Revenge of the Innumerates

There isn’t much good comedy that deals with mathematics, so a funny scene from Peggy Sue Got Married has stuck with me since that movie came out way back in 1986. The middle-aged Peggy Sue, distraught about her failing marriage, has been improbably transported back to her high school days. But she is completely aware of everything in her future life, so when she finds herself sitting in algebra class once again, she can't even pretend she cares. She blows off the exam, and when the disgruntled math teacher demands that she explain, she says dismissively: "I happen to know that in the future I will not have the slightest use for algebra."

Many people would no doubt applaud Peggy Sue, as a few did in the theater 20 years ago. Beyond basic arithmetic, isn’t math useful just for future math teachers, to torment another generation of high school students? Unhappily, such disdain for numbers has left a lot of Americans mathematically illiterate—or “innumerate” in the coinage of experts. And new evidence suggests that inept everyday mathematicians make unwise judgments and regrettable decisions in everything from personal health to con games. What’s more, those of us who are bad with numbers appear more likely to make bad choices because we are under the sway of our own misplaced emotions.

Psychologist Ellen Peters works at Decision Research, a company in Eugene, Oregon, that studies, well, how people make decisions. She is particularly interested in a phenomenon called “framing”—an idea in decision science that basically means how information is presented, how life’s questions are posed. So for example, people rate a hamburger as tastier and less greasy if it is labeled 75% lean rather than 25% fat. No, they really do. This is a good example of everyday innumeracy.

Peters and her colleagues decided to do a laboratory test of the connection between innumeracy, framing and emotion—emotion because choosing 75% lean over 25% fat is obviously not a purely logical choice. They did a set of experiments comparing mathematically savvy people with mathematically challenged. Let’s call them the nerds and the dimwits, just to save space. In one experiment, Peters asked volunteers to judge whether a mentally ill patient, recently released from the hospital, posed a danger to others in the months ahead. Sometimes they were told that 10 of 100 patients “like Mr. Jones” tend to commit acts of violence, while at other times they were told that 10% do so. The result? As reported in the journal Psychological Science, the dimwits were less fearful of the released patient if they were given a percentage rather than a number. One of Peters’ colleagues, Paul Slovic, has shown in a separate study that more abstract percentages conjure up benign images in the mind, whereas real numbers create frightening images: ten, count them, ten crazy people on the loose. The nerds, on the other hand, since they are facile with changing fractions and percentages back and forth, were not fooled by the ruse. Peters suspects the same dynamic is at work in her study.

Peters did a couple more tests to get at this dynamic in more detail. People are known to differ in how they make decisions, she explains, some being more deliberative and others more experiential and emotional. Peters wanted to explore these decision making styles, and whether numbers might have emotional meaning that influences people’s choices. To test this, she used jellybeans: In a large bowl, there were 100 jellybeans, nine colored and the rest white. In a second smaller bowl, there were ten jellybeans, one of which was colored. The bowls were clearly labeled 9% colored beans and 10% colored beans, to give the dim-witted every chance to make a smart choice. Yet they didn’t. When told they could win money by blindly picking a colored jellybean, they were way more likely to pick from the larger bowl despite the poorer odds of winning. Also, when asked about their feelings, they were much less precise about what motivated their choice, suggesting that the emotional “hit” from the vision of nine winners was just to irresistible to pass up. The nerds were too focused on the numbers to get sidetracked by irrelevant emotional images. Or, alternatively (and this is going to be hard for many of us dimwits to compute), they may actually get their emotional kicks from manipulating the numbers.

Now here is where it gets really entertaining. In a final experiment, Peters made up two wagers, and asked people which was the better bet. If these numbers seem a bit arbitrary, it’s because they are: In one wager, there was a 7-in-36 chance of winning $9 and a 29-in-36 chance of winning nothing. In the second, there was also a 7-in-36 chance of winning $9, but a 29-in-36 chance of losing a nickel. The point of this was to make the probabilities vague, not readily available even to the number lovers. What does it mean to win $9? Is that excellent, or unremarkable? Is 7-in-36 attractive? Interestingly, it was the nerds who made the worse decision in these somewhat murky circumstances. They chose the win-loss wager over the no-risk wager. It’s possible that the possibility of losing a nickel, as trivial as that is, provided context for understanding a $9 win, making it more appealing. Whatever the mental and emotional dynamics involved, the take-home message is one we innumerates have always known: Nerds can sometimes be too smart for their own good.

For more insights into human nature, visit the Association for Psychological Science website at www.psychologicalscience.org.