Just what is the evidence for this alleged terrorist threat that now dominates foreign affairs and the presidential election? The third anniversary of the Sept. 11 attacks on the Pentagon and New York's World Trade Center has come and gone without any terrorist attacks in the U.S. No terrorists attacked the Olympics in Greece, as so many feared. Nor did they attack the Republican convention in New York. And the big statistical picture of terrorism has changed little in years.
Deaths because of terrorism worldwide have increased a bit lately (especially after the school attack in Russia), but the number still remains on the order of about a thousand deaths a year, according to the State Department -- a small fraction of the 15,000 or so murders each year in the United States, or the 40,000 who die in car accidents.
The Bush administration and many others interpret these facts as proof that the government is winning its "war on terror" (even though Osama bin Laden still roams free and threatens from afar).
And they may be right. It's conceivable that there would have been some attacks by now if not for the government's stepped-up security at home and its vigorous anti-terrorism efforts abroad. We don't know. We do know that studies of our statistical competency show both that we systematically overestimate the probability of vivid, high-profile threats such as shark bites and terrorist bombings and that we poorly estimate the probability of less glamorous dangers like highway fatalities. The comparative absence of terrorism could just as easily (and I believe, more reasonably) support the very different conclusion that we have overestimated -- grossly overestimated -- the terrorist threat. We may be "winning" a war against terrorism simply because there are few terrorists out there posing a serious threat to the U.S. We may have traded substantial civil liberties and international goodwill in the last three years for a lot more security than we need.
Answering these questions involves a subtle type of formal reasoning called negative evidence: Sometimes a search that finds nothing is evidence that there is nothing. Suppose you shop in a store and then can't find your car keys. How much of the store must you search before you conclude the keys are not there? The negative evidence for this conclusion grows as the search widens and finds nothing.
The strength of the negative evidence depends on the size and complexity of the search area. For instance, we have good negative evidence that there is no Loch Ness monster because no sonar sweep of the Scottish lake has found such a creature. We have less good negative evidence that there is no Bigfoot because we have not fully searched the larger and more complex area of pine forests in Northern California. And we have no good negative evidence at all that we are alone in the cosmos because we have just started to search the vast heavens for signs of structured energy.
The war in Iraq gives a telling example of negative evidence. The coalition forces still cannot find the alleged stockpiles of weapons of mass destruction. The weapons may be there, but the negative evidence that they are not grows stronger each day as a wider search finds nothing.
The Bush administration has said, in effect, that it is better to be safe than sorry, not just with regard to weapons of mass destruction in Iraq but with terrorist threats at home. The trouble is that all bureaucracies have a well-known incentive to over-rely on being safe than sorry. No one wants to risk approving a new drug or airplane design that has even a slight chance of killing someone, even if the drug can save lives or the design can greatly increase flight efficiency.
A related problem is that terrorists have an incentive to exaggerate their strength in order to frighten their opponents and to attract recruits and donations. The result is an inadvertent global equilibrium where governments play it safe by overestimating the terrorist threat, while the terrorists oblige by overestimating their power. A tight presidential race only heightens these perverse incentives all around.
The bottom line is this: There will always be terrorists and legitimate efforts to catch and kill them. But meanwhile, the bigger statistical threat comes from the driver next to you who is talking on the cellphone.