What happened was remarkable. The global evidence of our previous failure should have shaken our confidence in our judgments of the candidates, but it did not. It should also have caused us to moderate our predictions, but it did not. We knew as a general fact that our predictions were little better than random guesses, but we continued to feel and act as if each of our specific predictions was valid. I was reminded of the Muller-Lyer illusion, in which we know the lines are of equal length yet still see them as being different. I was so struck by the analogy that I coined a term for our experience: the illusion of validity.

I had discovered my first cognitive illusion.

Decades later, I can see many of the central themes of my thinking-and of this book-in that old story. Our expectations for the soldiers' future performance were a clear instance of substitution, and of the representativeness heuristic in particular. Having observed one hour of a soldier's behavior in an artificial situation, we felt we knew how well he would face the challenges of officer training and of leadership in combat. Our predictions were completely nonregressive-we had no reservations about predicting failure or outstanding success from weak evidence. This was a clear instance of WYSIATI. We had compelling impressions of the behavior we observed and no good way to represent our ignorance of the factors that would eventually determine how well the candidate would perform as an officer.

Looking back, the most striking part of the story is that our knowledge of the general rule-that we could not predict-had no effect on our confidence in individual cases. I can see now that our reaction was similar to that of Nisbett and Borgida's students when they were told that most people did not help a stranger suffering a seizure. They certainly believed the statistics they were shown, but the base rates did not influence their judgment of whether an individual they saw on the video would or would not help a stranger. Just as Nisbett and Borgida showed, people are often reluctant to infer the particular from the general.

Subjective confidence in a judgment is not a reasoned evaluation of the probability that this judgment is correct. Confidence is a feeling, which reflects the coherence of the information and the cognitive ease of processing it. It is wise to take admissions of uncertainty seriously, but declarations of high confidence mainly tell you that an individual has constructed a coherent story in his mind, not necessarily that the story is true.The Illusion of Stock-Picking SkillIn 1984, Amos and I and our friend Richard Thaler visited a Wall Street firm. Our host, a senior investment manager, had invited us to discuss the role of judgment biases in investing. I knew so little about finance that I did not even know what to ask him, but I remember one exchange. "When you sell a stock," d nI asked, "who buys it?" He answered with a wave in the vague direction of the window, indicating that he expected the buyer to be someone else very much like him. That was odd: What made one person buy and the other sell? What did the sellers think they knew that the buyers did not?

Since then, my questions about the stock market have hardened into a larger puzzle: a major industry appears to be built largely on an illusion of skill. Billions of shares are traded every day, with many people buying each stock and others selling it to them. It is not unusual for more than 100 million shares of a single stock to change hands in one day. Most of the buyers and sellers know that they have the same information; they exchange the stocks primarily because they have different opinions. The buyers think the price is too low and likely to rise, while the sellers think the price is high and likely to drop. The puzzle is why buyers and sellers alike think that the current price is wrong. What makes them believe they know more about what the price should be than the market does? For most of them, that belief is an illusion.

In its broad outlines, the standard theory of how the stock market works is accepted by all the participants in the industry. Everybody in the investment business has read Burton Malkiel's wonderful book A Random Walk Down Wall Street. Malkiel's central idea is that a stock's price incorporates all the available knowledge about the value of the company and the best predictions about the future of the stock. If some people believe that the price of a stock will be higher tomorrow, they will buy more of it today. This, in turn, will cause its price to rise. If all assets in a market are correctly priced, no one can expect either to gain or to lose by trading. Perfect prices leave no scope for cleverness, but they also protect fools from their own folly. We now know, however, that the theory is not quite right. Many individual investors lose consistently by trading, an achievement that a dart-throwing chimp could not match. The first demonstration of this startling conclusion was collected by Terry Odean, a finance professor at UC Berkeley who was once my student.

Odean began by studying the trading records of 10,000 brokerage accounts of individual investors spanning a seven-year period. He was able to analyze every transaction the investors executed through that firm, nearly 163,000 trades. This rich set of data allowed Odean to identify all instances in which an investor sold some of his holdings in one stock and soon afterward bought another stock. By these actions the investor revealed that he (most of the investors were men) had a definite idea about the future of the two stocks: he expected the stock that he chose to buy to do better than the stock he chose to sell.

To determine whether those ideas were well founded, Odean compared the returns of the stock the investor had sold and the stock he had bought in its place, over the course of one year after the transaction. The results were unequivocally bad. On average, the shares that individual traders sold did better than those they bought, by a very substantial margin: 3.2 percentage points per year, above and beyond the significant costs of executing the two trades.

It is important to remember that this is a statement about averages: some individuals did much better, others did much worse. However, it is clear that for the large majority of individual investors, taking a shower and doing nothing would have been a better policy than implementing the ideas that came to their minds. Later research by Odean and his colleague Brad Barber supported this conclusion. In a paper titled "Trading Is Hazardous to Yourt-t Wealth," they showed that, on average, the most active traders had the poorest results, while the investors who traded the least earned the highest returns. In another paper, titled "Boys Will Be Boys," they showed that men acted on their useless ideas significantly more often than women, and that as a result women achieved better investment results than men.

Of course, there is always someone on the other side of each transaction; in general, these are financial institutions and professional investors, who are ready to take advantage of the mistakes that individual traders make in choosing a stock to sell and another stock to buy. Further research by Barber and Odean has shed light on these mistakes. Individual investors like to lock in their gains by selling "winners," stocks that have appreciated since they were purchased, and they hang on to their losers. Unfortunately for them, recent winners tend to do better than recent losers in the short run, so individuals sell the wrong stocks. They also buy the wrong stocks. Individual investors predictably flock to companies that draw their attention because they are in the news. Professional investors are more selective in responding to news. These findings provide some justification for the label of "smart money" that finance professionals apply to themselves.

Although professionals are able to extract a considerable amount of wealth from amateurs, few stock pickers, if any, have the skill needed to beat the market consistently, year after year. Professional investors, including fund managers, fail a basic test of skill: persistent achievement. The diagnostic for the existence of any skill is the consistency of individual differences in achievement. The logic is simple: if individual differences in any one year are due entirely to luck, the ranking of investors and funds will vary erratically and the year-to-year correlation will be zero. Where there is skill, however, the rankings will be more stable. The persistence of individual differences is the measure by which we confirm the existence of skill among golfers, car salespeople, orthodontists, or speedy toll collectors on the turnpike.

Mutual funds are run by highly experienced and hardworking professionals who buy and sell stocks to achieve the best possible results for their clients. Nevertheless, the evidence from more than fifty years of research is conclusive: for a large majority of fund managers, the selection of stocks is more like rolling dice than like playing poker. Typically at least two out of every three mutual funds underperform the overall market in any given year.

More important, the year-to-year correlation between the outcomes of mutual funds is very small, barely higher than zero. The successful funds in any given year are mostly lucky; they have a good roll of the dice. There is general agreement among researchers that nearly all stock pickers, whether they know it or not-and few of them do-are playing a game of chance. The subjective experience of traders is that they are making sensible educated guesses in a situation of great uncertainty. In highly efficient markets, however, educated guesses are no more accurate than blind guesses.

Some years ago I had an unusual opportunity to examine the illusion of financial skill up close. I had been invited to speak to a group of investment advisers in a firm that provided financial advice and other services to very wealthy clients. I asked for some data to prepare my presentation and was granted a small treasure: a spreadsheet summarizing the investment outcomes of some twenty-five anonymous wealth advisers, for each of eight consecutive years. Each adviser's scoof re for each year was his (most of them were men) main determinant of his year-end bonus. It was a simple matter to rank the advisers by their performance in each year and to determine whether there were persistent differences in skill among them and whether the same advisers consistently achieved better returns for their clients year after year.

To answer the question, I computed correlation coefficients between the rankings in each pair of years: year 1 with year 2, year 1 with year 3, and so on up through year 7 with year 8. That yielded 28 correlation coefficients, one for each pair of years. I knew the theory and was prepared to find weak evidence of persistence of skill. Still, I was surprised to find that the average of the 28 correlations was .01. In other words, zero. The consistent correlations that would indicate differences in skill were not to be found. The results resembled what you would expect from a dice-rolling contest, not a game of skill.

No one in the firm seemed to be aware of the nature of the game that its stock pickers were playing. The advisers themselves felt they were competent professionals doing a serious job, and their superiors agreed. On the evening before the seminar, Richard Thaler and I had dinner with some of the top executives of the firm, the people who decide on the size of bonuses. We asked them to guess the year-to-year correlation in the rankings of individual advisers. They thought they knew what was coming and smiled as they said "not very high" or "performance certainly fluctuates." It quickly became clear, however, that no one expected the average correlation to be zero.

Our message to the executives was that, at least when it came to building portfolios, the firm was rewarding luck as if it were skill. This should have been shocking news to them, but it was not. There was no sign that they disbelieved us. How could they? After all, we had analyzed their own results, and they were sophisticated enough to see the implications, which we politely refrained from spelling out. We all went on calmly with our dinner, and I have no doubt that both our findings and their implications were quickly swept under the rug and that life in the firm went on just as before. The illusion of skill is not only an individual aberration; it is deeply ingrained in the culture of the industry. Facts that challenge such basic assumptions-and thereby threaten people's livelihood and self-esteem-are simply not absorbed. The mind does not digest them. This is particularly true of statistical studies of performance, which provide base-rate information that people generally ignore when it clashes with their personal impressions from experience.

The next morning, we reported the findings to the advisers, and their response was equally bland. Their own experience of exercising careful judgment on complex problems was far more compelling to them than an obscure statistical fact. When we were done, one of the executives I had dined with the previous evening drove me to the airport. He told me, with a trace of defensiveness, "I have done very well for the firm and no one can take that away from me." I smiled and said nothing. But I thought, "Well, I took it away from you this morning. If your success was due mostly to chance, how much credit are you entitled to take for it?"What Supports the Illusions of Skill and Validity?Cognitive illusions can be more stubborn than visual illusions. What you learned about the Muller-Lyer illusion did not change the way you see the lines, but it changed your behavior. You now know that you cannot trust your impression of the lengllith of lines that have fins appended to them, and you also know that in the standard Muller-Lyer display you cannot trust what you see. When asked about the length of the lines, you will report your informed belief, not the illusion that you continue to see. In contrast, when my colleagues and I in the army learned that our leadership assessment tests had low validity, we accepted that fact intellectually, but it had no impact on either our feelings or our subsequent actions. The response we encountered in the financial firm was even more extreme. I am convinced that the message that Thaler and I delivered to both the executives and the portfolio managers was instantly put away in a dark corner of memory where it would cause no damage.

Why do investors, both amateur and professional, stubbornly believe that they can do better than the market, contrary to an economic theory that most of them accept, and contrary to what they could learn from a dispassionate evaluation of their personal experience? Many of the themes of previous chapters come up again in the explanation of the prevalence and persistence of an illusion of skill in the financial world.

The most potent psychological cause of the illusion is certainly that the people who pick stocks are exercising high-level skills. They consult economic data and forecasts, they examine income statements and balance sheets, they evaluate the quality of top management, and they assess the competition. All this is serious work that requires extensive training, and the people who do it have the immediate (and valid) experience of using these skills. Unfortunately, skill in evaluating the business prospects of a firm is not sufficient for successful stock trading, where the key question is whether the information about the firm is already incorporated in the price of its stock. Traders apparently lack the skill to answer this crucial question, but they appear to be ignorant of their ignorance. As I had discovered from watching cadets on the obstacle field, subjective confidence of traders is a feeling, not a judgment. Our understanding of cognitive ease and associative coherence locates subjective confidence firmly in System 1.

Finally, the illusions of validity and skill are supported by a powerful professional culture. We know that people can maintain an unshakable faith in any proposition, however absurd, when they are sustained by a community of like-minded believers. Given the professional culture of the financial community, it is not surprising that large numbers of individuals in that world believe themselves to be among the chosen few who can do what they believe others cannot.The Illusions of PunditsThe idea that the future is unpredictable is undermined every day by the ease with which the past is explained. As Nassim Taleb pointed out in The Black Swan, our tendency to construct and believe coherent narratives of the past makes it difficult for us to accept the limits of our forecasting ability. Everything makes sense in hindsight, a fact that financial pundits exploit every evening as they offer convincing accounts of the day's events. And we cannot suppress the powerful intuition that what makes sense in hindsight today was predictable yesterday. The illusion that we understand the past fosters overconfidence in our ability to predict the future.

The often-used image of the "march of history" implies order and direction. Marches, unlike strolls or walks, are not random. We think that we should be able to explain the past by focusing on either large social movements and cultural and technological developments or the intentions and abilities of a few g coreat men. The idea that large historical events are determined by luck is profoundly shocking, although it is demonstrably true. It is hard to think of the history of the twentieth century, including its large social movements, without bringing in the role of Hitler, Stalin, and Mao Zedong. But there was a moment in time, just before an egg was fertilized, when there was a fifty-fifty chance that the embryo that became Hitler could have been a female. Compounding the three events, there was a probability of one-eighth of a twentieth century without any of the three great villains and it is impossible to argue that history would have been roughly the same in their absence. The fertilization of these three eggs had momentous consequences, and it makes a joke of the idea that long-term developments are predictable.

Yet the illusion of valid prediction remains intact, a fact that is exploited by people whose business is prediction-not only financial experts but pundits in business and politics, too. Television and radio stations and newspapers have their panels of experts whose job it is to comment on the recent past and foretell the future. Viewers and readers have the impression that they are receiving information that is somehow privileged, or at least extremely insightful. And there is no doubt that the pundits and their promoters genuinely believe they are offering such information. Philip Tetlock, a psychologist at the University of Pennsylvania, explained these so-called expert predictions in a landmark twenty-year study, which he published in his 2005 book Expert Political Judgment: How Good Is It? How Can We Know? Tetlock has set the terms for any future discussion of this topic.

Tetlock interviewed 284 people who made their living "commenting or offering advice on political and economic trends." He asked them to assess the probabilities that certain events would occur in the not too distant future, both in areas of the world in which they specialized and in regions about which they had less knowledge. Would Gorbachev be ousted in a coup? Would the United States go to war in the Persian Gulf? Which country would become the next big emerging market? In all, Tetlock gathered more than 80,000 predictions. He also asked the experts how they reached their conclusions, how they reacted when proved wrong, and how they evaluated evidence that did not support their positions. Respondents were asked to rate the probabilities of three alternative outcomes in every case: the persistence of the status quo, more of something such as political freedom or economic growth, or less of that thing.

The results were devastating. The experts performed worse than they would have if they had simply assigned equal probabilities to each of the three potential outcomes. In other words, people who spend their time, and earn their living, studying a particular topic produce poorer predictions than dart-throwing monkeys who would have distributed their choices evenly over the options. Even in the region they knew best, experts were not significantly better than nonspecialists.

Those who know more forecast very slightly better than those who know less. But those with the most knowledge are often less reliable. The reason is that the person who acquires more knowledge develops an enhanced illusion of her skill and becomes unrealistically overconfident. "We reach the point of diminishing marginal predictive returns for knowledge disconcertingly quickly," Tetlock writes. "In this age of academic hyperspecialization, there is no reason for supposing that contributors to top journals-distinguished political scientists, area study specialists, economists, and so on-are any better than journalists or attentive readers of The New York Times in 'readingoul8217; emerging situations." The more famous the forecaster, Tetlock discovered, the more flamboyant the forecasts. "Experts in demand," he writes, "were more overconfident than their colleagues who eked out existences far from the limelight."

Tetlock also found that experts resisted admitting that they had been wrong, and when they were compelled to admit error, they had a large collection of excuses: they had been wrong only in their timing, an unforeseeable event had intervened, or they had been wrong but for the right reasons. Experts are just human in the end. They are dazzled by their own brilliance and hate to be wrong. Experts are led astray not by what they believe, but by how they think, says Tetlock. He uses the terminology from Isaiah Berlin's essay on Tolstoy, "The Hedgehog and the Fox." Hedgehogs "know one big thing" and have a theory about the world; they account for particular events within a coherent framework, bristle with impatience toward those who don't see things their way, and are confident in their forecasts. They are also especially reluctant to admit error. For hedgehogs, a failed prediction is almost always "off only on timing" or "very nearly right." They are opinionated and clear, which is exactly what television producers love to see on programs. Two hedgehogs on different sides of an issue, each attacking the idiotic ideas of the adversary, make for a good show.

Foxes, by contrast, are complex thinkers. They don't believe that one big thing drives the march of history (for example, they are unlikely to accept the view that Ronald Reagan single-handedly ended the cold war by standing tall against the Soviet Union). Instead the foxes recognize that reality emerges from the interactions of many different agents and forces, including blind luck, often producing large and unpredictable outcomes. It was the foxes who scored best in Tetlock's study, although their performance was still very poor. They are less likely than hedgehogs to be invited to participate in television debates.It is Not the Experts' Fault-The World is DifficultThe main point of this chapter is not that people who attempt to predict the future make many errors; that goes without saying. The first lesson is that errors of prediction are inevitable because the world is unpredictable. The second is that high subjective confidence is not to be trusted as an indicator of accuracy (low confidence could be more informative).

Short-term trends can be forecast, and behavior and achievements can be predicted with fair accuracy from previous behaviors and achievements. But we should not expect performance in officer training and in combat to be predictable from behavior on an obstacle field-behavior both on the test and in the real world is determined by many factors that are specific to the particular situation. Remove one highly assertive member from a group of eight candidates and everyone else's personalities will appear to change. Let a sniper's bullet move by a few centimeters and the performance of an officer will be transformed. I do not deny the validity of all tests-if a test predicts an important outcome with a validity of .20 or .30, the test should be used. But you should not expect more. You should expect little or nothing from Wall Street stock pickers who hope to be more accurate than the market in predicting the future of prices. And you should not expect much from pundits making long-term forecasts-although they may have valuable insights into the near future. The line that separates the possibly predictable future from the unpredictable distant future is in yet to be drawn.Sp

eaking of Illusory Skill

"He knows that the record indicates that the development of this illness is mostly unpredictable. How can he be so confident in this case? Sounds like an illusion of validity."

"She has a coherent story that explains all she knows, and the coherence makes her feel good."

"What makes him believe that he is smarter than the market? Is this an illusion of skill?"

"She is a hedgehog. She has a theory that explains everything, and it gives her the illusion that she understands the world."

"The question is not whether these experts are well trained. It is whether their world is predictable."

Intuitions vs. Formulas Paul Meehl was a strange and wonderful character, and one of the most versatile psychologists of the twentieth century. Among the departments in which he had faculty appointments at the University of Minnesota were psychology, law, psychiatry, neurology, and philosophy. He also wrote on religion, political science, and learning in rats. A statistically sophisticated researcher and a fierce critic of empty claims in clinical psychology, Meehl was also a practicing psychoanalyst. He wrote thoughtful essays on the philosophical foundations of psychological research that I almost memorized while I was a graduate student. I never met Meehl, but he was one of my heroes from the time I read his Clinical vs. Statistical Prediction: A Theoretical Analysis and a Review of the Evidence.

In the slim volume that he later called "my disturbing little book," Meehl reviewed the results of 20 studies that had analyzed whether clinical predictions based on the subjective impressions of trained professionals were more accurate than statistical predictions made by combining a few scores or ratings according to a rule. In a typical study, trained counselors predicted the grades of freshmen at the end of the school year. The counselors interviewed each student for forty-five minutes. They also had access to high school grades, several aptitude tests, and a four-page personal statement. The statistical algorithm used only a fraction of this information: high school grades and one aptitude test. Nevertheless, the formula was more accurate than 11 of the 14 counselors. Meehl reported generally similar results across a variety of other forecast outcomes, including violations of parole, success in pilot training, and criminal recidivism.

Not surprisingly, Meehl's book provoked shock and disbelief among clinical psychologists, and the controversy it started has engendered a stream of research that is still flowing today, more than fifty yephy diars after its publication. The number of studies reporting comparisons of clinical and statistical predictions has increased to roughly two hundred, but the score in the contest between algorithms and humans has not changed. About 60% of the studies have shown significantly better accuracy for the algorithms. The other comparisons scored a draw in accuracy, but a tie is tantamount to a win for the statistical rules, which are normally much less expensive to use than expert judgment. No exception has been convincingly documented.

The range of predicted outcomes has expanded to cover medical variables such as the longevity of cancer patients, the length of hospital stays, the diagnosis of cardiac disease, and the susceptibility of babies to sudden infant death syndrome; economic measures such as the prospects of success for new businesses, the evaluation of credit risks by banks, and the future career satisfaction of workers; questions of interest to government agencies, including assessments of the suitability of foster parents, the odds of recidivism among juvenile offenders, and the likelihood of other forms of violent behavior; and miscellaneous outcomes such as the evaluation of scientific presentations, the winners of football games, and the future prices of Bordeaux wine. Each of these domains entails a significant degree of uncertainty and unpredictability. We describe them as "low-validity environments." In every case, the accuracy of experts was matched or exceeded by a simple algorithm.

As Meehl pointed out with justified pride thirty years after the publication of his book, "There is no controversy in social science which shows such a large body of qualitatively diverse studies coming out so uniformly in the same direction as this one."

The Princeton economist and wine lover Orley Ashenfelter has offered a compelling demonstration of the power of simple statistics to outdo world-renowned experts. Ashenfelter wanted to predict the future value of fine Bordeaux wines from information available in the year they are made. The question is important because fine wines take years to reach their peak quality, and the prices of mature wines from the same vineyard vary dramatically across different vintages; bottles filled only twelve months apart can differ in value by a factor of 10 or more. An ability to forecast future prices is of substantial value, because investors buy wine, like art, in the anticipation that its value will appreciate.

It is generally agreed that the effect of vintage can be due only to variations in the weather during the grape-growing season. The best wines are produced when the summer is warm and dry, which makes the Bordeaux wine industry a likely beneficiary of global warming. The industry is also helped by wet springs, which increase quantity without much effect on quality. Ashenfelter converted that conventional knowledge into a statistical formula that predicts the price of a wine-for a particular property and at a particular age-by three features of the weather: the average temperature over the summer growing season, the amount of rain at harvest-time, and the total rainfall during the previous winter. His formula provides accurate price forecasts years and even decades into the future. Indeed, his formula forecasts future prices much more accurately than the current prices of young wines do. This new example of a "Meehl pattern" challenges the abilities of the experts whose opinions help shape the early price. It also challenges economic theory, according to which prices should reflect all the available information, including the weather. Ashenfelter's formula is extremely accurate-the correlation between his predictions and actual prices is above .90.

Why are experts e yinferior to algorithms? One reason, which Meehl suspected, is that experts try to be clever, think outside the box, and consider complex combinations of features in making their predictions. Complexity may work in the odd case, but more often than not it reduces validity. Simple combinations of features are better. Several studies have shown that human decision makers are inferior to a prediction formula even when they are given the score suggested by the formula! They feel that they can overrule the formula because they have additional information about the case, but they are wrong more often than not. According to Meehl, there are few circumstances under which it is a good idea to substitute judgment for a formula. In a famous thought experiment, he described a formula that predicts whether a particular person will go to the movies tonight and noted that it is proper to disregard the formula if information is received that the individual broke a leg today. The name "broken-leg rule" has stuck. The point, of course, is that broken legs are very rare-as well as decisive.

Another reason for the inferiority of expert judgment is that humans are incorrigibly inconsistent in making summary judgments of complex information. When asked to evaluate the same information twice, they frequently give different answers. The extent of the inconsistency is often a matter of real concern. Experienced radiologists who evaluate chest X-rays as "normal" or "abnormal" contradict themselves 20% of the time when they see the same picture on separate occasions. A study of 101 independent auditors who were asked to evaluate the reliability of internal corporate audits revealed a similar degree of inconsistency. A review of 41 separate studies of the reliability of judgments made by auditors, pathologists, psychologists, organizational managers, and other professionals suggests that this level of inconsistency is typical, even when a case is reevaluated within a few minutes. Unreliable judgments cannot be valid predictors of anything.

The widespread inconsistency is probably due to the extreme context dependency of System 1. We know from studies of priming that unnoticed stimuli in our environment have a substantial influence on our thoughts and actions. These influences fluctuate from moment to moment. The brief pleasure of a cool breeze on a hot day may make you slightly more positive and optimistic about whatever you are evaluating at the time. The prospects of a convict being granted parole may change significantly during the time that elapses between successive food breaks in the parole judges' schedule. Because you have little direct knowledge of what goes on in your mind, you will never know that you might have made a different judgment or reached a different decision under very slightly different circumstances. Formulas do not suffer from such problems. Given the same input, they always return the same answer. When predictability is poor-which it is in most of the studies reviewed by Meehl and his followers-inconsistency is destructive of any predictive validity.

The research suggests a surprising conclusion: to maximize predictive accuracy, final decisions should be left to formulas, especially in low-validity environments. In admission decisions for medical schools, for example, the final determination is often made by the faculty members who interview the candidate. The evidence is fragmentary, but there are solid grounds for a conjecture: conducting an interview is likely to diminish the accuracy of a selection procedure, if the interviewers also make the final admission decisions. Because interviewers are overconfident in their intuitions, they will assign too much weight to their personal impressions and too little weight to other sources of information, lowering validity. Similarly, the experts who evaluate the quas plity of immature wine to predict its future have a source of information that almost certainly makes things worse rather than better: they can taste the wine. In addition, of course, even if they have a good understanding of the effects of the weather on wine quality, they will not be able to maintain the consistency of a formula.

The most important development in the field since Meehl's original work is Robyn Dawes's famous article "The Robust Beauty of Improper Linear Models in Decision Making." The dominant statistical practice in the social sciences is to assign weights to the different predictors by following an algorithm, called multiple regression, that is now built into conventional software. The logic of multiple regression is unassailable: it finds the optimal formula for putting together a weighted combination of the predictors. However, Dawes observed that the complex statistical algorithm adds little or no value. One can do just as well by selecting a set of scores that have some validity for predicting the outcome and adjusting the values to make them comparable (by using standard scores or ranks). A formula that combines these predictors with equal weights is likely to be just as accurate in predicting new cases as the multiple-regression formula that was optimal in the original sample. More recent research went further: formulas that assign equal weights to all the predictors are often superior, because they are not affected by accidents of sampling.

The surprising success of equal-weighting schemes has an important practical implication: it is possible to develop useful algorithms without any prior statistical research. Simple equally weighted formulas based on existing statistics or on common sense are often very good predictors of significant outcomes. In a memorable example, Dawes showed that marital stability is well predicted by a formula: frequency of lovemaking minus frequency of quarrels

You don't want your result to be a negative number.