Having already revealed myself to be a grumpus about language, let’s do one on the quantitative side of the aisle so that no one thinks that I’m not broad-minded in my grumpiness.
This one comes to me via BoingBoing. It’s a Wired article purporting to show you that the dangers of terrorism are way overblown, compared to run-of-the-mill death machines like the one parked in your driveway. The centerpiece is this chart (which I reproduce without permission):
| S E V E R E
Driving off the road: 254,419
Accidental poisoning: 140,327
| H I G H
Dying from work: 59,730
Walking down the street: 52,000.
Accidentally drowning: 38,302
| E L E V A T E D
Killed by the flu: 19,415
Dying from a hernia: 16,742
| G U A R D E D
Accidental firing of a gun: 8,536
| L O W
Being shot by law enforcement: 3,949
Carbon monoxide in products: 1,554
This is based on counts of deaths from various causes in U.S. during the 11-year period 1995-2006. This is fine as far as it goes, and I really _want_ to like the piece, because I too oppose terrorist fear-mongering by the current presidential administration, and crave some sort of sane discussion of the risks of terrorism compared to other risks. But if the whole point is to be more numerate-than-thou, then you don’t want to be as quantitatively-challenged as this article is.
The problem is that the piece keeps referring to the “odds” of death-by-terrorism as though the death counts from 1995-2006 let you assess those odds accurately for 2007, and it winds up with cute summary sentences like “In fact, your appendix is more likely to kill you than al-Qaida is.”
So the Wired guys are closet frequentists. The frequentist approach can be the best way to estimate odds, when you have a good reason to think samples are random, and when you don’t have any other kind of knowledge, or explanatory model. But when you do have some extra knowledge (like, say, the knowledge that there probably do exist people who would like to kill even more people than died in 9/11), it’s silly to ignore that; and when we know that a sample isn’t very large, random, or representative, it’s silly to pretend that it is. (OK, I admit it – I’m a closet Bayesian.)
Some other frequentist (and otherwise knowledge-free) predictions:
o My own chances of dying tomorrow, based on my previous experience: 0.000000%
o Chances of U.S. civilian deaths in 2007 from nuclear reactor malfunction, based on counting such deaths in the U.S.: 0.000000%
o Your own chances of dying from human-transmitted bird flu in the U.S: 0.000000%
All of these estimates are probably, um, on the low side, and we know this because we know things about the underlying causes that aren’t reflected in the numbers (yet).
Even leaving causal theories out of it, the other thing the Wired article leaves out from the counting data is the variance. Just for fun, complete this series by predicting U.S. domestic terrorism deaths for 2003, based on 1999-2002:
o 1999: 0
o 2000: 0
o 2001: 2973
o 2002: 0
0 2003: ???
I think Wired’s answer would be something like 2973 / 4 = 743, plus or minus, um, an unspecified number.
To Wired’s main point: yeah, people are well known to be lousy risk estimators, and routinely underestimate the risks of the familiar. This is partly completely irrational, and partly … I’m not so sure.
Most people know intellectually that heart disease and traffic accidents are huge mass killers, and most people have developed policies (about seat belts, french fries) to try to mitigate that. And, once having settled into a policy, they typically don’t give it a lot more thought. Now, they may still at this point be implicitly underestimating the risk by a few orders of magnitude…. but at least the risk from a frequentist point of view is unlikely to suddenly change on them. The number of people who die from heart disease next year will probably be same as this year, plus or minus 10%. If you decided that your approach was good for 2006, then it’s probably OK for 2007 too.
What really seems to freak people out is when the risk is new, and they know they can’t bound it at _all_ (which, yes, makes them ripe for political manipulation). What’s the _largest_ number of people terrorism (or bird flu, or supervolcanoes) could conceivably kill next year in the U.S.? No one can say. What should you do differently in the presence of this strange new threat? It’s not clear. Don’t you have enough to think about already without this? Yes, including staying in your lane on the freeway. And if having to worry about this new threat bothers folks more than well-known automotive dangers, is that irrational? I dunno.
Anyway, given a choice between Dick Cheney’s all-panic-all-the-time 1% doctrine and the Wired piece’s if-it-hasn’t-happened-yet-then-it-can’t complacency, I’ll take Wired all the way, but only as a counterbalancing kind of stupidity.