Stop Telling Me How Dangerous My Bathtub Is

Comparing accidental deaths to terrorism is a mistake.

What lies beneath.

Photographer: Alexander Hassenstein/Getty Images

Last week, Financial Times columnist Janan Ganesh opined on what he called the “bathtub fallacy,” a common and in his view counterproductive liberal response to fears of terrorism:

Whenever the state imposes a counterterror measure, especially one as brute as the US president’s, statistics are dug out to show that fewer westerners perish in terror attacks than in everyday mishaps. Slipping in the bath is a tragicomic favourite. We chuckle, share the data and wait for voters and politicians to see sense.

Sure enough, a couple of days later, there was Nicholas Kristof in the New York Times, making Ganesh’s point for him:

The bottom line is that most years in the U.S., ladders kill far more Americans than Muslim terrorists do. Same with bathtubs. Ditto for stairs. And lightning.

Now, I love statistics. I cite them and sort them and chart them all the time. I even wrote a whole column last month about various causes of untimely death in the U.S. But I agree with Ganesh that comparing annual deaths due to bathtubs and terrorism is a mistake. Why? Three main reasons spring to mind.

First is that terrorism is designed to, you know, sow terror. As Ganesh writes,

most people can intuit the difference between domestic misfortune and political violence. The latter is an assault on the system: the rules and institutions that distinguish society from the state of nature. Bathroom deaths could multiply by 50 without a threat to civil order. 1  The incidence of terror could not.

Second is that ladders, stairs and bathtubs are undeniably useful. Terrorists, not so much. (I’ll get back to usefulness in a moment.)

Finally, comparing the incidence of terrorism with that of common accidents is an incompetent and irresponsible use of statistics. Household accidents are lots and lots of small, unrelated events. As a result, while individual accidents can’t be predicted, the overall risk is easy to quantify and is pretty stable from year to year.

Terrorism is different. There are small incidents, but there are also huge ones in which hundreds or thousands of people die. It’s a fat-tailed distribution, in which outliers are really important. It also isn’t stable: Five or 10 or even 50 years of data isn’t necessarily enough to allow one to predict with confidence what’s going to happen next year. It’s a little like housing prices -- the fact that they hadn’t declined on the national level for more than 50 years before 2006 didn’t mean they couldn’t decline. Meanwhile, the widespread belief that they wouldn’t decline made the housing collapse more likely and more costly.

I should credit the statistical argument above to Nassim Nicholas Taleb, because he has made it frequently and his writings on the subject have informed my views (although he’s not responsible for any mistakes I might have just made in paraphrasing them). But I know the argumentative Taleb rubs a lot of people the wrong way, so it’s worth pointing out that this is one topic where it’s not hard to find mild-mannered, highly credentialed professors who agree with him.

“People who just look at the average are doing the analysis wrong,” said one such person, Baruch Fischhoff, when I called him Monday. Fischhoff is the Howard Heinz University Professor at Carnegie Mellon University, past president of the Society for Risk Analysis, past member of multiple national and international commissions on the risks of terrorism and other bad stuff, and author of lots of books with “risk” in the title. As Daniel Kahneman’s research assistant at the Hebrew University of Jerusalem in the early 1970s, he was present at the creation of the school of psychological research that has shown how bad we humans can be at processing probabilities (this is what Michael Lewis’s new book is about). He is also to some extent responsible for the birth of behavioral economics -- during a car ride in California in 1976, Fischhoff introduced economist Richard Thaler to the work of Kahneman and Amos Tversky.

So Fischhoff is extremely familiar with the ways in which people misperceive risk. But he doesn’t think it’s irrational to fear terrorism more than falling in the bathtub. “It's different in terms of the uncertainty and the shape of the distribution, how well we understand it and the possibility of these large-scale events,” he said. Then, a little later in the conversation, he added, “whatever people are concerned about, if you dismiss their fears rather than take them seriously, you lose credibility.”

This, then, is the challenge. If you think that some people are more afraid than is reasonable of the threat of terrorist attack, and that the current administration is irresponsibly stoking those fears -- and yeah, I think both of those things -- how do you respond? Fischhoff didn’t have a simple answer, but he did offer a few interesting ideas.

One of them was that “people tolerate risks where they see a benefit.” As noted above, ladders and bathtubs are clearly useful, so we take the risks inherent in using them in stride. Similarly, if you live in a big urban area with lots of recent immigrants and visitors, and/or you travel overseas frequently yourself, you’re likely to see the relatively free movement of people across borders as something that benefits you. If you live in a small, homogeneous town and don’t get out much, you aren't.

This is reflected in poll results showing that residents of rural areas fear terrorism more than city dwellers do. Given that most terrorist attacks in the U.S. have been in cities, this is often painted as urbanites being more sophisticated about risk than country dwellers are. But as a resident of the city that is perhaps the nation’s most inviting terrorist target, I cannot claim to be making a rational calculation about risk in deciding to live here. I mostly just shove the possibility out of my mind. Meanwhile, I’m pretty sure that New York would be far less vibrant and appealing without lots of immigrants and visitors. So I focus on the benefit rather than the risk.

I don’t know if this reasoning can make Americans less fearful of terrorism (maybe I should be more fearful), but it does perhaps allow for more understanding. Along similar lines, Fischhoff argued that “people don’t want just an assertion of whether a risk is a particular size, but they also need a mental model or an intuitive sense of how big a risk is.” The more you know about how terrorists are radicalized, or how most recent immigrants view the U.S., the more nuanced a mental model of the risk of terrorism you’re likely to have.

More information is good, then, right? Well, up to a point. Fischhoff pointed me to a study conducted in the wake of the 2013 Boston Marathon bombings and published in the Proceedings of the National Academy of Sciences that found that

six or more daily hours of bombing-related media exposure in the week after the bombings was associated with higher acute stress than direct exposure to the bombings.

If you’re anywhere near six hours of media exposure of any kind today, please stop reading now. Don’t turn on the TV news. Go take a bath. You’ll be fine.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
  1. I’m not sure that this is the best example. If it suddenly became 50 times more dangerous to go to the bathroom, wouldn’t people stop going to the bathroom? And might that not pose a threat to the civil order?

To contact the author of this story:
Justin Fox at justinfox@bloomberg.net

To contact the editor responsible for this story:
Brooke Sample at bsample1@bloomberg.net

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