I received the following letter last week and the author gave me permission to quote without using his name.

Hi Dr. Henderson,

My name is X, I’m a fan of your writing, so I wanted to thank you for your work and insight that I’ve been able to enjoy…

I recently read your article “What should we fear most and what should we do about it” in the recent Regulation magazine, and while I generally agree with the policy prescriptions for the FDA I was somewhat confused about the discussion around people’s irrational reaction to different threats in life.  I’ve also heard other economists discuss irrational threat response behavior and honestly it strikes me as a bit misguided.  But I’m also not an economist or an academic so I may be missing something, and I’d be grateful to hear your thoughts on it..

One thing is that isn’t there a categorical mistake being made when comparing something like shark attacks to things like heart disease or cancer?  The latter two seem to be more or less results of aging (or long-term behaviors like excessive eating or smoking, for example).  In other words, aren’t illnesses or diseases that come with the territory of aging and dying categorically different than something like a shark attack?  I feel the same reasoning could be used to tell people not to worry about walking in a bad part of the city because your chances of dying from cancer are higher than getting shot.  It seems like a non-sequitur to me.  One way is a gruesome and sudden end to (hypothetically) a younger person’s life while the other is something that is more or less accepted by people as a very possible ending to their lives when they are older–illness and death at the end of life are accepted as part of the tragedy of the human condition.  This is not to say that I think people should be very worried about shark attacks, just that the statistical probability analysis comparing these events is missing something.

The second thing is the uncertainty of some risks as opposed to others.  I’d agree with the proposition that we shouldn’t go too far in restricting freedoms in order to prevent terrorism, but comparing it to illness or automobile accidents again seems misguided to me.  I think most people would have found it irrational to say, for example after the attack on Pearl Harbor, that people should be more worried about automobile safety and cancer than Japanese acts of war because their likelihood (at that point) of dying in an attack was much lower.  People worried about it because there was uncertainty about further attacks, a time sensitivity to stop aggression as early as possible, and the possible defeat of the US in a war.
Am I missing something here?  I appreciate your time and any thoughts you may have on this.  I look forward to reading more of your writings!

X was referring to this article by Charley Hooper and me.

Here’s my answer.

First, thanks for the compliment.

Second, let’s consider the shark versus heart disease/cancer point. They are different categories, but I don’t think there’s a category mistake. You’re right that the heart disease and cancer risk come with age whereas the shark attack is pretty much unrelated to age. They do come with the territory, but there’s a lot you can do about the territory. Just as you can avoid the almost infinitesimal risk of being killed by a shark by staying out of the ocean, you can substantially reduce a risk that’s a few orders of magnitude greater by, say, not smoking cigarettes, getting exercise, and eating in moderation. As someone who just turned 70, I don’t passively say, “Oh, that risk comes with the territory.” I want to make it to 100 and I’m doing a number of things will help me. And I haven’t even mentioned medications that will help me as I age.

Regarding the point about walking in certain parts of town, if the risk is high enough, then it easily could be the case that you’re more at risk from dying in an hour from walking in that part of town than you are at risk from dying from a heart attack or cancer in an hour. The sensible way to think about risk is per unit time, whether it be an hour, a day, or a year. As I’m sure you noticed in our article, we normalized by having it be risk in a year.

You said that comparing terrorism to illness or automobile accidents seems misguided, but you didn’t say why. Why do think that?

Re Pearl Harbor you wrote:

I think most people would have found it irrational to say, for example after the attack on Pearl Harbor, that people should be more worried about automobile safety and cancer than Japanese acts of war because their likelihood (at that point) of dying in an attack was much lower.  People worried about it because there was uncertainty about further attacks, a time sensitivity to stop aggression as early as possible, and the possible defeat of the US in a war.

You make a good point. The way to compare risks there is not to see Pearl Harbor as a one-off event but to put it in context. What was the probability of further attacks? What was the chance the United States would have been defeated in war and what would have been the consequences of that?

What that basically says is that it makes sense to look at the whole thing, not just a piece. I would give you my views on the war with Japan because they are different from the views of almost everyone else I know, but that would take us too far away from the statistical issues you’ve raised.

I shared the letter with my co-author Charley Hooper, who answered as follows:

If we don’t want to die, or at least die at a young age, there are certain actions we can take. These actions have a cost and an expected benefit. That expected benefit is the probability times the benefit.

There’s a cost I incur if I avoid swimming in the ocean to reduce my risk of a shark attack. The expected benefit is minuscule because the probability is already so low that it’s difficult to lower it further. In other words, the expected benefit is negligible.

There’s a cost I incur if I exercise more, take a medication, practice meditation, or avoid eating certain foods. The expected benefit may be large because I only need to reduce the probability of dying from a heart attack or cancer a little bit to make a noticeable improvement. In other words, the expected benefit is large.

X is saying that we accept heart disease and cancer because they are a part of aging. If that’s the case, then why are so many drugs sold, so many procedures completed, and so much medical attention devoted to treating cancer and heart disease? Plus, if you could prevent a death from any source, you’ve still prevented a death. A heart attack can kill you just as certainly as can a shark.

We don’t act as if we accept heart attacks and cancer. And even if we did, we shouldn’t.

Regarding Pearl Harbor and WWII, again it comes to probabilities, actions, and outcomes. An individual might have a greater chance of dying in a car crash than dying in the war, but the risk of war is more than death: it’s having your house destroyed, your family killed, your government overthrown, your wealth destroyed, and your daughter raped. War is hell.

We shouldn’t worry about either car crashes or wars; we can worry about both and take the appropriate steps to reduce the risk of each.