David R. Henderson  

Numeracy and the Paris Attacks

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One of my pleasures in teaching is learning that students have taken things they've learned and passing them on to their colleagues, friends, and families. That happened recently in my distance learning class. A few weeks ago, in a 40-minute section I teach on numeracy, I covered John Mueller's article in Regulation titled "A False Sense of Insecurity." I gave some of the highlights of Mueller's article in a post last month titled "Krugman, Mueller, and McCain on Terrorism."

Last Tuesday, a student in my class who is in D.C., Ali Nikravesh [he gave me permission to use his name], reported that after the Paris murders, he received an email message prohibiting unofficial travel of DoD personnel to France. He read it and thought it reflected a lack of numeracy and so he emailed a link to the Mueller article to his colleagues and texted the PDF to friends and family. The reaction he got from colleagues and from many family and friends was "I didn't know that, I never thought of it that way, and that helps."

I mention their reaction because a common complaint that many commenters have posted on my posts is that "people don't think that way, people can't think that way, people are innumerate and will retreat to their prejudices, so don't bother." This is evidence that it's worth bothering.

Update: I corrected the middle paragraph above after hearing from Ali. He told me that he does not have social media accounts.

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COMMENTS (19 to date)
E. Harding writes:

I give a 45% chance of at least one Islamist-related mass shooting or other terrorist attack happening within my area within the next two years. If it happens, I will not be surprised. Nevertheless, I'm not too worried about my personal safety from such an attack. I think most people think like I do.

Dustin writes:

Numeracy certainly provides an interesting comparative, but there are additional considerations in evaluating the rationality of our fear of terrorism.

First, there is no reason to suspect a potentially dramatic increase in deaths resulting from "lightning, accident-causing deer, or severe allergic reaction to peanuts". The uncertainty surrounding the source and frequency of terrorism does set it apart from non-malovelent threats.

Second, I can quite easily mitigate the threat of "lightning, accident-causing deer, or severe allergic reaction to peanuts." This brings me comfort. However, I cannot so easily or meaningfully mitigate the threat of being a victim to terrorism without significantly altering my lifestyle.

E. Harding writes:

How can you mitigate the threat of deer? They pop up in the most unexpected places.

Dustin writes:

Accident-causing deer tend to pop up on high speed avenues of travel, with the greatest incidence of vehicle collision at dawn/dusk, during mating season (autumn), in rural areas, and in the presence of other deer (deer are pack animals). Turns out that there are a number of ways to mitigate both the probability of collision with a deer and the damage that may occur in the event of collision. These include, for example, pay attention to the road and surrounding areas, take extra precaution when a deer is spotted, slow down and use headlights when driving during periods of low visibility, wear a seatbelt, use the center lane of a multi-lane roadway, do not swerve but slow down and honk if a deer is on or near the roadway, call emergency services in the event of a collision.



David R. Henderson writes:

So you’re saying that what makes you feel comfortable about the threat of "lightning, accident-causing deer, or severe allergic reaction to peanuts” is that you can reduce that probability, not that the probability is low?

Dustin writes:

More generally, in addition to the measured probability, the perceived probability or threat awareness, the variance/expected path of the probability, and our ability to control or mitigate the probability are three additional factors that influence how much we fear something.

The numeracy argument only addresses measured probability. While terrorism and lightning/deer/peanuts have a similar measured probability: 1) individuals have very little control over the terrorist threat, 2) a scenario of significant growth in number of terrorist victims is much more likely than a scenario of significant growth in number of deer victims, and 3) the perceived threat of terrorism is much higher than deer/lightning due to media coverage and general threat awareness.

For these three reasons, I think it is rational to fear terrorism more than deer/lightning/peanuts.

Otherwise, the populations most at risk of being a victim of deer/lightning are probably not the same populations most at risk of being victim of terrorism - this is a rural/urban split.

Lucas M. writes:

I think it's entirely rational to worry more about terrorism than accidents and natural disasters. And here is why: Past performance doesn't guarantee future performance.

It doesn't really matter the current probability of terrorism vs. natural disasters. What matter is the future probability of terrorism vs. natural disasters. There's good reason to believe that natural disasters and car accidents won't suddenly become more common in a year or two. Its distribution is probably pretty stable over time.

Social conflicts seem to be much less stable over time. World War I was much worse than previous wars. Of course, the upside is also true: there's always room for social improvement.

Therefore, we do not need to update our forecast for natural disasters after the latest tornado. But we should upgrade our forecasts for geopolitical conflict after the latest terrorist act.

Of course, there's a degree of irrational fear if one's too impressed by the imagery of the attacks. However, I believe there's room for a "rational fear" too. Moreover, the issue is not just the fear of terrorism itself, but of its consequences going forward. Will it change our political order? Will there be an escalation of violence? Should we worry about internal social conflict? And what about further engagement in foreign wars?

In short, accidents and natural disasters will probably remain as random as they already are. Social conflicts might escalate or de-escalate. It's entirely rational to worry about where the trend is taking us.

(Again: with the upside that the trend might be positive too. In both cases, however, we should treat the phenomenon in a different way.)

David R. Henderson writes:

I gather that you’re not going to answer my question.

JHanley writes:

Dustin is right about how people do tend to think, but he's wrong to argue that such thinking is rational. Even though we can reduce the probability of hitting a deer, the thing we should fear most remains that thing with the highest expected negative value (the cost multiplied by the probability of suffering it).

The insurance journal says there are over 1 million car-deer collisions a year, causing $4 billion in losses, and killing 200 people a year (another source says up to 10,000 people a year go to hospitals as a result of such collisions). That means that from 2001-2015 inclusive, more Americans have likely been killed by car-deer collisions than by terrorists. If you take out the outliers--the lucky blows of 9/11 that seem unlikely to be repeated--the deer are outdoing the terrorists quite handily.

Of course your actual risk is also dependent on where you are. A car-deer collision in NYC is presumably a quite unlikely even for the average person, while here in rural Michigan it's disturbingly likely.* Of course New Yorkers face other types of risks on a daily basis whose expected (negative) value is greater than the expected (negative) value of terrorism.

*I've never hit a moving deer, but I did crest a small hill and run straight over a recently hit deer (at full speed). It was a helluva jolt, and after a few miles the smell of cooking deer bits in my engine was nauseating. I've also almost hit a bison and once observed someone else hitting a bison at full speed, although amazingly with little damage.

Daublin writes:

Dustin and Lucas,

What about ISIS makes them especially likely to grow in danger over time? They are more than an order of magnitude short of the effectiveness of common street thugs.

Dustin writes:

The answer to your question is "no". I thought my response would clarify and expand on my earlier comment. To make it MORE clear. Holding the risk impact constant (i.e., death, in this case), the factors that determine how much we should fear a threat are something like:
1) Future probability of threat
2) Awareness of threat
3) Ability to mitigate the threat

You're numeracy argument only partially addresses one of these and is therefore inadequate.

As I've said (and Lucas illustrates more succinctly), terrorism is a highly dynamic threat. Looking to the past for insights on future probability is like driving in the rear view mirror. Not only does terrorism have hugely fat tails (9/11), the mean can shift dramatically given that the threat can potentially to grow by many orders of magnitude. In no future world will there be 100,000 deaths due to deer.

These lessons in risk management were learned decades ago. The threat of deer and terrorism are in no way comparable.

If you want to make a coherent argument, you'll say "the number of deaths due to terrorism and deer-related accidents in the US over the next year are equal. Therefore, we should collectively fear each equally over this time period." In this case, I'd agree with you.

Dustin writes:

"What about ISIS makes them especially likely to grow in danger over time?"

Why focus solely in ISIS? Terrorism is the central issue. And the drivers underlying the potential growth of the terrorist threat are 1) the proliferation of weapons and technologies that can cause massive injury and destruction (e.g., assault rifles, EMPs, dirty bombs, etc...) 2) communications and transportation technologies that enable terrorists to influence, organize, and conduct global attacks, and 3) the vulnerability/fragility/interconnectedness of our national infrastructure.

Consider a monte carlo simulator. The scenarios for deer-related fatalities are tightly bound about the historic mean, I imagine. Terrorism, however, would certainly have scenarios that include extreme numbers of casualties.

Maybe the US government should establish massive programs and agencies to guard against deer and peanuts ... Just look at the numbers would ya?!

"They are more than an order of magnitude short of the effectiveness of common street thugs."

Yes. I worry more about common street thugs over the near term than I do about terrorism.

Colombo writes:

It is funny that islamic terrorists are not afraid of nuclear weapons.
How many weapons do non-muslims have compared to how many do muslims have?
How good is the numeracy of these muslim terrorists?

Jon Murphy writes:


Couldn't one reduce the risk of terrorism to himself by simply not going out of the house? Terrorists rarely (if ever) target individuals. If one barricades himself in his house and goes into complete lock down, couldn't he reduce his risk from terrorism in the same way a person with a peanut allergy could reduce his risk by avoiding peanuts or a driver avoid deer?

Lucas M. writes:

Just to be clear: my argument makes me worry about terrorism, but I'm not saying that we should be completely scared by it. I'm just saying that when the nature of the phenomenon is different, the mere probability doesn't tell the whole story. Numeracy is not enough to prevent a "category mistake".

Allow me to explain my thought process:

Each terrorist act makes me slightly update my implicit forecast for further geopolitical conflict. It makes me read more about it and try to guess what it means going forward. Of course, I don't have any special predictive powers, but l can't help but to try to guess (which I assume everyone else also also tries to do).

If I hear about my neighbour being attacked by a moose (I'm in Canada), I'll be concern about that too. But I have no reason to start to worry about the next Canadian-Moose War. This is a conflict that is highly unlikely to escalate.

There was an attack here recently, by the way. But I'm never afraid of a new attack in the city. I know the odds are really small. But I did spent quite a while reading on the topic, because I think that it means more for my future than moose attacks. (If I'm about to go camping, I'll switch to reading on moose).

So, in short, I believe there's cause to worry more about social conflicts than random accidents. Which is not to say that everyone is acting perfectly rational about it.

In particular, I don't worry that much about ISIS itself. I find it quite scary and sad that there are other organizations (such as Boko Haram in Africa) that are also conducting acts of terror.

Moreover, it seems that demographic trends mean that Africa will play an increasingly large whole in international affairs in the future. The prospect of Nigeria becoming as populous as the USA and then be overtaken by radicals scares more than an escalation of moose attacks.

But yes, that's definitely not at all what scares me the most. Thugs are definitely much scarier than all that. Which is why I moved to Canada, while I haven't really done anything about my geopolitical concerns (except some googling and posting this comment).

Lucas M. writes:

To put it more succinctly:

1) In social phenomenons, trends matter more than current statistics. (Maybe an exception could me made for climate change causing more natural disasters, but I know nothing about it).

2) There's the "fat-tailed" aspect of risk that Dustin mentioned. Moose attacks are one-on-one affairs. I can protect myself individually. It's not a collective risk.

3) I don't think that terrorism is merely a problem in itself. I don't really worry about specific acts of terror (and in that sense maybe I agree with David Henderson about numeracy being important). The odds are too small. But I do worry about what it means for the future. More war? More state powers? More religious conflict? More prejudice? Less immigration? Random accidents won't fundamentally change our social orders.

4) I'm not saying that we should be running around screaming. But we should consider those news as relevant enough to update our priors about future conflicts.

5) That being said, predicting the future is hard. I'm not confidant about the current validity of my priors. There's more at stake than a single organization. The whole situation is pretty messy. I'm more concern now than I used to be, but I don't have any solid prediction going forward. So, I do worry, but I don't worry that much either.

Chris Wegener writes:

It surprises me that there is this belief that there will be more terrorist attacks in the future. This seems only likely if we fall for the mistaken belief that Western Countries have the ability to become involved in the Middle East and North Africa militarily and effectively leave those areas better off than before our invasion.

I would suggest that our misadventures in Iraq and Afghanistan should show the futility of that belief. As long as we prevent ISIL and other terrorist organizations from succeeding in creating the another Western Crusade we should be fine. (In levels of fine that involve intermittent small scale terrorist attacks in western countries. Since we live with much higher levels of domestic terrorism now.)

If we do succumb to the ever present drum beat of "doing something" and get actively involved in what is essentially a Sunni Shia Reformation then yes we can expect an increase in foreign incited terrorism.

At the end of the day, the point that in a country of 329 million people the odds of becoming a victim of foreign inspired terrorism are much lower then most risks of death or injury that ever American faces every day. And it must be said that that risk is quite low because America has become amazingly safe thus causing people to have time to be terrified of such a tiny risk as terrorism.

Dustin writes:

Chris Wegner,
"At the end of the day, the point that in a country of 329 million people the odds of becoming a victim of foreign inspired terrorism are much lower then most risks of death or injury that ever American faces every day. And it must be said that that risk is quite low because America has become amazingly safe thus causing people to have time to be terrified of such a tiny risk as terrorism."

I agree with all of this. My issue was with the claim that because victims of accident-causing deer and terrorism are similar over that past 50 years, we should fear each threat similarly.

Yes absolutely. All risk can be bought down, but the price of doing so can be quite high. To me, as an individual, mitigating the risk of a ruminant-induced fatality is less costly than mitigating the risk of a terrorist attack.

Hugh writes:

I understand that about 3,400 people were lynched during the 84 years when the first Klan was active. That's an anemic 40 per year.

Should we therefore teach that lynchings were just a statistical blip of no real importance? I say no. A few lynchings per year may have been sufficient to cower the rest of the negro population into a more submissive attitude.

Medieval kings knew that you do not have to kill a large number of your subjects to obtain obedience: a few severed heads at the city gates were enough

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