FREAKONOMICSA Rogue EconomistExplores the HiddenSide of EverythingRevised and Expanded EditionSteven D. LevittandStephen J. Dubner

CONTENTSAN EXPLANATORY NOTEIn which the origins of this book are clarified.viiPREFACE TO THE REVISED AND EXPANDED EDITIONxiINTRODUCTION: The Hidden Side of Everything1In which the book’s central idea is set forth: namely, if morality represents how people would like the world to work, then economics showshow it actually does work.Why the conventional wisdom is so often wrong . . . How “experts”—from criminologists to real-estate agents to political scientists—bend thefacts . . . Why knowing what to measure, and how to measure it, is the keyto understanding modern life . . . What is “freakonomics,” anyway?1. What Do Schoolteachers and Sumo Wrestlers Havein Common?15In which we explore the beauty of incentives, as well as their darkside—cheating.

ContentsWho cheats? Just about everyone . . . How cheaters cheat, and how tocatch them . . . Stories from an Israeli day-care center . . . The sudden disappearance of seven million American children . . . Cheating schoolteachersin Chicago . . . Why cheating to lose is worse than cheating to win . . .Could sumo wrestling, the national sport of Japan, be corrupt? . . . Whatthe Bagel Man saw: mankind may be more honest than we think.2. How Is the Ku Klux Klan Like a Groupof Real-Estate Agents?49In which it is argued that nothing is more powerful than information,especially when its power is abused.Spilling the Ku Klux Klan’s secrets . . . Why experts of every kind are inthe perfect position to exploit you . . . The antidote to information abuse:the Internet . . . Why a new car is suddenly worth so much less the momentit leaves the lot . . . Breaking the real-estate agent code: what “well maintained” really means . . . Is Trent Lott more racist than the average WeakestLink contestant? . . . What do online daters lie about?3. Why Do Drug Dealers Still Live with Their Moms?79In which the conventional wisdom is often found to be a web of fabrication, self-interest, and convenience.Why experts routinely make up statistics; the invention of chronic halitosis . . . How to ask a good question . . . Sudhir Venkatesh’s long, strangetrip into the crack den . . . Life is a tournament . . . Why prostitutes earnmore than architects . . . What a drug dealer, a high-school quarterback,and an editorial assistant have in common . . . How the invention of crackcocaine mirrored the invention of nylon stockings . . . Was crack the worstthing to hit black Americans since Jim Crow?4. Where Have All the Criminals Gone?105In which the facts of crime are sorted out from the fictions.What Nicolae Ceauşescu learned—the hard way—about abortion . . .iv

ContentsWhy the 1960s was a great time to be a criminal . . . Think the roaring1990s economy put a crimp on crime? Think again . . . Why capital punishment doesn’t deter criminals . . . Do police actually lower crime rates?. . . Prisons, prisons everywhere . . . Seeing through the New York City police “miracle” . . . What is a gun, really? . . . Why early crack dealers werelike Microsoft millionaires and later crack dealers were like . . .The superpredator versus the senior citizen . . . Jane Roe, crime stopper:how the legalization of abortion changed everything.5. What Makes a Perfect Parent?133In which we ask, from a variety of angles, a pressing question: do parents really matter?The conversion of parenting from an art to a science . . . Why parentingexperts like to scare parents to death . . . Which is more dangerous: a gun ora swimming pool? . . . The economics of fear . . . Obsessive parents and thenature-nurture quagmire . . . Why a good school isn’t as good as you mightthink . . . The black-white test gap and “acting white” . . . Eight thingsthat make a child do better in school and eight that don’t.6. Perfect Parenting, Part II; or: Would aRoshanda by Any Other Name Smell as Sweet?163In which we weigh the importance of a parent’s first official act—naming the baby.A boy named Winner and his brother, Loser . . . The blackest namesand the whitest names . . . The segregation of culture: why Seinfeld nevermade the top fifty among black viewers . . . If you have a really bad name,should you just change it? . . . High-end names and low-end names (andhow one becomes the other) . . . Britney Spears: a symptom, not a cause . . .Is Aviva the next Madison? . . . What your parents were telling the worldwhen they gave you your name.v

ContentsEPILOGUE: Two Paths to HarvardIn which the dependability of data meets the randomness of life.189Bonus Material Added to the Revised and Expanded2006 Edition193Notes285Acknowledgments309IndexAbout the AuthorsCreditsCoverCopyrightAbout the Publishervi311

AN EXPLANATORY NOTEIn the summer of 2003, the New York Times Magazine sent Stephen J.Dubner, an author and journalist, to write a profile of Steven D.Levitt, a heralded young economist at the University of Chicago.Dubner, who was researching a book about the psychology ofmoney, had lately been interviewing many economists and found thatthey often spoke English as if it were a fourth or fifth language. Levitt,who had just won the John Bates Clark Medal (a sort of junior NobelPrize for young economists), had lately been interviewed by manyjournalists and found that their thinking wasn’t very . . . robust, as aneconomist might say.But Levitt decided that Dubner wasn’t a complete idiot. And Dubner found that Levitt wasn’t a human slide rule. The writer was dazzled by the inventiveness of the economist’s work and his knack forexplaining it. Despite Levitt’s elite credentials (Harvard undergrad, aPhD from MIT, a stack of awards), he approached economics in a notably unorthodox way. He seemed to look at the world not so much as

An Explanatory Notean academic but as a very smart and curious explorer—a documentary filmmaker, perhaps, or a forensic investigator or a bookie whosemarkets ranged from sports to crime to pop culture. He professed little interest in the sort of monetary issues that come to mind whenmost people think about economics; he practically blustered withself-effacement. “I just don’t know very much about the field of economics,” he told Dubner at one point, swiping the hair from his eyes.“I’m not good at math, I don’t know a lot of econometrics, and I alsodon’t know how to do theory. If you ask me about whether the stockmarket’s going to go up or down, if you ask me whether the economy’sgoing to grow or shrink, if you ask me whether deflation’s good orbad, if you ask me about taxes—I mean, it would be total fakery if Isaid I knew anything about any of those things.”What interested Levitt were the riddles of everyday life. His investigations were a feast for anyone wanting to know how the world really works. His singular attitude was evoked in Dubner’s resultingarticle:As Levitt sees it, economics is a science with excellent tools for gaining answers but a serious shortage of interesting questions. His particular gift is the ability to ask such questions. For instance: If drugdealers make so much money, why do they still live with theirmothers? Which is more dangerous, a gun or a swimming pool?What really caused crime rates to plunge during the past decade?Do real-estate agents have their clients’ best interests at heart? Whydo black parents give their children names that may hurt their career prospects? Do schoolteachers cheat to meet high-stakes testingstandards? Is sumo wrestling corrupt?Many people—including a fair number of his peers—mightnot recognize Levitt’s work as economics at all. But he has merelydistilled the so-called dismal science to its most primal aim: explaining how people get what they want. Unlike most academics,viii

An Explanatory Notehe is unafraid of using personal observations and curiosities; he isalso unafraid of anecdote and storytelling (although he is afraid ofcalculus). He is an intuitionist. He sifts through a pile of data tofind a story that no one else has found. He figures a way to measurean effect that veteran economists had declared unmeasurable. Hisabiding interests—though he says he has never trafficked in themhimself—are cheating, corruption, and crime.Levitt’s blazing curiosity also proved attractive to thousands ofNew York Times readers. He was beset by questions and queries, riddles and requests—from General Motors and the New York Yankeesand U.S. senators but also from prisoners and parents and a man whofor twenty years had kept precise data on his sales of bagels. A formerTour de France champion called Levitt to ask his help in proving thatthe current Tour is rife with doping; the Central Intelligence Agencywanted to know how Levitt might use data to catch money launderersand terrorists.What they were all responding to was the force of Levitt’s underlying belief: that the modern world, despite a surfeit of obfuscation,complication, and downright deceit, is not impenetrable, is not unknowable, and—if the right questions are asked—is even more intriguing than we think. All it takes is a new way of looking.In New York City, the publishers were telling Levitt he shouldwrite a book.“Write a book?” he said. “I don’t want to write a book.” He alreadyhad a million more riddles to solve than time to solve them. Nordid he think himself much of a writer. So he said that no, he wasn’tinterested—“unless,” he proposed, “maybe Dubner and I could do ittogether.”Collaboration isn’t for everyone. But the two of them—henceforthknown as the two of us—decided to talk things over to see if such abook might work. We decided it could. We hope you agree.ix

PREFACETO THE REVISED ANDEXPANDED EDITIONAs we were writing Freakonomics, we had grave doubts that anyonewould actually read it—and we certainly never envisioned the needfor this revised and expanded edition. But we are very happy, andgrateful, to have been wrong.So why bother with a revised edition?There are a few reasons. The first is that the world is a living,breathing, changing thing, whereas a book is not. Once a manuscriptis finished, it sits, dead in the water, for nearly a year until it is madeready by the publisher for its debut. This doesn’t pose much of a problem if you have written, say, a history of the Third Punic War. But because Freakonomics explores all sorts of modern real-world issues, andbecause the modern world tends to change quite fast, we have gonethrough the book and made a number of minor updates.Also, we made some mistakes. It was usually a reader who wouldbring a mistake to our attention, and we very much appreciate thisinput. Again, most of these changes are quite minor.

P re fa ce to t h e Rev i se d a n d E x pa n d e d Ed i t i o nThe most aggressively revised section of the book is the beginningof chapter 2, which tells the story of one man’s crusade against the KuKlux Klan. Several months after Freakonomics was first published, itwas brought to our attention that this man’s portrayal of his crusade,and of various other Klan matters, was considerably overstated. (For afuller explanation, see an essay called “Hoodwinked?” on page 231.)As unpleasant as it was to acknowledge this error, and to diminish thereputation of a man beloved in many quarters, we felt it was important to set straight the historical record.We have also futzed a bit with the architecture of the book. In theoriginal version, each chapter was preceded by an excerpt from theNew York Times Magazine profile that one of us (Dubner) wrote aboutthe other (Levitt), and which led to our collaboration on this book.Because some readers found these excerpts intrusive (and/or egomaniacal, and/or sycophantic), we have removed them, instead reprinting the complete Times profile in the back of this edition in thesection called “Bonus Material” (page 193). There, it can be easilyskipped over if one so chooses, or read in isolation.The further bonus material is what accounts for our havingcalled this edition “expanded” in addition to “revised.” Soon after theoriginal publication of Freakonomics, in April 2005, we began writinga monthly column for the New York Times Magazine. We have included in this edition several of these columns, on subjects rangingfrom voting behavior to dog poop to the economics of sexual preference.We have also included a variety of writings from our blog(—which, like this revised edition,was not planned. In the beginning, we built a website merely to perform archival and trafficking functions. We blogged reluctantly, tentatively, infrequently. But as the months went on, and as wediscovered an audience of people who had read Freakonomics andxii

P re fa ce to t h e Rev i se d a n d E x pa n d e d Ed i t i o nwere eager to bat its ideas back and forth, we took to it more enthusiastically.A blog, as it turns out, is an author’s perfect antidote for that sickening feeling of being dead in the water once a manuscript has beencompleted. Particularly for a book like this one, a book of ideas, thereis nothing more intoxicating than to be able to extend those ideas, tocontinue to refine and challenge and wrestle with them, even as theworld marches on.xiii

INTRODUCTION:The Hidden Side ofEverythingAnyone living in the United States in the early 1990s and paying evena whisper of attention to the nightly news or a daily paper could beforgiven for having been scared out of his skin.The culprit was crime. It had been rising relentlessly—a graphplotting the crime rate in any American city over recent decadeslooked like a ski slope in profile—and it seemed now to herald theend of the world as we knew it. Death by gunfire, intentional and otherwise, had become commonplace. So too had carjacking and crackdealing, robbery and rape. Violent crime was a gruesome, constantcompanion. And things were about to get even worse. Much worse.All the experts were saying so.The cause was the so-called superpredator. For a time, he waseverywhere. Glowering from the cover of newsweeklies. Swaggeringhis way through foot-thick government reports. He was a scrawny,big-city teenager with a cheap gun in his hand and nothing in hisheart but ruthlessness. There were thousands out there just like him,

F R E A KO N O M I CSwe were told, a generation of killers about to hurl the country intodeepest chaos.In 1995 the criminologist James Alan Fox wrote a report for theU.S. attorney general that grimly detailed the coming spike in murders by teenagers. Fox proposed optimistic and pessimistic scenarios.In the optimistic scenario, he believed, the rate of teen homicideswould rise another 15 percent over the next decade; in the pessimisticscenario, it would more than double. “The next crime wave will get sobad,” he said, “that it will make 1995 look like the good old days.”Other criminologists, political scientists, and similarly learnedforecasters laid out the same horrible future, as did President Clinton.“We know we’ve got about six years to turn this juvenile crime thingaround,” Clinton said, “or our country is going to be living withchaos. And my successors will not be giving speeches about the wonderful opportunities of the global economy; they’ll be trying to keepbody and soul together for people on the streets of these cities.” Thesmart money was plainly on the criminals.And then, instead of going up and up and up, crime began to fall.And fall and fall and fall some more. The crime drop was startling inseveral respects. It was ubiquitous, with every category of crime fallingin every part of the country. It was persistent, with incremental decreases year after year. And it was entirely unanticipated—especiallyby the very experts who had been predicting the opposite.The magnitude of the reversal was astounding. The teenage murder rate, instead of rising 100 percent or even 15 percent as JamesAlan Fox had warned, fell more than 50 percent within five years. By2000 the overall murder rate in the United States had dropped to itslowest level in thirty-five years. So had the rate of just about everyother sort of crime, from assault to car theft.Even though the experts had failed to anticipate the crime drop—which was in fact well under way even as they made their horrifying2

I n t ro d u c t i o n : Th e H i d d e n S i d e of Eve r y t h i n gpredictions—they now hurried to explain it. Most of their theoriessounded perfectly logical. It was the roaring 1990s economy, theysaid, that helped turn back crime. It was the proliferation of gun control laws, they said. It was the sort of innovative policing strategies putinto place in New York City, where murders would fall from 2,262 in1990 to 540 in 2005.These theories were not only logical; they were also encouraging,for they attributed the crime drop to specific and recent humaninitiatives. If it was gun control and clever police strategies and betterpaying jobs that quelled crime—well then, the power to stop criminals had been within our reach all along. As it would be the next time,God forbid, that crime got so bad.These theories made their way, seemingly without friction, fromthe experts’ mouths to journalists’ ears to the public’s mind. In shortcourse, they became conventional wisdom.There was only one problem: they weren’t true.There was another factor, meanwhile, that had greatly contributedto the massive crime drop of the 1990s. It had taken shape more thantwenty years earlier and concerned a young woman in Dallas namedNorma McCorvey.Like the proverbial butterfly that flaps its wings on one continentand eventually causes a hurricane on another, Norma McCorvey dramatically altered the course of events without intending to. All shehad wanted was an abortion. She was a poor, uneducated, unskilled,alcoholic, drug-using twenty-one-year-old woman who had alreadygiven up two children for adoption and now, in 1970, found herselfpregnant again. But in Texas, as in all but a few states at that time,abortion was illegal. McCorvey’s cause came to be adopted by peoplefar more powerful than she. They made her the lead plaintiff in aclass-action lawsuit seeking to legalize abortion. The defendant wasHenry Wade, the Dallas County district attorney. The case ultimately3

F R E A KO N O M I CSmade it to the U.S. Supreme Court, by which time McCorvey’s namehad been disguised as Jane Roe. On January 22, 1973, the court ruledin favor of Ms. Roe, allowing legalized abortion throughout theUnited States. By this time, of course, it was far too late for Ms.McCorvey/Roe to have her abortion. She had given birth and put thechild up for adoption. (Years later she would renounce her allegianceto legalized abortion and become a pro-life activist.)So how did Roe v. Wade help trigger, a generation later, the greatestcrime drop in recorded history?As far as crime is concerned, it turns out that not all children areborn equal. Not even close. Decades of studies have shown that achild born into an adverse family environment is far more likely thanother children to become a criminal. And the millions of womenmost likely to have an abortion in the wake of Roe v. Wade—poor, unmarried, and teenage mothers for whom illegal abortions had beentoo expensive or too hard to get—were often models of adversity.They were the very women whose children, if born, would have beenmuch more likely than average to become criminals. But because ofRoe v. Wade, these children weren’t being born. This powerful causewould have a drastic, distant effect: years later, just as these unbornchildren would have entered their criminal primes, the rate of crimebegan to plummet.It wasn’t gun control or a strong economy or new police strategiesthat finally blunted the American crime wave. It was, among otherfactors, the reality that the pool of potential criminals had dramatically shrunk.Now, as the crime-drop experts (the former crime doomsayers)spun their theories to the media, how many times did they cite legalized abortion as a cause?Zero.4

I n t ro d u c t i o n : Th e H i d d e n S i d e of Eve r y t h i n gIt is the quintessential blend of commerce and camaraderie: you hirea real-estate agent to sell your home.She sizes up its charms, snaps some pictures, sets the price, writes aseductive ad, shows the house aggressively, negotiates the offers, andsees the deal through to its end. Sure, it’s a lot of work, but she’s getting a nice cut. On the sale of a 300,000 house, a typical 6 percentagent fee yields 18,000. Eighteen thousand dollars, you say to yourself: that’s a lot of money. But you also tell yourself that you nevercould have sold the house for 300,000 on your own. The agent knewhow to—what’s that phrase she used?—“maximize the house’s value.”She got you top dollar, right?Right?A real-estate agent is a different breed of expert than a criminologist, but she is every bit the expert. That is, she knows her field far better than the layman on whose behalf she is acting. She is betterinformed about the house’s value, the state of the housing market,even the buyer’s frame of mind. You depend on her for this information. That, in fact, is why you hired an expert.As the world has grown more specialized, countless such expertshave made themselves similarly indispensable. Doctors, lawyers, contractors, stockbrokers, auto mechanics, mortgage brokers, financialplanners: they all enjoy a gigantic informational advantage. And theyuse that advantage to help you, the person who hired them, get exactly what you want for the best price.Right?It would be lovely to think so. But experts are human, and humansrespond to incentives. How any given expert treats you, therefore, willdepend on how that expert’s incentives are set up. Sometimes his incentives may work in your favor. For instance: a study of Californiaauto mechanics found they often passed up a small repair bill byletting failing cars pass emissions inspections—the reason being that5

F R E A KO N O M I CSlenient mechanics are rewarded with repeat business. But in a different case, an expert’s incentives may work against you. In a medicalstudy, it turned out that obstetricians in areas with declining birthrates are much more likely to perform cesarean-section deliveries thanobstetricians in growing areas—suggesting that, when business istough, doctors try to ring up more expensive procedures.It is one thing to muse about experts’ abusing their position andanother to prove it. The best way to do so would be to measure howan expert treats you versus how he performs the same service for himself. Unfortunately a surgeon doesn’t operate on himself. Nor is hismedical file a matter of public record; neither is an auto mechanic’s repair log for his own car.Real-estate sales, however, are a matter of public record. And realestate agents often do sell their own homes. A recent set of data covering the sale of nearly 100,000 houses in suburban Chicago shows thatmore than 3,000 of those houses were owned by the agents themselves.Before plunging into the data, it helps to ask a question: what isthe real-estate agent’s incentive when she is selling her own home?Simple: to make the best deal possible. Presumably this is also your incentive when you are selling your home. And so your incentive andthe real-estate agent’s incentive would seem to be nicely aligned. Hercommission, after all, is based on the sale price.But as incentives go, commissions are tricky. First of all, a 6 percent real-estate commission is typically split between the seller’s agentand the buyer’s. Each agent then kicks back roughly half of her take tothe agency. Which means that only 1.5 percent of the purchase pricegoes directly into your agent’s pocket.So on the sale of your 300,000 house, her personal take of the 18,000 commission is 4,500. Still not bad, you say. But what if thehouse was actually worth more than 300,000? What if, with a little6

I n t ro d u c t i o n : Th e H i d d e n S i d e of Eve r y t h i n gmore effort and patience and a few more newspaper ads, she couldhave sold it for 310,000? After the commission, that puts an additional 9,400 in your pocket. But the agent’s additional share—herpersonal 1.5 percent of the extra 10,000—is a mere 150. If youearn 9,400 while she earns only 150, maybe your incentives aren’taligned after all. (Especially when she’s the one paying for the ads anddoing all the work.) Is the agent willing to put out all that extra time,money, and energy for just 150?There’s one way to find out: measure the difference between thesales data for houses that belong to real-estate agents themselves andthe houses they sold on behalf of clients. Using the data from the salesof those 100,000 Chicago homes, and controlling for any number ofvariables—location, age and quality of the house, aesthetics, whetheror not the property was an investment, and so on—it turns out that areal-estate agent keeps her own home on the market an average of tendays longer and sells it for an extra 3-plus percent, or 10,000 on a 300,000 house. When she sells her own house, an agent holds outfor the best offer; when she sells yours, she encourages you to take thefirst decent offer that comes along. Like a stockbroker churning commissions, she wants to make deals and make them fast. Why not? Hershare of a better offer— 150—is too puny an incentive to encourageher to do otherwise.Of all the truisms about politics, one is held to be truer than the rest:money buys elections. Arnold Schwarzenegger, Michael Bloomberg,Jon Corzine—these are but a few recent, dramatic examples of thetruism at work. (Disregard for a moment the contrary examples ofSteve Forbes, Michael Huffington, and especially Thomas Golisano,who over the course of three gubernatorial elections in New Yorkspent 93 million of his own money and won 4 percent, 8 percent,7

F R E A KO N O M I CSand 14 percent, respectively, of the vote.) Most people would agreethat money has an undue influence on elections and that far toomuch money is spent on political campaigns.Indeed, election data show it is true that the candidate who spendsmore money in a campaign usually wins. But is money the cause of thevictory?It might seem logical to think so, much as it might have seemedlogical that a booming 1990s economy helped reduce crime. But justbecause two things are correlated does not mean that one causes theother. A correlation simply means that a relationship exists betweentwo factors—let’s call them X and Y—but it tells you nothing aboutthe direction of that relationship. It’s possible that X causes Y; it’s alsopossible that Y causes X; and it may be that X and Y are both beingcaused by some other factor, Z.Think about this correlation: cities with a lot of murders also tendto have a lot of police officers. Consider now the police/murder correlation in a pair of real cities. Denver and Washington, D.C., haveabout the same population—but Washington has nearly three timesas many police as Denver, and it also has eight times the number ofmurders. Unless you have more information, however, it’s hard to saywhat’s causing what. Someone who didn’t know better might contemplate these figures and conclude that it is all those extra police inWashington who are causing the extra murders. Such wayward thinking, which has a long history, generally provokes a wayward response.Consider the folktale of the czar who learned that the most diseaseridden province in his empire was also the province with the mostdoctors. His solution? He promptly ordered all the doctors shot dead.Now, returning to the issue of campaign spending: in order to figure out the relationship between money and elections, it helps to consider the incentives at play in campaign finance. Let’s say you are thekind of person who might contribute 1,000 to a candidate. Chances8

I n t ro d u c t i o n : Th e H i d d e n S i d e of Eve r y t h i n gare you’ll give the money in one of two situations: a close race, inwhich you think the money will influence the outcome; or a campaign in which one candidate is a sure winner and you would like tobask in reflected glory or receive some future in-kind consideration.The one candidate you won’t contribute to is a sure loser. ( Just ask anypresidential hopeful who bombs in Iowa and New Hampshire.) Sofront-runners and incumbents raise a lot more money than longshots. And what about spending that money? Incumbents and frontrunners obviously have more cash, but they only spend a lot of itwhen they stand a legitimate chance of losing; otherwise, why dipinto a war chest that might be more useful later on, when a more formidable opponent appears?Now picture two candidates, one intrinsically appealing and theother not so. The appealing candidate raises much more money andwins easily. But was it the money that won him the votes, or was it hisappeal that won the votes and the money?That’s a crucial question but a very hard one to answer. Voter appeal, after all, isn’t easy to quantify. How can it be measured?It can’t, really—except in one special case. The key is to measure acandidate against . . . himself. That is, Candidate A today is likely tobe similar to Candidate A two or four years hence. The same could besaid for Candidate B. If only Candidate A ran against Candidate B intwo consecutive elections but in each case spent different amounts ofmoney. Then, with the candidates’ appeal more or less constant, wecould measure the money’s impact.As it turns out, the same two candidates run against each other inconsecutive elections all the time—indeed, in nearly a thousand U.S.congressional races since 1972. What do the numbers have to sayabout such cases?Here’s the surprise: the amount of money spent by the candidateshardly matters at all. A winning candidate can cut his spending in half9

F R E A KO N O M I CSand lose only 1 percent of the vote. Meanwhile, a losing candidatewho doubles his spending can expect to shift the vote in his favor

cause Freakonomics explores all sorts of modern real-world issues, and because the modern world tends to change quite fast, we have gone through the book and made a number of minor updates. Also, we made some mistakes. It was usually a reader who would bring a mistake to our attention, and we very much appreciate this input.