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Skepticism is rarely enough to finish off a dubious but useful number, however. In April 2006, U.S. Attorney General Alberto Gonzales gave a speech to the National Center for Missing and Exploited Children in which he said, “It is simply astonishing how many predators there are. . . . At any given time, 50,000 predators are on the Internet prowling for children.” The source of this figure, Gonzales said, was “the television program Dateline.”

The attorney general should listen to National Public Radio more often. When journalists from NPR asked Dateline to explain where they got this number, they were told by the show’s Chris Hansen that they had interviewed an expert and asked him whether this number that “keeps surfacing” is accurate. The expert replied, as paraphrased by Hansen: “I’ve heard it, but depending on how you define what is a predator, it could actually be a very low estimate.” Dateline took this as confirmation that the number is accurate and repeated it as unqualified fact on three different shows.

The expert Dateline spoke to was FBI agent Ken Lanning. When NPR asked Lanning about the magic number, he said, “I didn’t know where it came from. I couldn’t confirm it, but I couldn’t refute it, either, but I felt it was a fairly reasonable figure.” Lanning also noted a curious coincidence: 50,000 has made appearances as a key number in at least two previous panics in recent years. In the early 1980s, it was supposed to be the number of children kidnapped by strangers every year. At the end of the decade, it was the number of murders committed by Satanic cults. These claims, widely reported and believed at the time, were later revealed to be nothing more than hysterical guesses that became “fact” in the retelling.

Now, it may be that, as Lanning thinks, the 50,000 figure is close to the reality. But it may also be way off the mark. There may be five million pedophiles on the Internet at any given moment, or five hundred, or five. Nobodyreally knows. This number is, at best, a guess made by persons unknown.

I’ve taken the time to give this figure a thorough dissection because—as we will see later in the book—unreliable statistics are all too common in public discourse. And the influence of those numbers is not limited to the gullible. In fact, psychologists have demonstrated that even the toughest skeptics will find it difficult, or even impossible, to keep bogus statistics from worming into their brains and influencing their judgments.

The problem, as usual, lies in the division between Head and Gut. It’s Head that scoffs at the “50,000 pedophiles” figure. Gut isn’t so sure.

To illustrate, I’ll ask a question that may at first seem somewhat unrelated to the subject at hand: Was Gandhi older or younger than nine when he died? Of course, that’s a silly question. The answer is obvious. It is also irrelevant. Completely irrelevant. Please forget I asked.

Let’s move along to another question: How old was Gandhi when he died? Now, if you actually know how old Gandhi was when he died, you are excused from this exercise. Go get a cup of tea and come back in a few paragraphs. This question is for those who are uncertain and have to guess.

I wish I could amaze and astound the reader by writing precisely what you have guessed. I cannot. I can, however, say with great confidence that your answer to the second question was powerfully influenced by the number nine.

I know this because the questions I’ve asked come from a study conducted by German psychologists Fritz Strack and Thomas Mussweiler. They asked people two versions of the Gandhi questions. One version is what I’ve repeated here. The other began by asking people whether Gandhi was older or younger than 140 when he died, which was followed by the same direction to guess Gandhi’s age when he died. Strack and Mussweiler found that when the first question mentioned the number nine, the average guess on the following question was fifty. In the second version, the average guess was sixty-seven. So those who heard the lower number before guessing guessed lower. Those who heard the higher number, guessed higher.

Psychologists have conducted many different variations on this experiment. In one version, participants were first asked to construct a single number from their own phone numbers. They were then asked to guess the year in which Attila the Hun was defeated in Europe. In another study, participants were asked to spin a wheel of fortune in order to select a random number—and then they were asked to estimate the number of African nations represented in the United Nations. In every case, the results are the same: The number people hear prior to making a guess influences that guess. The fact that the number is unmistakably irrelevant doesn’t matter. In some studies, researchers have even told people that the number they heard is irrelevant and specifically asked them not to let it influence their judgment. Still, it did.

What’s happening here is that Gut is using something psychologists call the anchoring and adjustment heuristic, or what I’ll call the Anchoring Rule. When we are uncertain about the correct answer and we make a guess, Gut grabs hold of the nearest number—which is the most recent number it heard. Head then adjusts but “adjustments tend to be insufficient,” write psychologists Nicholas Epley and Thomas Gilovich, “leaving people’s final estimates biased toward the initial anchor value.”

In the Gandhi quiz, Head and Gut first hear the number nine. When the question of Gandhi’s age at the time of his death follows, the answer isn’t known. So Gut latches onto the nearest anchor—the number nine— and passes it along to Head. Head, meanwhile, may recall the image of Gandhi as a thin, hunched old man, and so it adjusts upward from nine to something that fits what it knows. In this case, that turns out to be fifty, which is a long way from nine, but that is still much lower than the average guess of those who were given 140 as the anchor. What’s happening here, in other words, isn’t mind control. It’s more like mind influence. And Head has no idea it’s happening: When psychologists ask people if the first number they hear influences their guess, the answer is always no.

The Anchoring Rule is rich with possibilities for manipulation. Retail sales are an obvious example. A grocery store that wants to sell a large shipment of tomato soup in a hurry can set up a prominent display and top it off with a sign that reads LIMIT 12 PER CUSTOMER, or BUY 18 FOR YOUR CUPBOARD. The message on the sign isn’t important. Only the number is. When a customer is deciding how many cans to buy, Gut will use the Anchoring Rule: It will start at eighteen or twelve and adjust downward, settling on a number that is higher than it would have been without the sign. When psychologists Brian Wansink, Robert Kent, and Stephen Hoch carried out several variations on this scenario in actual supermarkets, they got startling results. Without a sign limiting purchases to twelve, almost half the shoppers bought only one or two cans of soup; with a limit of twelve, most shoppers bought between four and ten cans, while not one shopper bought only one or two cans.

Or imagine you’re a lawyer and your client is about to be sentenced by a judge who has discretion as to how long the sentence will be. The Anchoring Rule suggests one way to put a thumb on the scales of justice. In a 2006 study, Strack and Mussweiler brought together a group of experienced German judges and provided them with a written outline of a case in which a man had been convicted of rape. The outline detailed all the facts of the case, including the evidence that supported the conviction. After the judges read the outline, they were asked to imagine that while the court was in recess they got a phone call from a journalist who asked if the sentence would be higher or lower than three years. Of course, the researchers told the judges, you properly refuse to answer and return to the courtroom. Now . . . what sentence will you give in this case? The average was thirty-three months in prison. But unknown to this group of judges, another group was run through precisely the same scenario—except the number mentioned by the imaginary journalist was one year, not three. In that case, the average sentence imposed by the judges was twenty-five months.