Our almost unlimited ability to ignore our ignorance.

 

Our comforting conviction that the world makes sense rests on a secure foundation: our almost unlimited ability to ignore our ignorance.

I have heard of too many people who “knew well before it happened that the 2008 financial crisis was inevitable.” This sentence contains a highly objectionable word, which should be removed from our vocabulary in discussions of major events. The word is, of course, knew. Some people thought well in advance that there would be a crisis, but they did not know it. They now say they knew it because the crisis did in fact happen. This is a misuse of an important concept. In everyday language, we apply the word know only when what was known is true and can be shown to be true. We can know something only if it is both true and knowable. But the people who thought there would be a crisis (and there are fewer of them than now remember thinking it) could not conclusively show it at the time. Many intelligent and well-informed people were keenly interested in the future of the economy and did not believe a catastrophe was imminent; I infer from this fact that the crisis was not knowable. What is perverse about the use of know in this context is not that some individuals get credit for prescience that they do not deserve. It is that the language implies that the world is more knowable than it is. It helps perpetuate a pernicious illusion.

The core of the illusion is that we believe we understand the past, which implies that the future also should be knowable, but in fact we understand the past less than we believe we do. Know is not the only word that fosters this illusion. In common usage, the words intuition and premonition also are reserved for past thoughts that turned out to be true. The statement “I had a premonition that the marriage would not last, but I was wrong” sounds odd, as does any sentence about an intuition that turned out to be false. To think clearly about the future, we need to clean up the language that we use in labeling the beliefs we had in the past.

** 

The mind that makes up narratives about the past is a sense-making organ. When an unpredicted event occurs, we immediately adjust our view of the world to accommodate the surprise. Imagine yourself before a football game between two teams that have the same record of wins and losses. Now the game is over, and one team trashed the other. In your revised model of the world, the winning team is much stronger than the loser, and your view of the past as well as of the future has been altered by that new perception. Learning from surprises is a reasonable thing to do, but it can have some dangerous consequences.

A general limitation of the human mind is its imperfect ability to reconstruct past states of knowledge, or beliefs that have changed. Once you adopt a new view of the world (or of any part of it), you immediately lose much of your ability to recall what you used to believe before your mind changed

**

Hindsight bias has pernicious effects on the evaluations of decision makers. It leads observers to assess the quality of a decision not by whether the process was sound but by whether its outcome was good or bad. Consider a low-risk surgical intervention in which an unpredictable accident occurred that caused the patient’s death. The jury will be prone to believe, after the fact, that the operation was actually risky and that the doctor who ordered it should have known better. This outcome bias makes it almost impossible to evaluate a decision properly—in terms of the beliefs that were reasonable when the decision was made.

Hindsight is especially unkind to decision makers who act as agents for others—physicians, financial advisers, third-base coaches, CEOs, social workers, diplomats, politicians. We are prone to blame decision makers for good decisions that worked out badly and to give them too little credit for successful moves that appear obvious only after the fact. There is a clear outcome bias. When the outcomes are bad, the clients often blame their agents for not seeing the handwriting on the wall—forgetting that it was written in invisible ink that became legible only afterward. Actions that seemed prudent in foresight can look irresponsibly negligent in hindsight. Based on an actual legal case, students in California were asked whether the city of Duluth, Minnesota, should have shouldered the considerable cost of hiring a full-time bridge monitor to protect against the risk that debris might get caught and block the free flow of water. One group was shown only the evidence available at the time of the city’s decision; 24% of these people felt that Duluth should take on the expense of hiring a flood monitor. The second group was informed that debris had blocked the river, causing major flood damage; 56% of these people said the city should have hired the monitor, although they had been explicitly instructed not to let hindsight distort their judgment.

The worse the consequence, the greater the hindsight bias. In the case of a catastrophe, such as 9/11, we are especially ready to believe that the officials who failed to anticipate it were negligent or blind. On July 10, 2001, the Central Intelligence Agency obtained information that al-Qaeda might be planning a major attack against the United States. George Tenet, director of the CIA, brought the information not to President George W. Bush but to National Security Adviser Condoleezza Rice. When the facts later emerged, Ben Bradlee, the legendary executive editor of The Washington Post, declared, “It seems to me elementary that if you’ve got the story that’s going to dominate history you might as well go right to the president.” But on July 10, no one knew—or could have known—that this tidbit of intelligence would turn out to dominate history.

Because adherence to standard operating procedures is difficult to second-guess, decision makers who expect to have their decisions scrutinized with hindsight are driven to bureaucratic solutions—and to an extreme reluctance to take risks. As malpractice litigation became more common, physicians changed their procedures in multiple ways: ordered more tests, referred more cases to specialists, applied conventional treatments even when they were unlikely to help. These actions protected the physicians more than they benefited the patients, creating the potential for conflicts of interest. Increased accountability is a mixed blessing.

Although hindsight and the outcome bias generally foster risk aversion, they also bring undeserved rewards to irresponsible risk seekers, such as a general or an entrepreneur who took a crazy gamble and won. Leaders who have been lucky are never punished for having taken too much risk. Instead, they are believed to have had the flair and foresight to anticipate success, and the sensible people who doubted them are seen in hindsight as mediocre, timid, and weak. A few lucky gambles can crown a reckless leader with a halo of prescience and boldness.

**

The CEO of a successful company is likely to be called flexible, methodical, and decisive. Imagine that a year has passed and things have gone sour. The same executive is now described as confused, rigid, and authoritarian. Both descriptions sound right at the time: it seems almost absurd to call a successful leader rigid and confused, or a struggling leader flexible and methodical.

Indeed, the halo effect is so powerful that you probably find yourself resisting the idea that the same person and the same behaviors appear methodical when things are going well and rigid when things are going poorly. Because of the halo effect, we get the causal relationship backward: we are prone to believe that the firm fails because its CEO is rigid, when the truth is that the CEO appears to be rigid because the firm is failing. This is how illusions of understanding are born.

Surprise!

 

People who are taught surprising statistical facts about human behavior may be impressed to the point of telling their friends about what they have heard, but this does not mean that their understanding of the world has really changed. The test of learning psychology is whether your understanding of situations you encounter has changed, not whether you have learned a new fact. There is a deep gap between our thinking about statistics and our thinking about individual cases. Statistical results with a causal interpretation have a stronger effect on our thinking than noncausal information. But even compelling causal statistics will not change long-held beliefs or beliefs rooted in personal experience. On the other hand, surprising individual cases have a powerful impact and are a more effective tool for teaching psychology because the incongruity must be resolved and embedded in a causal story. That is why this book contains questions that are addressed personally to the reader. You are more likely to learn something by finding surprises in your own behavior than by hearing surprising facts about people in general.

Availability Effect and Emotions

 

Students of risk were quick to see that the idea of availability was relevant to their concerns. Even before our work was published, the economist Howard Kunreuther, who was then in the early stages of a career that he has devoted to the study of risk and insurance, noticed that availability effects help explain the pattern of insurance purchase and protective action after disasters. Victims and near victims are very concerned after a disaster. After each significant earthquake, Californians are for a while diligent in purchasing insurance and adopting measures of protection and mitigation. They tie down their boiler to reduce quake damage, seal their basement doors against floods, and maintain emergency supplies in good order. However, the memories of the disaster dim over time, and so do worry and diligence. The dynamics of memory help explain the recurrent cycles of disaster, concern, and growing complacency that are familiar to students of large-scale emergencies.

Kunreuther also observed that protective actions, whether by individuals or governments, are usually designed to be adequate to the worst disaster actually experienced. As long ago as pharaonic Egypt, societies have tracked the high-water mark of rivers that periodically flood—and have always prepared accordingly, apparently assuming that floods will not rise higher than the existing high-water mark. Images of a worse disaster do not come easily to mind.

**

The world in our heads is not a precise replica of reality; our expectations about the frequency of events are distorted by the prevalence and emotional intensity of the messages to which we are exposed. 

**

People’s emotional evaluations of outcomes, and the bodily states and the approach and avoidance tendencies associated with them, all play a central role in guiding decision making. Damasio and his colleagues have observed that people who do not display the appropriate emotions before they decide, sometimes because of brain damage, also have an impaired ability to make good decisions. An inability to be guided by a “healthy fear” of bad consequences is a disastrous flaw.

**

“The emotional tail wags the rational dog.” The affect heuristic simplifies our lives by creating a world that is much tidier than reality. Good technologies have few costs in the imaginary world we inhabit, bad technologies have no benefits, and all decisions are easy. In the real world, of course, we often face painful tradeoffs between benefits and costs.

 

**

Sunstein and a collaborator, the jurist Timur Kuran, invented a name for the mechanism through which biases flow into policy: the availability cascade. They comment that in the social context, “all heuristics are equal, but availability is more equal than the others.” They have in mind an expanded notion of the heuristic, in which availability provides a heuristic for judgments other than frequency. In particular, the importance of an idea is often judged by the fluency (and emotional charge) with which that idea comes to mind.

An availability cascade is a self-sustaining chain of events, which may start from media reports of a relatively minor event and lead up to public panic and large-scale government action. On some occasions, a media story about a risk catches the attention of a segment of the public, which becomes aroused and worried. This emotional reaction becomes a story in itself, prompting additional coverage in the media, which in turn produces greater concern and involvement. The cycle is sometimes sped along deliberately by “availability entrepreneurs,” individuals or organizations who work to ensure a continuous flow of worrying news. The danger is increasingly exaggerated as the media compete for attention-grabbing headlines. Scientists and others who try to dampen the increasing fear and revulsion attract little attention, most of it hostile: anyone who claims that the danger is overstated is suspected of association with a “heinous cover-up.” The issue becomes politically important because it is on everyone’s mind, and the response of the political system is guided by the intensity of public sentiment. The availability cascade has now reset priorities. Other risks, and other ways that resources could be applied for the public good, all have faded into the background.

**

The Alar incident, known to detractors of environmental concerns as the “Alar scare” of 1989. Alar is a chemical that was sprayed on apples to regulate their growth and improve their appearance. The scare began with press stories that the chemical, when consumed in gigantic doses, caused cancerous tumors in rats and mice. The stories understandably frightened the public, and those fears encouraged more media coverage, the basic mechanism of an availability cascade. The topic dominated the news and produced dramatic media events such as the testimony of the actress Meryl Streep before Congress. The apple industry sustained large losses as apples and apple products became objects of fear. Kuran and Sunstein quote a citizen who called in to ask “whether it was safer to pour apple juice down the drain or to take it to a toxic waste dump.” The manufacturer withdrew the product and the FDA banned it. Subsequent research confirmed that the substance might pose a very small risk as a possible carcinogen, but the Alar incident was certainly an enormous overreaction to a minor problem. The net effect of the incident on public health was probably detrimental because fewer good apples were consumed.

The Alar tale illustrates a basic limitation in the ability of our mind to deal with small risks: we either ignore them altogether or give them far too much weight—nothing in between. Every parent who has stayed up waiting for a teenage daughter who is late from a party will recognize the feeling. You may know that there is really (almost) nothing to worry about, but you cannot help images of disaster from coming to mind. As Slovic has argued, the amount of concern is not adequately sensitive to the probability of harm; you are imagining the numerator—the tragic story you saw on the news—and not thinking about the denominator. Sunstein has coined the phrase “probability neglect” to describe the pattern. The combination of probability neglect with the social mechanisms of availability cascades inevitably leads to gross exaggeration of minor threats, sometimes with important consequences.

October 12, 1492: Genocide not discovery

 

Roxanne Durban-Ortiz, Lithub

Mahmood Mamdani, in Neither Settler nor Native, locates the founding moment of the modern nation-state at 1492, noting it emerged out of two developments in Iberia. “One was ethnic cleansing, whereby the Castilian monarchy sought to create a homogeneous national homeland for Christian Spaniards by ejecting and converting those among them who were strangers to the nation—Moors and Jews. The other development was the taking of overseas colonies in the Americas by the same Castilian monarchy that spearheaded ethnic cleansing.” Mamdani emphasizes that modern colonialism didn’t suddenly start occurring in the 18th century but that European colonialism and the modern state were co-constituted.

*

A few months after Catholic entry into ethnically cleansed Granada, the Spanish monarchs contracted with a Genoese seaman who promised he could reach India by a shorter route by sailing west. Columbus landed not at already European “discovered” India but, rather, on an island of what is now called the Bahamas. The thriving Indigenous residents informed him that to the north and south and east and west stretched a huge landmass, two massive continents teeming with cities and tens of millions of acres of farmlands that would come to constitute the major portion of humanity’s food production. The rapacious crusade-hardened mercenaries representing Christendom were skeptical, until some voyages later they reached the continent at Central America, which they named Cabo Gracias a Díos (Thanks to God Cape). Two decades later a Spanish army would possess the heart of that landmass, destroying the most populated city in the world at the time, Tenochtitlán, in the valley of México.

October 12, 1492, is etched in the brains of many as the day of “discovery,” but the Indigenous peoples of the Western Hemisphere and of Africa and descendants of enslaved Africans regard the date as the symbol of infamy, domination, slavery, and genocide. Haitian historian Michel-Rolph Trouillot writes, “To call ‘discovery’ the first invasions of inhabited lands by Europeans is an exercise in Eurocentric power that already frames future narratives of the event so described Once discovered by Europeans, the Other finally enters the human world.”

Math Education

 

Kerstin Jordaan, 

What does quantum physics have in common with DNA or the modern computer or nuclear deterrence? What do these concepts share with fractals or with Monte Carlo simulations? Or with quantum logic, mathematical economics, linear programming, statistics, operator theory, fluid dynamics or game theory?

Maybe I should have asked “who” they have in common rather than “what” - John von Neumann!

Von Neumann was a mathematician in the first half of the 20th century who made valuable contributions in each of the fields I have mentioned. The mathematics he developed has largely impacted many areas that affect how we do and understand life around us today.

Climate change? Yes! Investments? Yes! Nanomedicines? Yes! Economics? Yes! Your cellphone? Yes! Your computer? Yes!

Von Neumann showed us how mathematics affects much of what we take for granted in everyday life. Mathematics touches every aspect of our modern life in some way or form. Mathematics forms the framework of most fields.

Mathematics underpins all innovation in finance, science, engineering, and business. However, mathematicians are the inventors but seldom the executors or the agents of their ideas. There is a disconnect between mathematics as a science and the utilisation of mathematics in the life that surrounds us.

The electrician works out the resistance or electrical supply to the new house. A plumber works out the angle to connect a drainage pipe. The painter works out the amount of paint he needs to paint your home - all numbers-based, subject to calculations, and somewhere, at different levels, related to mathematics.

**

Our mathematics hero, Von Neumann, illustrated this bridge by inventing the mathematical area known as game theory. It involves studying the best decision to make in any situation. Von Neumann proved the minimax theorem for two-player games where both players have all the information needed to make choices.

His result showed that the best strategy in such a game is where the worst-case situation has the least awful outcomes. He later extended this to games with incomplete information.

Scientists famously implemented game theory during the Cold War, where both the USA and the USSR had nuclear weapons. The game-theoretical approach to prevent use of the weaponry, was to ensure that retaliation would totally obliterate the opposing side.

This type of concrete application of mathematics is often not at all expected or even suspected. It is never clear what theory may end up solving a real-life problem, and this is precisely where the actual value of mathematics lies.

Kerstin Jordaan, Mathematics is much more than the numbers!

You are not in control

 

Our thoughts and our behavior are influenced, much more than we know or want, by the environment of the moment. Many people find the priming results unbelievable, because they do not correspond to subjective experience. Many others find the results upsetting, because they threaten the subjective sense of agency and autonomy. If the content of a screen saver on an irrelevant computer can affect your willingness to help strangers without your being aware of it, how free are you? Anchoring effects are threatening in a similar way. You are always aware of the anchor and even pay attention to it, but you do not know how it guides and constrains your thinking, because you cannot imagine how you would have thought if the anchor had been different (or absent). However, you should assume that any number that is on the table has had an anchoring effect on you, and if the stakes are high you should mobilize yourself (your System 2) to combat the effect.

The hot hand is a cognitive illusion

The widespread misunderstanding of randomness sometimes has significant consequences. In our article on representativeness, Amos and I cited the statistician William Feller, who illustrated the ease with which people see patterns where none exists. During the intensive rocket bombing of London in World War II, it was generally believed that the bombing could not be random because a map of the hits revealed conspicuous gaps. Some suspected that German spies were located in the unharmed areas. A careful statistical analysis revealed that the distribution of hits was typical of a random process—and typical as well in evoking a strong impression that it was not random. “To the untrained eye,” Feller remarks, “randomness appears as regularity or tendency to cluster.”

I soon had an occasion to apply what I had learned from Feller. The Yom Kippur War broke out in 1973, and my only significant contribution to the war effort was to advise high officers in the Israeli Air Force to stop an investigation. The air war initially went quite badly for Israel, because of the unexpectedly good performance of Egyptian ground-to-air missiles. Losses were high, and they appeared to be unevenly distributed. I was told of two squadrons flying from the same base, one of which had lost four planes while the other had lost none. An inquiry was initiated in the hope of learning what it was that the unfortunate squadron was doing wrong. There was no prior reason to believe that one of the squadrons was more effective than the other, and no operational differences were found, but of course the lives of the pilots differed in many random ways, including, as I recall, how often they went home between missions and something about the conduct of debriefings. My advice was that the command should accept that the different outcomes were due to blind luck, and that the interviewing of the pilots should stop. I reasoned that luck was the most likely answer, that a random search for a nonobvious cause was hopeless, and that in the meantime the pilots in the squadron that had sustained losses did not need the extra burden of being made to feel that they and their dead friends were at fault.

Some years later, Amos and his students Tom Gilovich and Robert Vallone caused a stir with their study of misperceptions of randomness in basketball. The “fact” that players occasionally acquire a hot hand is generally accepted by players, coaches, and fans. The inference is irresistible: a player sinks three or four baskets in a row and you cannot help forming the causal judgment that this player is now hot, with a temporarily increased propensity to score. Players on both teams adapt to this judgment—teammates are more likely to pass to the hot scorer and the defense is more likely to double team. Analysis of thousands of sequences of shots led to a disappointing conclusion: there is no such thing as a hot hand in professional basketball, either in shooting from the field or scoring from the foul line. Of course, some players are more accurate than others, but the sequence of successes and missed shots satisfies all tests of randomness. The hot hand is entirely in the eye of the beholders, who are consistently too quick to perceive order and causality in randomness. The hot hand is a massive and widespread cognitive illusion.

Answering Questions

 

A remarkable aspect of your mental life is that you are rarely stumped. True, you occasionally face a question such as 17 × 24 = ? to which no answer comes immediately to mind, but these dumbfounded moments are rare. The normal state of your mind is that you have intuitive feelings and opinions about almost everything that comes your way. You like or dislike people long before you know much about them; you trust or distrust strangers without knowing why; you feel that an enterprise is bound to succeed without analyzing it. Whether you state them or not, you often have answers to questions that you do not completely understand, relying on evidence that you can neither explain nor defend.

**

I propose a simple account of how we generate intuitive opinions on complex matters. If a satisfactory answer to a hard question is not found quickly, System 1 will find a related question that is easier and will answer it. I call the operation of answering one question in place of another substitution. I also adopt the following terms:

 

-The target question is the assessment you intend to produce.

-The heuristic question is the simpler question that you answer instead.

Halo Effect and Decorrelating the Error

 

If you like the president’s politics, you probably like his voice and his appearance as well. The tendency to like (or dislike) everything about a person—including things you have not observed—is known as the halo effect. The term has been in use in psychology for a century, but it has not come into wide use in everyday language. This is a pity, because the halo effect is a good name for a common bias that plays a large role in shaping our view of people and situations. It is one of the ways the representation of the world that System 1 generates is simpler and more coherent than the real thing. 

**

The procedure I adopted to tame the halo effect conforms to a general principle: decorrelate error! To understand how this principle works, imagine that a large number of observers are shown glass jars containing pennies and are challenged to estimate the number of pennies in each jar. As James Surowiecki explained in his best-selling The Wisdom of Crowds, this is the kind of task in which individuals do very poorly, but pools of individual judgments do remarkably well. Some individuals greatly overestimate the true number, others underestimate it, but when many judgments are averaged, the average tends to be quite accurate. The mechanism is straightforward: all individuals look at the same jar, and all their judgments have a common basis. On the other hand, the errors that individuals make are independent of the errors made by others, and (in the absence of a systematic bias) they tend to average to zero. However, the magic of error reduction works well only when the observations are independent and their errors uncorrelated. If the observers share a bias, the aggregation of judgments will not reduce it. Allowing the observers to influence each other effectively reduces the size of the sample, and with it the precision of the group estimate.

To derive the most useful information from multiple sources of evidence, you should always try to make these sources independent of each other. This rule is part of good police procedure. When there are multiple witnesses to an event, they are not allowed to discuss it before giving their testimony. The goal is not only to prevent collusion by hostile witnesses, it is also to prevent unbiased witnesses from influencing each other. Witnesses who exchange their experiences will tend to make similar errors in their testimony, reducing the total value of the information they provide. Eliminating redundancy from your sources of information is always a good idea.

The principle of independent judgments (and decorrelated errors) has immediate applications for the conduct of meetings, an activity in which executives in organizations spend a great deal of their working days. A simple rule can help: before an issue is discussed, all members of the committee should be asked to write a very brief summary of their position. This procedure makes good use of the value of the diversity of knowledge and opinion in the group. The standard practice of open discussion gives too much weight to the opinions of those who speak early and assertively, causing others to line up behind them.

Good Mood

 

Good mood, intuition, creativity, gullibility, and increased reliance on System 1 form a cluster. At the other pole, sadness, vigilance, suspicion, an analytic approach, and increased effort also go together. A happy mood loosens the control of System 2 over performance: when in a good mood, people become more intuitive and more creative but also less vigilant and more prone to logical errors. Here again, as in the mere exposure effect, the connection makes biological sense. A good mood is a signal that things are generally going well, the environment is safe, and it is all right to let one’s guard down. A bad mood indicates that things are not going very well, there may be a threat, and vigilance is required. Cognitive ease is both a cause and a consequence of a pleasant feeling.

Multiple Computations in the Brain

 

Whenever you are conscious, and perhaps even when you are not, multiple computations are going on in your brain, which maintain and update current answers to some key questions: Is anything new going on? Is there a threat? Are things going well? Should my attention be redirected? Is more effort needed for this task? You can think of a cockpit, with a set of dials that indicate the current values of each of these essential variables. The assessments are carried out automatically by System 1, and one of their functions is to determine whether extra effort is required from System 2.

You know far less about yourself than you feel you do

 

I will adopt an expansive view of what an idea is. It can be concrete or abstract, and it can be expressed in many ways: as a verb, as a noun, as an adjective, or as a clenched fist. Psychologists think of ideas as nodes in a vast network, called associative memory, in which each idea is linked to many others. There are different types of links: causes are linked to their effects (virus>>>cold); things to their properties (lime>>>green); things to the categories to which they belong (banana>>>fruit). One way we have advanced beyond Hume is that we no longer think of the mind as going through a sequence of conscious ideas, one at a time. In the current view of how associative memory works, a great deal happens at once. An idea that has been activated does not merely evoke one other idea. It activates many ideas, which in turn activate others. Furthermore, only a few of the activated ideas will register in consciousness; most of the work of associative thinking is silent, hidden from our conscious selves. The notion that we have limited access to the workings of our minds is difficult to accept because, naturally, it is alien to our experience, but it is true: you know far less about yourself than you feel you do.

Lazy "System 2"

  

It is now a well-established proposition that both self-control and cognitive effort are forms of mental work. Several psychological studies have shown that people who are simultaneously challenged by a demanding cognitive task and by a temptation are more likely to yield to the temptation. Imagine that you are asked to retain a list of seven digits for a minute or two. You are told that remembering the digits is your top priority. While your attention is focused on the digits, you are offered a choice between two desserts: a sinful chocolate cake and a virtuous fruit salad. The evidence suggests that you would be more likely to select the tempting chocolate cake when your mind is loaded with digits. System 1 has more influence on behavior when System 2 is busy, and it has a sweet tooth.

People who are cognitively busy are also more likely to make selfish choices, use sexist language, and make superficial judgments in social situations. Memorizing and repeating digits loosens the hold of System 2 on behavior, but of course cognitive load is not the only cause of weakened self-control. A few drinks have the same effect, as does a sleepless night. The self-control of morning people is impaired at night; the reverse is true of night people. Too much concern about how well one is doing in a task sometimes disrupts performance by loading short-term memory with pointless anxious thoughts. The conclusion is straightforward: self-control requires attention and effort. Another way of saying this is that controlling thoughts and behaviors is one of the tasks that System 2 performs.

One of the main functions of System 2 is to monitor and control thoughts and actions “suggested” by System 1, allowing some to be expressed directly in behavior and suppressing or modifying others.

For an example, here is a simple puzzle. Do not try to solve it but listen to your intuition:

A bat and ball cost $1.10.

The bat costs one dollar more than the ball.

How much does the ball cost?

A number came to your mind. The number, of course, is 10: 10¢. The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing, and wrong. Do the math, and you will see. If the ball costs 10¢, then the total cost will be $1.20 (10¢ for the ball and $1.10 for the bat), not $1.10. The correct answer is 5¢. It is safe to assume that the intuitive answer also came to the mind of those who ended up with the correct number—they somehow managed to resist the intuition.

Shane Frederick and I worked together on a theory of judgment based on two systems, and he used the bat-and-ball puzzle to study a central question: How closely does System 2 monitor the suggestions of System 1? His reasoning was that we know a significant fact about anyone who says that the ball costs 10¢: that person did not actively check whether the answer was correct, and her System 2 endorsed an intuitive answer that it could have rejected with a small investment of effort. Furthermore, we also know that the people who give the intuitive answer have missed an obvious social cue; they should have wondered why anyone would include in a questionnaire a puzzle with such an obvious answer. A failure to check is remarkable because the cost of checking is so low: a few seconds of mental work (the problem is moderately difficult), with slightly tensed muscles and dilated pupils, could avoid an embarrassing mistake. People who say 10¢ appear to be ardent followers of the law of least effort. People who avoid that answer appear to have more active minds.

Many thousands of university students have answered the bat-and-ball puzzle, and the results are shocking. More than 50% of students at Harvard, MIT, and Princeton gave the intuitive—incorrect—answer. At less selective universities, the rate of demonstrable failure to check was in excess of 80%. The bat-and-ball problem is our first encounter with an observation that will be a recurrent theme of this book: many people are overconfident, prone to place too much faith in their intuitions. They apparently find cognitive effort at least mildly unpleasant and avoid it as much as possible.

Now I will show you a logical argument—two premises and a conclusion. Try to determine, as quickly as you can, if the argument is logically valid. Does the conclusion follow from the premises?

All roses are flowers.

Some flowers fade quickly.

Therefore some roses fade quickly.

A large majority of college students endorse this syllogism as valid. In fact the argument is flawed, because it is possible that there are no roses among the flowers that fade quickly. Just as in the bat-and-ball problem, a plausible answer comes to mind immediately. Overriding it requires hard work—the insistent idea that “it’s true, it’s true!” makes it difficult to check the logic, and most people do not take the trouble to think through the problem.

This experiment has discouraging implications for reasoning in everyday life. It suggests that when people believe a conclusion is true, they are also very likely to believe arguments that appear to support it, even when these arguments are unsound. If System 1 is involved, the conclusion comes first and the arguments follow.

**

Intelligence is not only the ability to reason; it is also the ability to find relevant material in memory and to deploy attention when needed. Memory function is an attribute of System 1. However, everyone has the option of slowing down to conduct an active search of memory for all possibly relevant facts—just as they could slow down to check the intuitive answer in the bat-and-ball problem. The extent of deliberate checking and search is a characteristic of System 2, which varies among individuals.