Substitution Heuristic

Substitution

To experience the heuristic process, please try your hand at answering the following question, which illustrates several essential themes of the heuristics and biases approach. As usual, you will get more from the example if you produce your own answers.

Bill is thirty-three years old. He is intelligent but unimaginative, compulsive, and generally lifeless. In school, he was strong in mathematics but weak in social studies and humanities.

The following is a list of eight possibilities for Bill’s current situation.

Please go over the list and select the two that you consider most probable.

• Bill is a physician who plays poker as a hobby.
• Bill is an architect.
• Bill is an accountant.
• Bill plays jazz as a hobby.
• Bill surfs as a hobby.
• Bill is a reporter.
• Bill is an accountant who plays jazz as a hobby.
• Bill climbs mountains as a hobby.

Now, go back over the list and select the two categories where Bill most resembles a typical person in that category. You may pick the same or different categories as before.

We are almost certain that you picked the same categories as highest in probability and in resemblance. The reason for our confidence is that multiple experiments have shown that people give identical answers to the two questions. But similarity and probability are actually quite different. For example, ask yourself, which of the following statements makes more sense?

• Bill fits my idea of a person who plays jazz as a hobby.
• Bill fits my idea of an accountant who plays jazz as a hobby.

Neither of these statements is a good fit, but one of them is clearly less awful than the other. Bill has more in common with an accountant who plays jazz as a hobby than with a person who plays jazz as a hobby. Now consider this: which of the following is more probable?

• Bill plays jazz as a hobby.
• Bill is an accountant who plays jazz as a hobby.

You may be tempted to pick the second answer, but logic won’t allow it. The probability that Bill plays jazz as a hobby must be at least as high as the probability of his being a jazz-playing accountant. Remember your Venn diagrams! If Bill is a jazz player and an accountant, he is certainly a jazz player. Adding a condition to a description cannot increase its probability, although it can make it more representative, and thus a better “fit,” as in the present case.

The theory of judgment heuristics proposes that people will sometimes use the answer to an easier question in responding to the harder one. So, which question is more easily answered: “How similar is Bill to a typical amateur jazz player?” or “How probable is it that Bill is an amateur jazz player?” By acclamation, the similarity question is easier, which makes it likely that it was the one that people answer when asked to assess probability.

You have now experienced the essential idea of the heuristics and biases program: a heuristic for answering a difficult question is to find the answer to an easier one. The substitution of one question for the other causes predictable errors, called psychological biases.

This sort of bias is manifest in the Bill example. Substituting similarity for probability can produce errors because probability must obey rules that resemblance judgments need not follow. In particular, the Venn-diagram inclusion rule constrains probability, not resemblance. Hence the predictable logical error that many people make.

For another example of a neglected statistical property, consider the Gambardi question from the book’s chapter 4, which asks whether a particular CEO will succeed. If you are like most people, your assessment of Michael Gambardi’s chances of success was based entirely on what the case told you about him. You then attempted to match his description to the image of a successful CEO.

Did it occur to you to consider the probability that a randomly chosen CEO will still hold the same job two years later? Probably not. You can think of this base-rate information as a measure of the difficulty of surviving as a CEO. If this approach seems odd, consider how you would estimate the probability that a particular student would pass a test. Surely, the proportion of students who fail the test is relevant, as it gives you an indication of how difficult the test is. In the same manner, the base rate of CEO survival is relevant to the Gambardi problem. Both questions are examples of taking what we have called the outside view: when you take this view, you think of the student, or of Gambardi, as a member of a class of similar cases. You think statistically about the class, instead of thinking causally about the focal case.

Taking the outside view can make a large difference and prevent significant errors. The book uses an estimated annual CEO turnover rate of around 15% in US companies. Assuming the same departure rate in each year, this gives a roughly 72% probability of remaining after two years. A rate for comparable incoming CEOs would be a better starting point than a rate for all CEOs. Of course, this number is only a starting point, and the specifics of Gambardi’s case will affect your final estimate. But if you focused solely on what you were told about Gambardi, you neglected a key piece of information. (Full disclosure: We wrote the Gambardi case to illustrate noisy judgment; it took us weeks before we realized that it was also a prime example of the bias we describe here, which is called base-rate neglect. Thinking of base rates is no more automatic for the authors of this book than for anyone else.)

Substitution of one question for another is not restricted to similarity and probability. Another example is the replacement of a judgment of frequency by an impression of the ease with which instances come to mind. For example, the perception of the risk of airplane crashes or hurricanes rises briefly after well-publicized instances of such events. A risk estimate should use relevant frequency data and account for changing conditions. A recent incident can instead receive extra weight simply because it comes easily to mind. Substituting a judgment of how easily examples come to mind for an assessment of frequency is known as the availability heuristic.

The substitution of an easy judgment for a hard one is not limited to these examples. In fact, it is very common. Answering an easier question can be thought of as a general-purpose procedure for answering a question that could stump you. Consider how we tend to answer each of the following questions by using its easier substitute:

• Do I believe in climate change? → Do I trust the people who say it exists?
• Do I think this surgeon is competent? → Does this individual speak with confidence and authority?
• Will the project be completed on schedule? → Is it on schedule now?
• Is nuclear energy necessary? → Do I recoil at the word nuclear?
• Am I satisfied with my life as a whole? → What is my mood right now?

When the substitute leaves out relevant evidence or gives it the wrong weight, the resulting judgment can be wrong. For example, a full answer to a question about life satisfaction clearly requires consulting more than your current mood, but evidence suggests that mood is in fact overly weighted.

In the same manner, substituting similarity for probability leads to neglect of base rates, which are quite properly irrelevant when judging similarity. And factors such as irrelevant variations in the aesthetics of the document that presents a business plan should be given little or no weight in assessing the value of a company. Giving irrelevant presentation details weight can distort that judgment.

Conclusion Biases

At a key moment in the development of the screenplay for Return of the Jedi, the third Star Wars film, George Lucas, the mastermind behind the series, had a heated debate with his great collaborator Lawrence Kasdan. Kasdan strongly advised Lucas, “I think you should kill Luke and have Leia take over.” Lucas promptly rejected the idea. Kasdan suggested that if Luke lived, another major character should die. Lucas again disagreed, adding, “You don’t go around killing people.” Kasdan responded with a heartfelt claim about the nature of cinema. He explained to Lucas that “the movie has more emotional weight if someone you love is lost along the way; the journey has more impact.”

Lucas’s response was quick and unequivocal: “I don’t like that and I don’t believe that.”

The thought process here looks quite different from the one you experienced when you thought about Bill, the jazz-playing accountant. Read Lucas’s answer again: “Not liking” precedes “Not believing.” Lucas had an automatic response to Kasdan’s suggestion. That response helped motivate his judgment (even if it turned out to be right).

This example illustrates a different type of bias, which we call conclusion bias, or prejudgment. Like Lucas, we often start the process of judgment with an inclination to reach a particular conclusion. When we do that, we let our fast, intuitive System 1 thinking suggest a conclusion. Either we jump to that conclusion and simply bypass the process of gathering and integrating information, or we mobilize System 2 thinking—engaging in deliberate thought—to come up with arguments that support our prejudgment. In that case, the evidence will be selective and distorted: because of confirmation bias and desirability bias, we will tend to collect and interpret evidence selectively to favor a judgment that, respectively, we already believe or wish to be true.

People often come up with plausible rationalizations for their judgments and will actually think that they are the cause of their beliefs. A good test of the role of prejudgment is to imagine that the arguments seemingly supporting our belief are suddenly proven invalid. Kasdan, for instance, might well have pointed out to Lucas that “You don’t go around killing people” is hardly a compelling argument. The author of Romeo and Juliet would not have agreed with Lucas, and if the writers of The Sopranos and Game of Thrones had decided against killings, both shows would probably have been canceled in their first season. But we can bet that a strong counterargument wouldn’t have changed Lucas’s mind. Instead, he would have come up with other arguments to support his judgment. (For example, “Star Wars is different.”)

Prejudgments are evident wherever we look. Like Lucas’s reaction, they often have an emotional component. The psychologist Paul Slovic terms this the affect heuristic: people determine what they think by consulting their feelings. We like most things about politicians we favor, and we dislike even the looks and the voices of politicians we dislike. That is one reason that smart companies work so hard to attach a positive affect to their brand. Professors often notice that in a year when they get high marks for teaching, students also give the course material a high rating. In a year when students don’t like the professor so much, they give a low rating to the identical assigned readings. The same mechanism is at work even when emotion is not involved: regardless of the true reasons for your belief, you will be inclined to accept any argument that appears to support it, even when the reasoning is wrong.

A subtler example of a conclusion bias is the anchoring effect, which is the effect that an arbitrary number has on people who must make a quantitative judgment. In a typical demonstration, you might be presented with a number of items whose price is not easy to guess, such as an unfamiliar bottle of wine. You are asked to jot down the last two digits of your Social Security number and indicate whether you would pay that amount for the bottle. Finally, you are asked to state the maximum amount you would be willing to pay for it. The results show that anchoring on your Social Security number will affect your final buying price. In one study, people whose Social Security numbers generated a high anchor (more than eighty dollars) stated that they were willing to pay about three times more than those with a low anchor (less than twenty dollars).

Clearly, your Social Security number should not have a large effect on your judgment about how much a bottle of wine is worth, but it does. Anchoring has been observed in many settings and is often used deliberately in negotiations. An opening offer can draw the recipient toward that number by prompting reasons it might be reasonable. Whether going first helps also depends on how much each side knows and how credible the offer is.

Excessive Coherence

Here is another experiment that will help you experience a third type of bias. You will read a description of a candidate for an executive position. The description consists of four adjectives, each written on a card. The deck of cards has just been shuffled. The first two cards have these two descriptors:

Intelligent, Persistent.

It would be reasonable to wait until the information is complete. Yet you may already have formed a positive impression, before deliberately evaluating the candidate.

Next, you draw the last two cards. Here is the full description now:

Intelligent, Persistent, Cunning, Unprincipled.

Your evaluation may now be less favorable. Compare it with the impression produced by the same information in a different order. For comparison, consider the following description, which another shuffling of the deck could have produced:

Unprincipled, Cunning, Persistent, Intelligent.

This second description consists of the same adjectives, yet the order can make it less appealing than the first. The word Cunning was only mildly negative when it followed Intelligent and Persistent, because we still believed (without reason) that the executive’s intentions were good. Yet when it follows Unprincipled, the word Cunning is awful. In this context, persistence and intelligence are not positives anymore: they make a bad person even more dangerous.

This experiment illustrates excessive coherence: we form coherent impressions quickly and are slow to change them. In this example, we immediately developed a positive attitude toward the candidate, in light of little evidence. Confirmation bias—the same tendency that leads us, when we have a prejudgment, to disregard conflicting evidence altogether—made us assign less importance than we should to subsequent data. (Another term to describe this phenomenon is the halo effect, because the candidate was evaluated in the positive “halo” of the first impression. We will see in chapter 24 that the halo effect is a serious problem in hiring decisions.)

Here is another example. In the United States, public officials have required chain restaurants to include calorie labels to ensure that consumers see the calories associated with, for example, cheeseburgers, hamburgers, and salads. After seeing those labels, do consumers change their choices? The evidence is disputed and mixed. But in a revealing study, consumers were found to be more likely to be affected by calorie labels if they were placed to the left of the food item rather than the right. When calories are on the left, consumers receive that information first and evidently think “a lot of calories!” or “not so many calories!” before they see the item. Their initial positive or negative reaction greatly affects their choices. By contrast, when people see the food item first, they apparently think “delicious!” or “not so great!” before they see the calorie label. Here again, their initial reaction greatly affects their choices. This hypothesis is supported by the authors’ finding that for Hebrew speakers, who read right to left, the calorie label has a significantly larger impact if it is on the right rather than the left.

In general, we jump to conclusions, then stick to them. We think we base our opinions on evidence, but the evidence we consider and our interpretation of it are likely to be distorted, at least to some extent, to fit our initial snap judgment. As a result, we maintain the coherence of the overall story that has emerged in our mind. This process is fine, of course, if the conclusions are correct. When the initial evaluation is erroneous, however, the tendency to stick to it in the face of contradictory evidence is likely to amplify errors. And this effect is difficult to control, because information that we have heard or seen is impossible to ignore and often difficult to forget. In court, judges sometimes instruct jurors to disregard an inadmissible piece of evidence they have heard, but this is not a realistic instruction (although it may be helpful in jury deliberation, where arguments explicitly based on this evidence can be rejected).

Psychological Biases Cause Noise

We have briefly presented three types of biases that operate in different ways: substitution biases, which lead to a misweighting of the evidence; conclusion biases, which lead us either to bypass the evidence or to consider it in a distorted way; and excessive coherence, which magnifies the effect of initial impressions and reduces the impact of contradictory information. All three types of biases can, of course, produce statistical bias. They can also produce noise.

Let’s start with substitution. Most people judge the probability that Bill is an accountant by the similarity of his profile to a stereotype: the result, in this experiment, is a shared bias. If every respondent makes the same mistake, there is no noise. But substitution does not always produce such unanimity. When the question “Is there climate change?” is replaced with “Do I trust the people who say it is real?,” it is easy to see that the answer will vary from one person to the next, depending on that person’s social circles, preferred sources of information, political affiliation, and so on. The same psychological bias creates variable judgments and between-person noise.

Substitution can also be a source of occasion noise. If a question on life satisfaction is answered by consulting one’s immediate mood, the answer will inevitably vary for the same person from one moment to the next. A happy morning can be followed by a distressing afternoon, and changing moods over time can lead to very different reports of life satisfaction depending on when the interviewer happens to call. In chapter 7, we reviewed examples of occasion noise that can be traced to psychological biases.

Prejudgments also produce both bias and noise. Return to an example we mentioned in the introduction: the shocking disparities in the percentage of asylum seekers that judges admit. When one judge admits 5% of applicants and another in the same courthouse admits 88%, we can be quite certain that they are biased in different directions. From a broader perspective, individual differences in biases can cause massive system noise. Of course, the system can also be biased to the extent that most or all judges are biased similarly.

Finally, excessive coherence can produce either bias or noise, depending on whether the sequence of information and the meaning assigned to it are identical for all (or most) judges. Consider, for instance, a physically attractive candidate whose good looks create an early positive impression in most recruiters. If physical appearance is irrelevant to the position for which the candidate is considered, this positive halo will result in a shared error: a bias.

On the other hand, many complex decisions require compiling information that arrives in an essentially random order. Consider the claims adjusters of chapter 2. The order in which data about a claim becomes available varies haphazardly from one adjuster to the next and from one case to the next, causing random variation in initial impressions. Excessive coherence means that these random variations will produce random distortions in the final judgments. The effect will be system noise.

In short, psychological biases, as a mechanism, are universal, and they often produce shared errors. But when there are large individual differences in biases (different prejudgments) or when the effect of biases depends on context (different triggers), there will be noise.

Both bias and noise create error. Reducing psychological biases can improve judgment, but an intervention should be assessed for its effects on both. We will return to the topic of debiasing, or removing bias, in part 5. But for now, we continue our exploration of the process of judgment.

Matching and Coherence

You met Bill in the previous chapter, and here he is again: “Bill is thirty-three years old. He is intelligent but unimaginative, compulsive and generally lifeless. In school, he was strong in mathematics but weak in social studies and humanities.” We asked you to estimate the probability that Bill had various occupations and hobbies, and we saw that you answered this question by substituting a judgment of similarity for one of probability. You did not really ask how likely Bill was to be an accountant, but how similar he was to the stereotype of that profession. We now turn to a question we left unanswered: how you made that judgment.

It is not difficult to assess the degree to which Bill’s description matches the stereotypes of professions and hobbies. Bill is clearly less similar to a typical jazz player than to an accountant, and he is even less similar to a surfer. The example illustrates the extraordinary versatility of matching, which is particularly obvious in judgments about people. There is hardly a limit to the questions you could have answered about Bill. For example, how would you feel about being stranded on a desert island with him? You probably had an immediate intuitive answer to this question on the basis of the scant information provided. Yet, we have news for you: Bill, as we know him, happens to be a hardened explorer with extraordinary survival skills. If this surprises you (and it probably does), you just experienced a failure to achieve coherence.

The surprise is intense because the new information is incompatible with the image of Bill that you had constructed earlier. Now imagine that Bill’s prowess and survival skills had been included in the original description. You would have ended up with a different overall image of the man, perhaps as a person who comes alive only in the great outdoors. The overall impression of Bill would have been less coherent, and therefore more difficult to match to categories of professions or hobbies, but you would have experienced far less dissonance than you just did.

Conflicting cues make it more difficult to achieve a sense of coherence and to find a judgment that is a satisfactory match. The presence of conflicting cues characterizes complex judgments, in which we expect to find a lot of noise. The Gambardi problem, where some of the indications were positive and others negative, was such a judgment. We return to complex judgments in chapter 16. In the remainder of this chapter we focus on relatively simple judgments—especially those made on intensity scales.

Matching Intensities

Some of the scales on which we express judgments are qualitative: professions, hobbies, and medical diagnoses are examples. They are identified by the fact that the values of the scale are not ordered: red is neither more nor less than blue.

Many judgments, however, are made on quantitative intensity scales. Physical measurements of size, weight, brightness, temperature, or loudness; measures of cost or value; judgments of probability or frequency—all these are quantitative. So are judgments on more abstract scales, like confidence, strength, attractiveness, anger, fear, immorality, or the severity of punishments.

The distinctive feature shared by these quantitative dimensions is that the question “Which is more?” can be answered about any pair of values on the same dimension. You can tell that a flogging is a more severe punishment than a slap on the wrist or that you like Hamlet more than you liked Waiting for Godot, just as you can tell that the sun is brighter than the moon, that an elephant weighs more than a hamster, and that the average temperature in Miami is higher than in Toronto.

People have a remarkable intuitive ability to match intensities across unrelated dimensions, by mapping one intensity scale onto another. You can match the intensity of your affection for different singers to the height of buildings in your city. (If you think that Bob Dylan is especially great, for example, you might match your level of enthusiasm for him to the tallest building in your city.) You could match the current level of political discord in your country to a summer temperature in a city you know well. (If there is remarkable political harmony, you might match it to a breezy seventy-degree summer day in New York.) And if you were asked to express your appreciation of a restaurant by comparing it to the length of a novel instead of the usual 1-to-5-star rating scale, this request would strike you as quite bizarre but not at all infeasible. (Your favorite restaurant might be like War and Peace.) In each case, it is—oddly—quite clear what you mean.

In ordinary conversation, the range of values for a scale is a function of the context. The comment “She has been saving a lot of money” has a different meaning when you are toasting the retirement of a successful investment banker than it has when you are congratulating a teenager who has been babysitting. And the meaning of words like large and small depends entirely on a frame of reference. We can, for example, make sense of a statement like “The large mouse ran up the trunk of the small elephant.”

The Bias of Matching Predictions

The following puzzle illustrates both the power of matching and a systematic judgment error that is associated with it.

Julie is a graduating student at a university. Read the following piece of information about her, then guess her GPA (on the standard scale of 0.0 to 4.0):

Julie read fluently when she was four years old.

What is her GPA?

If you are familiar with the grade point average system in the United States, a number came to your mind quite quickly, and it was probably close to 3.7 or 3.8. How a guess about Julie’s GPA instantly came to your mind illustrates the matching process we just described.

First, you evaluated how precocious a reader Julie was. The evaluation was easy because Julie read unusually early, and that precociousness placed Julie in a category on some scale. If you had to describe the scale you used, you would probably say its highest category is something like “extraordinarily precocious,” and you would note that Julie does not quite belong in that category (some children read before they are two). Julie probably belongs in the next one, the band of “unusually but not extraordinarily precocious” children.

In the second step, you matched a judgment of GPA to your evaluation of Julie. Although you were unaware of doing so, you must have been looking for a value of GPA that would also fit the label “unusual but not extraordinary.” A matching prediction came to your mind, seemingly out of nowhere, when you heard Julie’s story.

Deliberately carrying out the calculations required to perform these tasks of evaluation and matching would take quite a while, but in fast, System 1 thinking, the judgment is achieved quickly and effortlessly. The story we tell here about guessing Julie’s GPA involves a complex, multistage sequence of mental events that cannot be directly observed. The specificity of the mental mechanism of matching is unusual in psychology—but the evidence for it is unusually conclusive. In similar experiments, groups asked the following two questions give strikingly similar estimates:

• What percentage of Julie’s class read at an earlier age than she did?
• What percentage of Julie’s class has a higher GPA than she does?

The first question is manageable on its own: it simply asks you to evaluate the evidence you were given about Julie. The second question, which requires a distant prediction, is certainly harder—but it is intuitively tempting to answer it by answering the first.

The two questions we ask about Julie are analogous to two questions that we described as universally confusing in an earlier discussion of the illusion of validity. The first question about Julie requires you to evaluate the “intensity” of the information you have about her case. The second question asks about the intensity of a prediction. And we suspect that they are still difficult to tell apart.

The intuitive prediction of Julie’s GPA is a case of the psychological mechanism that we described in chapter 13: the substitution of an easy question for a difficult one. Your System 1 simplifies a difficult prediction question by answering a much easier one: how impressive was Julie’s achievement as a four-year-old reader? An extra step of matching is required to move directly from reading age, measured in years, to GPA, measured in points.

The information must seem relevant for this kind of substitution to be tempting. Knowing that Julie was a fast runner or a mediocre dancer gives no clear basis for estimating her GPA. A fact that seems to indicate intelligence is a more plausible substitute, even if its predictive value is weak.

Substituting one question for another inevitably causes errors when the true answers to the two questions are different. Substituting reading age for GPA, though seemingly plausible, is manifestly absurd. To see why, think of events that could have happened since Julie was four years old. She could have been in a terrible accident. Her parents could have had a traumatic divorce. She could have encountered an inspiring teacher who influenced her greatly. She could have become pregnant. Any of these events and many more could have affected her work in college.

The matching prediction can be justified only if reading precocity and college GPA are perfectly correlated, which is clearly not the case. On the other hand, completely ignoring the information about Julie’s reading age would also be a mistake, because her reading age does provide some relevant information. The optimal prediction must lie between these two extremes of perfect knowledge and zero knowledge.

What do you know about a case when you know nothing specific about it—only the category to which it belongs? The answer to that question is what we have called the outside view of the case. If we were asked to predict Julie’s GPA but given no information about her, we would surely predict the average—perhaps 3.2. This is the outside-view prediction. If early reading is a positive but imperfect predictor, the estimate should move above the assumed average of 3.2 without going as far as the matching estimate of 3.8. The precise location of the estimate depends on the predictive value of the information: the more you trust reading age as a predictor of GPA, the higher the estimate. In Julie’s case, the information is certainly quite weak, and the most reasonable prediction will accordingly be closer to the average GPA. There is a technical but fairly easy way to correct the error of matching predictions; we detail it in appendix C.

Although they lead to statistically absurd predictions, predictions that match the evidence are hard to resist. Sales managers often assume that the salesperson who was more successful than the rest of the sales team last year will continue to overperform. Senior executives sometimes meet an exceptionally talented candidate and imagine how the new hire will rise to the top of the organization. Producers routinely anticipate that the next movie of a director whose previous movie was a hit will be just as successful.

These examples of matching predictions are more likely than not to end in disappointment. On the other hand, matching predictions that are made when things are at their worst are more likely than not to be overly negative. Intuitive predictions that match the evidence are too extreme, both when they are optimistic and when they are pessimistic. (The technical term for such prediction errors is that they are nonregressive, because they fail to take into account a statistical phenomenon called regression to the mean.)

Substitution and matching do not always govern predictions. In the language of two systems, the intuitive System 1 proposes quick associative solutions to problems as they arise, but these intuitions must be endorsed by the more reflective System 2 before they become beliefs. Matching predictions are sometimes rejected in favor of more complex responses. For example, people are more reluctant to match predictions to unfavorable than to favorable evidence. We suspect that you would hesitate to make a matching prediction of inferior college performance if Julie had been a late reader. The asymmetry between favorable and unfavorable predictions disappears when more information is available.

We offer the outside view as a corrective for intuitive predictions of all kinds. In an earlier discussion of Michael Gambardi’s future prospects, for example, we recommended anchoring your judgment about Michael’s probability of success on the relevant base rate (the two-year success rate for incoming CEOs). In the case of quantitative predictions such as Julie’s GPA, taking the outside view means anchoring your prediction on the average outcome. The outside view can be neglected only in very easy problems, when the information available supports a prediction that can be made with complete confidence. When serious judgment is necessary, the outside view must be part of the solution.

Noise in Matching: Limitations of Absolute Judgment

Our limited ability to distinguish categories on intensity scales constrains the accuracy of the matching operation. Words such as large or rich assign the same label to a range of values on the dimension of size or wealth. This is a potentially important source of noise.

The retiring investment banker surely deserves the label rich, but how rich is she? We have many adjectives to choose from: well-off, affluent, comfortable, wealthy, super-rich, and others. If you were given detailed descriptions of the wealth of some individuals and had to attach an adjective to each, how many distinct categories could you form—without resorting to detailed comparisons across cases?

A classic article in psychology, published in 1956, describes limits on absolute judgments in its title: “The Magical Number Seven, Plus or Minus Two.” Beyond this limit, people tend to start to make errors—for instance, to assign A to a higher category than B when they would in fact rate B higher than A in a head-to-head comparison.

Imagine a set of lines of four different lengths of between 2 and 4 inches, each line the same amount longer than the next one. You are shown one line at a time and have to call out a number between 1 and 4, where 1 goes with the shortest line and 4 with the longest. The task is easy. Now suppose you are shown lines of five different lengths and have to repeat the task calling out numbers 1 through 5. Still easy. When will you start making errors? Around the magical number of seven lines. Surprisingly, this number depends very little on the range of line lengths: if the lines were spaced between 2 and 6 inches, rather than between 2 and 4, you would still start making mistakes beyond seven lines. Much the same result is obtained when you are presented with tones that vary in loudness, or with lights of different brightness. These tasks reveal limits on assigning distinct labels to stimuli along a dimension. The exact limit varies with the task and conditions; seven is not a universal capacity.

This limit of our discriminating power matters, because our ability to match values across intensity dimensions cannot be better than our ability to assign values on these dimensions. The matching operation is a versatile tool of fast, System 1 thinking and the core of many intuitive judgments, but it is crude.

The magical number is not an absolute constraint. People can be trained to make finer distinctions by hierarchical categorization. For example, we can certainly discriminate several categories of wealth among multimillionaires, and judges can discriminate degrees of severity in multiple categories of crimes, themselves ordered in severity. For this refinement process to work, however, the categories must exist in advance and their boundaries must be clear. When assigning labels to a set of lines, you cannot decide to separate the longer lines from the shorter ones and treat them as two separate categories. Categorization is not under voluntary control when you are in the fast-thinking mode.

There is a way to overcome the limited resolution of adjective scales: instead of using labels, use comparisons. Our ability to compare cases is much better than our ability to place them on a scale.

Consider what you would do if instructed to use a twenty-point scale of quality to evaluate a large set of restaurants, or singers. A five-star scale would be easily manageable, but you could not possibly maintain perfect reliability with a twenty-point scale. (Joe’s Pizza is worth three stars, but is it an eleven or a twelve?) The solution to this problem is simple, if time-consuming. You would first rate the restaurants, or singers, using the five-point rating scale to sort them into five categories. You would then rank the cases within each category, which you will usually be able to do with only a few ties: you probably know whether you prefer Joe’s Pizza to Fred’s Burgers, or Taylor Swift to Bob Dylan, even if you assigned them to the same category. To keep things simple, you could now distinguish four levels within each of the five categories. You can probably discriminate levels of contempt even among the singers you most dislike.

The psychology of this exercise is straightforward. Explicit comparisons between objects of judgment support much finer discriminations than do ratings of objects evaluated one at a time. Judgments of line length tell a similar story: your ability to compare the length of lines that are shown in immediate succession is much better than your ability to label lengths, and you will be even more accurate when comparing lines that are in view at the same time.

The advantage of comparative judgments applies to many domains. If you have a rough idea of people’s wealth, you will do better comparing individuals in the same range than you would by labeling their wealth individually. If you grade essays, you will be more precise when you rank them from best to worst than you are when you read and grade essays one by one. Comparative or relative judgments are more sensitive than categorical or absolute ones. As these examples suggest, they are also more effortful and time-consuming.

Rating objects individually on scales that are explicitly comparative retains some of the benefits of comparative judgment. In some contexts, notably in education, recommendations of candidates for acceptance or promotion often require the recommender to locate the candidate in the “top 5%” or “top 20%” of some designated population, such as “students that you have taught” or “programmers with the same level of experience.” These ratings rarely deserve to be taken at face value because there is no way to keep the recommenders accountable for using the scale properly. Accountability is possible in some contexts: when managers rate employees or when analysts assess investments, a person who assigns 90% of cases to the “top 20%” category can be identified and corrected. The use of comparative judgments is one of the remedies for noise that we will discuss in part 5.

Many tasks of judgment require matching individual cases to a category on a scale (for instance, a seven-point agreement scale) or using an ordered set of adjectives (for example, “unlikely” or “extremely unlikely” in rating the probabilities of events). This type of matching is noisy because it is crude. Individuals may differ in the interpretation of labels even when they agree on the substance of the judgment. A procedure that compels explicitly comparative judgments is likely to reduce noise. In the next chapter, we further explore how using the wrong scales can add to noise.

Scales

Imagine yourself a juror in a civil trial. You have heard the evidence summarized below, and you will be required to make some judgments about it.

Hypothetical case: Joan Glover v. General Assistance

Joan Glover, a six-year-old child, ingested a large number of pills of Allerfree, a nonprescription allergy medicine, and required an extensive hospital stay. Because the overdose weakened her respiratory system, she will be more susceptible to breathing-related diseases such as asthma and emphysema for the rest of her life. The Allerfree bottle used an inadequately designed childproof safety cap.

The manufacturer of Allerfree is General Assistance, a large company (with annual profits of $100 million to $200 million) that produces a variety of nonprescription medicines. A federal regulation requires childproof safety caps on all medicine bottles. General Assistance has systematically ignored the intent of this regulation by using a childproof safety cap that had a much higher failure rate than that of others in the industry. An internal company document says that “this stupid, unnecessary federal regulation is a waste of our money” and states that the risk of being punished is low. The document adds that, in any case, “the punishments for violating the regulation are extremely mild; basically we’d be asked to improve the safety caps in the future.” Although it was warned about its safety cap by an official of the US Food and Drug Administration, the company decided to take no corrective action.

Next we ask you to make three judgments. Please slow down enough to choose your answers.

Outrage:

Which of the following best expresses your opinion of the defendant’s actions? (Please circle your answer.)

Completely acceptable: 0 1 Objectionable: 2 3 Shocking: 4 5 Absolutely outrageous: 6

Punitive intent:

In addition to paying compensatory damages, how much should the defendant be punished? (Please circle the number that best expresses your opinion of the appropriate level of punishment.)

No punishment: 0 1 Mild punishment: 2 3 Severe punishment: 4 5 Extremely severe punishment: 6

Damages:

In addition to paying compensatory damages, what amount of punitive damages (if any) should the defendant be required to pay as punishment and to deter the defendant and others from similar actions in the future? (Please write your answer in the blank below.)

$_______

The fictional story of Joan Glover is a slightly abbreviated version of a case used in a study that two of us (Kahneman and Sunstein, along with our friend and collaborator David Schkade) reported in 1998. We describe this study in some detail in this chapter, and we wanted you to experience one of the tasks the study includes, because we now see it as an instructive example of a noise audit, which reprises many of the themes of this book.

This chapter focuses on the role of the response scale as a pervasive source of noise. People may differ in their judgments, not because they disagree on the substance but because they use the scale in different ways. If you were rating the performance of an employee, you might say that on a scale of 0 to 6, the performance was a 4—which, in your view, is pretty good. Someone else might say that on the same scale, the employee’s performance was a 3—which, in his view, is also pretty good. Ambiguity in the wording of scales is a general problem. Much research has been conducted on the difficulties of communication that arise from vague expressions such as “beyond a reasonable doubt,” “clear and convincing evidence,” “outstanding performance,” and “unlikely to happen.” Judgments that are expressed in such phrases are inevitably noisy because they are interpreted differently by both speakers and listeners.

In the study for which the Joan Glover case was written, we observed the effects of an ambiguous scale in a situation in which it has serious consequences. The topic of the study was noise in jury-awarded punitive damages. As you could infer from the third question about Joan Glover’s case, the law in the United States (and in some other countries) allows juries in civil cases to impose punitive damages on a defendant whose actions were particularly egregious. Punitive damages are supplemental to compensatory awards, which are designed to make injured people whole. When, as in the Glover example, a product has caused injuries and plaintiffs have successfully sued the company, they will be awarded money to pay their medical bills and any lost wages. But they could also receive a punitive award, intended to send the defendant and similar companies a warning. The behavior of General Assistance in this case was obviously reprehensible; it falls in the range of actions for which a jury could reasonably impose punitive damages.

A major concern about the institution of punitive damages has been their unpredictability. The same wrongdoing may be punished by damages that range from very modest to massive. Using the terminology of this book, we would say the system is noisy. Requests for punitive damages are often denied, and even when they are granted, the awards frequently do not add much to compensatory damage. There are striking exceptions, however, and the very large amounts that juries sometimes award appear surprising and arbitrary. An often-mentioned example is a punitive award of $4 million imposed on a car dealership for nondisclosure of the fact that the plaintiff’s new BMW had been repainted.

In our study of punitive damages, 899 participants were asked to evaluate Joan Glover’s case and nine other similar cases—all of them involving plaintiffs who had suffered some harm and sued the company that was allegedly responsible. Unlike you, the participants answered only one of the three questions (outrage, punitive intent, or dollar amount) for all ten cases. The participants were further divided into smaller groups, each assigned to one version of each case. The different versions varied the harm suffered by the plaintiff and the revenue of the defendant company. There were a total of twenty-eight scenarios. Our goals were to test a theory about the psychology of punitive damages and to investigate the role of the monetary scale (here dollars) as a main source of noise in this legal institution.

The Outrage Hypothesis

How to determine a just punishment has been debated by philosophers and legal scholars for centuries. Our hypothesis, however, was that the question that philosophers find difficult is quite easy for ordinary people, who simplify the task by substituting an easy question for the hard one. The easy question, which is answered immediately when you are asked how much General Assistance should be punished is, “How angry am I?” The intensity of the intended punishment will then be matched to the intensity of the outrage.

To test this outrage hypothesis, we asked different groups of participants to answer either the punitive intent question or the outrage question. We then compared the average ratings obtained on the two questions for the twenty-eight scenarios used in the study. As expected from the substitution idea, the correlation between the mean ratings of outrage and of punitive intent was a close-to-perfect 0.98 (PC = 94%). This correlation is consistent with the outrage hypothesis: scenarios that provoked more outrage also elicited stronger punitive intent. The correlation alone does not establish the causal process.

Outrage is the main driver of punitive intent but not the only one. Did you notice anything in Joan’s story that attracted more attention when you rated punitive intent than when you rated outrage? If you did, we suspect it was the harm she suffered. You can tell whether a behavior is outrageous without knowing its consequences; in this instance, the behavior of General Assistance was surely outrageous. In contrast, intuitions about punitive intent have a retributive aspect, which is crudely expressed in the eye-for-an-eye principle. The urge for retribution explains why attempted murder and murder are treated differently by the law and by juries; a would-be murderer who is lucky enough to miss his target will be punished less severely.

To find out whether harm does indeed make a difference in punitive intent but not in outrage, we showed different groups of respondents “severe-harm” and “mild-harm” versions of the Joan Glover case and of several others. The severe-harm version is the one you saw. In the mild-harm version, Joan “had to spend several days in a hospital and is now deeply traumatized by pills of any kind. When her parents try to get her to take even beneficial medications such as vitamins, aspirin, or cold remedies, she cries uncontrollably and says that she is afraid.” This version describes a traumatic experience for the child, but a much lower level of harm than the long-term medical damage described in the first version you read. As expected, the average ratings of outrage were almost identical for the severe-harm version (4.24) and the mild-harm version (4.19). In this comparison, changing the consequences had little effect on the average outrage rating. In contrast, the ratings of punitive intent averaged 4.93 for severe harm and 4.65 for mild harm, a small but statistically reliable difference. The median monetary awards were two million dollars for the severe-harm version and one million for the milder version. Similar results were obtained for several other cases.

These findings highlight a key feature of the process of judgment: the subtle effect of the judgment task on the weighting of different aspects of the evidence. The participants who rated punitive intent and outrage were not aware that they were taking a stand on the philosophical issue of whether justice should be retributive. They were not even aware of assigning weights to the various features of the case. Nevertheless, they assigned a near-zero weight to harm when rating outrage and a significant weight to the same factor when determining punishment. Recall that the participants saw only one version of the story; their assignment of a higher punishment to the worse harm was not an explicit comparison. It was the outcome of an automatic operation of matching in the two conditions. The responses of participants relied more on fast than on slow thinking.

Noisy Scales

The second goal of the study was to find out why punitive damages are noisy. Our hypothesis was that jurors generally agree on how severely they wish the defendant to be punished but differ widely in how they translate their punitive intent onto the scale of dollars.

The design of the study allows us to compare the amount of noise in judgments of the same cases on three scales: outrage, punitive intent, and damage awards in dollars. To measure noise, we apply the method that was used to analyze the results of the noise audit of federal judges in chapter 6. We assume, as we did in that analysis, that the average of individual judgments of a case can be treated as an unbiased, just value. (This is an assumption for purposes of analysis; we emphasize that it might be wrong.) In an ideal world, all jurors who use a particular scale would agree in their judgments of every case. Any deviation from the average judgment counts as an error, and these errors are the source of system noise.

As we also noted in chapter 6, system noise can be broken down into level noise and pattern noise. Here, level noise is the variability among jurors in how severe they are in general. Pattern noise is the variability in how a given juror responds to particular cases, relative to this juror’s own average. We can therefore break down the overall variance of judgments into three elements:

Variance of Judgments = Variance of Just Punishments + (Level Noise)² + (Pattern Noise)²

This analysis, decomposing the variance of judgments into three terms, was conducted separately for the three judgments of outrage, punitive intent, and dollar award.

Figure 13 shows the results. The least noisy scale is punitive intent, where system noise accounts for 51% of the variance—about as much variation within cases as between the case averages used as the study’s benchmarks. The outrage scale is distinctly noisier: 71% noise. And the dollar scale is by far the worst: fully 94% of the variance in judgments is noise!

The differences are striking because the three scales are, in terms of their content, almost identical. We saw earlier that the just values of outrage and punitive intent were almost perfectly correlated, as implied by the outrage hypothesis. The ratings of punitive intent and the dollar awards answer precisely the same question—how severely General Assistance should be punished—in different units. How can we explain the large differences seen in figure 13?

We can probably agree that outrage is not a very precise scale. True, there is such a thing as “completely acceptable” behavior, but if there is a limit to how angry you can get at General Assistance or at the other defendants, that limit is rather vague. What does it mean for a behavior to be “absolutely outrageous”? The lack of clarity on the upper end of the scale makes some noise inevitable.

Punitive intent is more specific. “Severe punishment” is more precise than “absolutely outrageous,” because an “extremely severe punishment” is bounded by the maximum prescribed by the law. You may wish to “throw the book” at the culprit, but you may not, for instance, recommend putting the CEO of General Assistance and its entire executive team to death. (We hope.) The punitive-intent scale is less ambiguous because its upper bound is more clearly specified. As we might expect, it is also less noisy.