http://online.wsj.com/articles/how-to-trick-the-guilty-and-gullible-into-revealing-themselves-1399680248

King Solomon built the First Temple in Jerusalem and was known throughout the land for his wisdom.

David Lee Roth

fronted the rock band Van Halen and was known throughout the land for his prima-donna excess.

What could these two men possibly have had in common? Well, both were Jewish; both got a lot of girls; and both wrote the lyrics to a No. 1 pop song ("Jump" in Mr. Roth's case and, in Solomon's, several verses from Ecclesiastes that appeared in the Byrds' 1965 hit "Turn! Turn! Turn"). But most improbably, they both dabbled in game theory, as seen in classic stories about their clever strategic thinking.

Early in Solomon's reign, two women came to him with a dilemma. They lived together—they were prostitutes by trade—and within the space of a few days had each given birth to a baby boy. One child had died, and now both women claimed the surviving baby as her own.

"Fetch me a sword," Solomon said. "Divide the living child in two, and give half to the one, and half to the other."

One woman embraced his solution. But the other begged Solomon not to hurt the baby and give it to her rival instead. Solomon promptly ruled in her favor, figuring that the real mother would rather give up her child than see it die.

GAME THEORISTS: David Lee Roth stipulated 'ABSOLUTELY NO' brown M&M's in Van Halen's touring contract. Redferns/Getty Images

As clever as that was, David Lee Roth may have been a bit cleverer—according, at least, to Mr. Roth himself. Here is how he tells the story in a Vimeo video. By the early 1980s, Van Halen had become one of the biggest rock bands in history. Their touring contract carried a 53-page rider that laid out technical and security specs as well as food and beverage requirements. The "Munchies" section demanded potato chips, nuts, pretzels and "M&M's (WARNING: ABSOLUTELY NO BROWN ONES)."

When the M&M clause found its way into the press, it seemed like a typical case of rock-star excess, of the band "being abusive of others simply because we could," Mr. Roth said. But, he explained, "the reality is quite different."

Van Halen's live show boasted a colossal stage, booming audio and spectacular lighting. All this required a great deal of structural support, electrical power and the like. Thus the 53-page rider, which gave point-by-point instructions to ensure that no one got killed by a collapsing stage or a short-circuiting light tower. But how could Van Halen be sure that the local promoter in each city had read the whole thing and done everything properly?

Cue the brown M&M's. As Roth tells it, he would immediately go backstage to check out the bowl of M&M's. If he saw brown ones, he knew the promoter hadn't read the rider carefully—and that "we had to do a serious line check" to make sure that the more important details hadn't been botched either.

And so it was that David Lee Roth and King Solomon both engaged in a fruitful bit of game theory—which, narrowly defined, is the art of beating your opponent by anticipating his next move.

Both men faced a similar problem: How to sift the guilty from the innocent when no one is stepping forward to profess their guilt? A person who is lying or cheating will often respond to an incentive differently than an honest person. Wouldn't it be nice if this fact could be exploited to ferret out the bad guys?

We believe it can—by tricking the guilty parties into unwittingly revealing their guilt through their own behavior. What should this trick be called? In honor of King Solomon, we'll name it as if it is a lost proverb: Teach Your Garden to Weed Itself.

* * *

King Solomon famously threatened to cut a baby in half during a dispute between two women who both claimed to be its mother. The tactics were designed to make cheaters reveal themselves. Alinari/Getty Images

Imagine you've been accused of a crime. The police say that you stole something, but the evidence is murky.

So the judge comes up with a creative solution: He decrees that you must plunge your arm into a caldron of boiling water. If you come away unhurt, you will go free; if your arm is disfigured, you will go to prison.

This is what happened in Europe for hundreds of years. During the Middle Ages, if a court couldn't determine whether a defendant was guilty, it often turned the case over to a priest who would administer an "ordeal" using boiling water or a smoking-hot iron bar. The idea was that God, who knew the truth, would miraculously deliver from harm any suspect who had been wrongly accused.

As a means of establishing guilt, the medieval ordeal sounds barbaric and nonsensical. But according to

Peter Leeson,

an economist at George Mason University, it was surprisingly effective—because it let the garden weed itself.

Dr. Leeson analyzed a set of church records from 13th-century Hungary; it included 308 cases that entered the trial-by-ordeal phase. Of these, 100 were aborted before producing a final result. That left 208 cases in which the defendant was summoned by a priest to the church, climbed the altar and was forced to grab hold of a red-hot iron bar.

How many of those 208 people do you think were badly burned? All 208? We're talking about red-hot iron here. Maybe 207 or 206?

The actual number was 78. Which means that the remaining 130—nearly two-thirds of the defendants—were miraculously unharmed and thereby exonerated.

Unless these 130 miracles were miracles, how can they be explained? Dr. Leeson thinks he knows the answer: "priestly rigging"—that is, the priest somehow tinkered with the setup to make the ordeal look legitimate while ensuring that the defendant wouldn't be disfigured. Maybe the priest swapped out the hot iron bar for a cooler one, or—if using the boiling-water ordeal—dumped a pail of cold water into the caldron before the congregants entered the church.

Why would a priest do this? Was he simply showing mercy? Had he taken a bribe from a wealthy defendant?

Dr. Leeson sees a different explanation. As we noted, a guilty person and an innocent one often respond differently to the same incentive. So, facing a medieval ordeal, what might the guilty suspects and the innocent ones be thinking?

A guilty person is probably thinking: God knows I am guilty. Therefore, if I undergo the ordeal, I will be horribly scalded. Not only will I then be imprisoned or fined, but I'll spend the rest of my life in pain. So perhaps I should go ahead and confess.

And what would an innocent person think? God knows I am innocent. Therefore I will undergo the ordeal since God would never allow this fiery curse to harm me.

All this, Dr. Leeson writes, "created a separating equilibrium in which only innocent defendants were willing to undergo ordeals." This helps explain why 100 of the 308 ordeals were aborted: The defendants in these cases settled before the ordeal stage—often, presumably, because the defendant was guilty and figured he'd be better off accepting his punishment without the additional pain of being burned.

But 78 defendants in this data set were scalded and then fined or sent to prison. What happened in those cases?

Our best guess is that either the priests believed these defendants really were guilty—or the priests had to keep up appearances to show that trial by ordeal really worked. So these folks were sacrificed.

Of course, the threat would lose its power if the defendants didn't believe in an all-powerful, all-knowing God who punished the guilty and pardoned the innocent. Without that fear, a trial by ordeal would be as scary as the father who's always threatening to spank his child but never does. But history suggests that most people of the time did indeed believe in an all-powerful, justice-seeking God.

Which leads us to the most bizarre twist in this bizarre story: If medieval priests did manipulate the ordeals, that might make them the only parties who thought an all-knowing God didn't exist—or if He did, that He had enough faith in his priestly deputies to see their tampering as part of a divine quest for justice.

* * *

You, too, can play God once in a while if you learn to set up a self-weeding garden.

Consider one of the most basic business transactions: hiring. This consumes a lot of time and money, especially in industries where workers come and go. So wouldn't it be great to find some quick, clever, cheap way of weeding out bad employees before they are hired?

Zappos, the online shoe-and-clothing store, has come up with one such trick. Its customer-service reps are central to the firm's success, so Zappos wants to know that each new employee is fully committed to the company's ethos.

That's where "The Offer" comes in. After a new employee has completed a few weeks of training, Zappos offers them a chance to quit. Even better, the quitter will be paid for their training time and get a bonus representing their first month's salary—roughly $2,000—just for quitting! All they have to do is go through an exit interview and surrender their eligibility to be rehired at Zappos.

What kind of company would offer a new employee $2,000 not to work?

A clever one. "It's really putting the employee in the position of, 'Do you care more about money, or do you care more about this culture and the company?' " said

Tony Hsieh,

the company's CEO, in a radio interview. "And if they care more about the easy money, then we probably aren't the right fit for them."

Mr. Hsieh figured that any worker who would take the easy $2,000 was the kind of worker who would end up losing the firm a lot more in the long run. By one industry estimate, it costs an average of roughly $4,000 to replace a single employee, and one recent survey of 2,500 companies found that a single bad hire can cost more than $25,000 in lost productivity, lower morale and the like. So Zappos decided to pay a measly $2,000 upfront and let the bad hires weed themselves out before they took root. As of this writing, fewer than 1% of new hires at Zappos accept "The Offer."

* * *

Seducing people into sorting themselves into different categories can be all sorts of useful—and not just in admirable ways.

Have you, for instance, ever received an email from someone purporting to be a government official from Nigeria, or perhaps a deposed prince or billionaire's widow from that country, asking for your assistance in securing a large fortune?

Of course you have! The writer, in florid language, describes the millions of dollars he has the rights to, if only he could extract it from some rigid bureaucracy or uncooperative bank.

That's where you come in. If you will send along your bank-account information, the widow or prince or government official can safely park the money in your account until everything is straightened out. Of course, you may need to advance a few thousand dollars for upfront fees. But you'll be richly rewarded for your trouble.

Variations of this scam have been practiced for centuries. Today, it lives primarily on the Internet and is often called the Nigerian scam because more emails of this sort invoke Nigeria than all other countries combined.

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Which might lead you to wonder: If the Nigerian scam is so famous, why would a Nigerian scammer ever admit he is from Nigeria? That was the question

Cormac Herley,

a computer scientist at Microsoft Research, began to ask himself.

He'd never thought much about the Nigerian scam until he heard two people mention it from opposite angles. One talked about the billions of dollars the scammers earn. The other noted how stupid these scammers must be to send out letters full of such outlandish stories. How, Dr. Herley wondered, could both statements be true? If the scammers are so dumb and their letters so obviously a scam, how could they be successful?

He began to examine the scam from the scammers' perspective. (An August 2012 article in these pages discussed Dr. Herley's research.) For anyone wishing to commit fraud, the Internet has been a wondrous gift: It makes it easy and cheap to send out millions of bait letters to potential victims. But converting a potential victim into a real one will require a good deal of time and effort.

Imagine that for every 10,000 emails you send, 100 people take the initial bait and write back. The 9,900 who trashed your email haven't cost you anything. But now you start to invest significantly in those 100 potential victims. For every one of them who wises up or simply loses interest, your profit margin decreases.

How many of these 100 will end up actually paying you? Let's say one of them goes all the way. The other 99 are, in the parlance of statistics, false positives.

Internet fraud is hardly the only realm haunted by false positives. Roughly 95% of the burglar alarms that U.S. police respond to are false alarms, at a yearly cost of some $2 billion. One recent medical study found an astonishingly high rate of false positives—60% for men, 49% for women—among patients who were regularly screened for various cancers.

So how can a Nigerian scammer minimize his false positives?

Dr. Herley, while modeling this question, identified the most valuable characteristic in a potential victim: gullibility. Who else but a supremely gullible person would send thousands of dollars to a faraway stranger based on a kooky letter?

But how can a Nigerian scammer tell who is gullible and who isn't? He can't. Gullibility is, in this case, an unobservable trait. But the scammer could invite the gullible people to reveal themselves.

How? By sending out such a ridiculous letter—including prominent mentions of Nigeria—that only a gullible person would take it seriously. Anyone with an ounce of sense or experience would immediately trash the email. "The scammer wants to find the guy who hasn't heard of it," Dr. Herley says. "Anybody who doesn't fall off their chair laughing is exactly who he wants to talk to." Here's how Dr. Herley put it in a research paper: "The goal of the e-mail is not so much to attract viable users as to repel the nonviable ones, who greatly outnumber them."

So if your first instinct was to think that Nigerian scammers are stupid, perhaps you have been convinced, as Cormac Herley was, that this is exactly the kind of stupid we should all aspire to be. The ridiculous-sounding Nigerian emails seem to be quite good at getting the scammers' massive garden to weed itself.

This essay is adapted from the latest book by Messrs. Levitt and Dubner, "Think Like a Freak," which will be published on May 12 by Morrow. Their previous books include "Freakonomics" and "SuperFreakonomics."