July 2, 2006 — -- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.
In his heralded new book, "The One Percent Doctrine," Ron Suskind writes that Vice President Dick Cheney forcefully stated that the war on terror empowered the Bush administration to act without the need for evidence or extensive analysis.
Suskind describes the Cheney doctrine as follows: "Even if there's just a 1 percent chance of the unimaginable coming due, act as if it is a certainty. It's not about 'our analysis,' as Cheney said. It's about 'our response.' … Justified or not, fact-based or not, 'our response' is what matters. As to 'evidence,' the bar was set so low that the word itself almost didn't apply."
There is a complex interplay between an act's possible consequences, evidence, and the probabilities involved. And sometimes, of course, the probability justifying action of some sort is even less than 1 percent. Vaccines are routinely given, for example, even for diseases whose risk of being contracted is much less than 1 percent.
That being granted, the simplistic doctrine of "if at least 1 percent, then act" is especially frightening in international conflicts, not least because the number of threats misconstrued (by someone or other) to meet the 1 percent threshold is huge and the consequences of military action are so terrible and irrevocable.
Imagine what would happen in various everyday situations were the Cheney doctrine to be applied. A young man is in a bar and another man gives him a hard stare. If the young Cheneyite feels threatened and believes the probability to be at least 1 percent that the other man will shoot him, then he has a right to preemptively shoot him in "self-defense."
Or an older woman visits her Cheneyite doctor who, finding that the woman has suffered from a sore throat and fatigue for months, orders that she be put on chemotherapy since the likelihood of cancer is in his opinion at least 1 percent. Further tests, he might argue, would take too long.
A Cheneyite gambler would be a casino's dream. The chance of rolling a 12 with a pair of dice, for example, is 1/36, almost 3 percent, and hence would justify the gambler betting his house on rolling a 12.
And what about a Cheneyite scientist, hard as that may be to conceive? If this scientist decided that the "evidence" for some crackpot scientific theory suggested to him that its probability were at least 1 percent, the scientist would feel comfortable touting it as a reasonable alternative to established theory.
Needless to say, standards for action or decision are generally far more stringent. For a conventional scientist running a statistical test of a hypothesis the threshold is usually 95 percent, not 1 percent. More precisely, if the scientist runs the test, and obtains, based on the tentative assumption of the hypothesis, an outcome having a probability of less than 5 percent, then he or she generally rejects the hypothesis.
And certainly in criminal trials the statistical burden is much greater; it's beyond a reasonable doubt (that is, an indeterminate, but very high probability), not 1 percent. In civil cases the probability standard is lower, but still nowhere near 1 percent.
The substitution of mere suspicion for evidence seems to color the thinking of many -- on Iraq (as the Suskind book amply documents), on fiscal policy and on science as well. From stem cells to creation science, from illegal wiretaps to war planning, if it feels good and accords with ideology, then it's the right thing to do. Real men don't need evidence or probability.
Nor do they need consistency. A companion to the Cheney 1 percent action doctrine (if the probability is at least 1 percent, act) is the administration's non-action doctrine (if the probability is less than 99 percent, then don't act). This latter doctrine is generally invoked in discussions of global warming, where it seems absolute certainty is required to justify any significant action. Ideology determines which of these two inconsistent doctrines to invoke.
Of course, these attitudes and variations of these doctrines are very widespread throughout society, and it's sometimes very difficult to decide whether to act or not. In fact, it's an interesting exercise to come up with other situations leading to rules of the form, "if the probability is X percent, then act." Surprisingly many of the everyday rules guiding us can be put into this form.
A trivial example is provided by elections where X percent is 50 percent, but let me end with a somewhat unusual and counterintuitive example, which involves an idealization of the dating process. Say that a woman has reason to believe she will have up to N sequential suitors during her dating life and wants to maximize her chances of choosing the "best" one. The optimal strategy she should follow is to reject the first 37 percent of her suitors and then accept the next one who is better than all his predecessors.
Whether the issue is war, science, or a myriad of other issues, probability and evidence should play a critical role.
Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.