Before I reveal the results, think about what you would do in that situation. Someone comes up to you at the mall and offers you free money to roll a die. If you wanted to make a few extra bucks, you could lie about what you rolled. Nobody would know, and nobody would be harmed.

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Imagine you went into that booth and rolled a 1. What would you do? Would you be dishonest? Would you say you rolled a six, just to get the largest payout?

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The researchers, Bradley Ruffle of Wilfrid Laurier University and Yossef Tobol, of the Jerusalem College of Technology, wanted to know what kinds of people would lie in this situation. So they asked everyone about their backgrounds, whether they considered themselves honest, whether they thought honesty was important. They asked whether people were employed, how much money they earned, and whether they were religious. They also gave people a quick intelligence test.

Out of all those attributes, brainpower stood out. Smarter people were less likely to lie about the number they rolled.

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It didn’t matter whether they claimed they were honest or not; it didn’t matter whether they were religious, whether they were male or female, or whether they lived in a city. Money didn’t seem to be a factor either. Even after controlling for incomes, the researchers found that the most honest people were the ones who scored highest on the intelligence test.

Here’s what the responses looked like for people with low scores. A six-sided die has an equal chance of landing on any of its faces. That means that on average, we should see about 1/6th — or 16.6% — of people reporting a one, 1/6th of people reporting a two, and so on.

Instead, we see that among the low-scorers, practically nobody reported rolling a 1, 2 or 3. Nearly half reported rolling a six. This is clear evidence of chicanery.

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People with high intelligence scores were a lot more honest. But some of them were also guilty of fudging the numbers. About 28 percent of them said they rolled a four, which is statistically improbable. And only 7 percent of them admitted to rolling a two.

What’s also interesting is how the smart people lied differently. The low-intelligence liars overwhelmingly went big — most of them claimed they rolled a six, which gave them the highest payoff. But the high-intelligence liars were more modest. They were more likely to lie and say they rolled a four or a five.

There are two mysteries here. First, why were the less intelligent people more likely to lie? Second, why were the smarter liars so sheepish about going for the maximum payoff?

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Ruffle and Tobol believe that more intelligent people may be more cautious about the consequences of lying. Dishonesty can make a situation better in the short term, but who knows what will happen down the road, especially if the lie eventually comes out?

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“[W]hile everyone is aware of the gain from telling a lie in a given situation, higher cognitive-ability types may be more aware or better able to assess the expected costs,” the researchers say in their report.

In this case, for instance, the smarter people might have been more suspicious of the whole setup. They might have guessed that this was a game to test their honesty. They might have wondered if there was a camera watching them in the supposedly private booth (there wasn’t). They might have suspected that there would be some secret punishment for lying.

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It’s also possible that the smarter people are also more concerned with their self-image. This could explain the second mystery. Perhaps more intelligent people take pleasure in thinking of themselves as honest, upstanding citizens. They might lie a little — zhuzh their numbers up a point or two — but they would avoid making a big lie in order to preserve a little bit of self respect.

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“[One possibility is that] subjects who score high on the cognitive tests recognize that inflating their report to the maximum possible outcome of 6 forces them to confront the reality that they are cheaters,” Ruffle and Tobol write.

There’s a more sinister explanation too. This die-rolling honesty game was invented by researchers in Germany, who first ran the experiment on Swiss university students. They found the same pattern of partial cheating that the Israeli researchers observed among their smarter test subjects. The Swiss students would make small lies, but few of them would go as far as to claim that they rolled a six.

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The German researchers suggested that people might prefer more modest lies in order to increase their chances of getting away with it. (Unlike the Israeli researchers, they don't test for intelligence.)

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“If ever anybody is called upon to tell what he has done in our experiment, the person who can say he reported a 4 with a clear conscience might seem more credible,” the German researchers write in their paper, published in the Journal of the European Economic Association in 2013.

It will take more than one experiment to establish a connection between honesty and intelligence. The matter is still somewhat up in the air. For instance, research in 2012 from Francesca Gino, of Harvard Business School, and Dan Ariely, of Duke, found a connection between creativity and dishonesty, but not intelligence and dishonesty.

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Thus far, Ruffle and Tobol have replicated their results with Israeli soldiers as well as the Israeli mall shoppers. But there will need to be more experiments, in different countries and different cultural contexts. And just because someone tells the truth in a game doesn’t necessarily mean they are more or less honest in real life.

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So it's important not to take this research too seriously (yet). It does, however, raise meaningful questions: Why are some people are more honest than others? And why do some people refuse to lie even when there are no real consequences?