billion dollars per life saved. Good grief!

P.S. Kudos to Viscusi for being willing to go on the record here. If Overcoming Bias named a man of year, I'd be voting for Kip.

"A billion dollars per life saved" seems to me to be a blatantly static estimate. It does not do to simply take the amount of money spent, take the projected number of deaths, and divide. Kip's estimate implicitly assumes that the government will spend those billions. If you want to determine the cost per life saved, you have to take the amount spent, and divide by Kip's estimate of how many people would die

if the government spent no money at allon terrorism prevention. Overcoming bias, indeed.Something seems out of sync in this analysis. I must preface my comments with the fact that I have no expertise in this field and would like to feel more comfortable with the nuances so in the spirit of meaningful dialog let me voice my concern and maybe someone can enlighten me.

It seems that this analysis coldly calculates and predicts adverse outcomes and then compares costs and benefits to assess whether it was worth the investment.

It seems there is some kind of time inconsistency problem with this analysis. Our expenditures on anti-terrorism should be viewed as investments in avoiding negative outcomes associated with terrorism taking hold.

An analogue to the prosecution of the Iraq war seems appropriate. If you recall, at the outset of the war there was quite a debate about whether we should go in light (the Rumsfeld approach) or go in heavy (the old school Pentagon approach). In retrospect, by going in light we allowed chaos to breakout with looting and the destruction of the Iraqi army which ultimately led to allowing the insurgency to take hold rather than having overwhelming force. The long-run consequences have, from a cost benefit perspective, been a big failure. Were we to make the more expensive commitment at the outset, we might have avoided a very costly outcome. A strict cost-benefit analysis after the fact might have shown the strategy to be very costly. However, the reality has been the other way around.

The parallel with anti-terrorism is that we may be taking an overwhelming force approach and are avoiding allowing terrorism to take hold. We will never know what will have happened as we will be left wringing our hands under either scenario. If we use overwhelming force and succeed (aka overkill) we get a poor benefit-cost result. If we go in light and terrorism is an order of magnitude greater than it otherwise will have been then the benefit-cost result is also very poor. The end result is going to be disappointment regardless of the strategic plan chosen.

Oh yea, by the way, this same concern applies to the global warming issue.

I am missing something.

The number of deaths from terrorism can be zero or positive, but never negative. So how can the median number of deaths be zero, since the median must split the distribution in half?

Did you mean the mode of the distribution?

BH, you are missing something. In the series [0, 0, 0, 0, 0, 300], 0 is both the median and the mode. In a series of 6 ranked from low to high, the median is the 3.5th number. That is how it "splits it in half". In this case it is (3rd number + 4th number)/2 = 0. The mean is 50.

I'm still more curious as to whether Viscusi said anything more about his objection to prediction markets. Is his real take along the same line as Taleb's objection? In simplified form, Taleb's objection is that prediction markets fail in "high moment applications, heavy-tailed environments" due to "huge estimation error". Or did he merely reassert his original statements?

If Viscusi is right, it's safe to say that we're annually spending more than a billion dollars per life saved.Umm, no. If he's right, he's saying that we're annually spending more than a billion dollars per life that will die anyway despite the money we're spending. But that's a nearly useless statistic-- obviously you want the delta between lives that would be lost if the money weren't being spent in various areas.

I agree that there are plenty of ways in which money is being wasted. But your argument here is an offense against statistics and reason.

I think the problem with estimates of $X dollars per mean or median lives saved are likely to be highly misleading with respect to terrorism for the following reasons:

1. I suspect that the distribution of the cost of terrorist events is likely to be characterized by the stable Paretian distribution which is typical of many natural phenomena governed by power laws.

2. A key feature of such distributions is that the uncertainty the capture is so wild that typical concepts like means and standard deviations become meaningless since the "fat-tailed" events can be on a totally different order of magnitude of normal experience. Taleb talks about normal Gaussian distributions (for which mean and variance are meaningful) as the realm of "mediocristan" but suggests that many natural phenomena are best thought of as belonging to the realm of "extremistan."

3. In concrete terms, even if the mean and median deaths per year are zero and fifty respectively, it would only take one terrorist nuke to cause one million deaths. Then you can toss the historical data out the window. (This begs the question of whether your efforts to prevent such an event are likely to be effective.)

A good discussion of stable Paretian distributions and wild uncertainty can be found in Art DeVany's book "Hollywood Economics." Although DeVany's focus is on showing how difficult it is to predict blockbuster movies and why their revenues are an order of magnitude different from those of run-of-the mill films, his analytical framework could easily be extended to many other fields, including terrorism. Unfortunately, one of his maxims comes from screenwriter W. Golding who once famously said with respect to predicting outcomes in Hollywood that "Nobody knows anything."

The same is probably true with respect to estimates of anti-terrorism costs and benefits.

Even if there is only 1 incident of domestic terrorism in the coming year preventing that one act would make America the 'strong horse' and lead to fewer subsequent terrorist acts.

Britain is a good example of a country with an inability to stop repeated terror acts, and now they have to spend a huge amount of money on video cameras everywhere.

9/11 caused $40 billion in insurance claims for property damage, workers' compensation and business interruption. The American Academy of Actuaries have modeled loss estimates for an NBCR event (nuclear, biological, chemical, radiological) in New York City to run upwards of $800 billion.

I don't pretend to know if the current expenditures are efficient. I suspect they're not, but any assessment needs to begin with the recognition that there are other sorts of costs beyond loss of life that terror prevention efforts wish to avoid.

It seems to me that there is so much wrong with this post, much of which has been pointed out by previous comments. A couple other points:

1. The median number of deaths gives very little insight into this topic. Are we to infer that the probability of more than zero deaths is 50%? If so, then Viscusi believes that there is a 0.5 probability of a deadly terrorist act. I doubt that is what he meant, but it is consistent with a median of zero. (Remember, for this question the median is not the 'middle' realization, because we will only see one realization of the number of deaths in the coming year. Instead, the median is the number of deaths for which the probabilities of seeing more or less are equal.)

2. For 'black swan' events like terrorism, the mean number of deaths provides very little insight into the number of lives saved. What is the probability of one or more terrorist events in the US? Let's say it is 1/1000 for one event and 0 for more than one. If the mean is 50, then the number that will be killed by this single event is 50,000. Even if the probability is 1/2, then the number killed by the event would need to be 100. So, like previous comments, I have no idea how to arrive at the conclusion that we're "annually spending more than a billion dollars per life saved" based on the mean of 50, even if the logical error pointed out in previous comments was corrected. Simply stated, the mean doesn't give us enough information to say how many deaths are prevented. We would need more information. This is the problem of using means (or medians) to assess rare events.

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Excellent references that address the common mistakes of using the mean in this type of analysis are the books by Nassim Taleb, "Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets" and "The Black Swan: The Impact of the Highly Improbable".