These questionnaires were based on a previously developed research instrument called the Free Will and Determinism Scale. The workers were asked how strongly they agreed with statements like “Strength of mind can always overcome the body’s desires” or “People can overcome any obstacles if they truly want to” or “People do not choose to be in the situations they end up in — it just happens.”

The psychologists also measured other factors, including the workers’ general satisfaction with their lives, how energetic they felt, how strongly they endorsed an ethic of hard work. None of these factors was a reliable predictor of their actual performance on the job, as rated by their supervisors. But the higher the workers scored on the scale of belief in free will, the better their ratings on the job.

“Free will guides people’s choices toward being more moral and better performers,” Dr. Vohs said. “It’s adaptive for societies and individuals to hold a belief in free will, as it helps people adhere to cultural codes of conduct that portend healthy, wealthy and happy life outcomes.”

Intellectual concepts of free will can vary enormously, but there seems to be a fairly universal gut belief in the concept starting at a young age. When children age 3 to 5 see a ball rolling into a box, they say that the ball couldn’t have done anything else. But when they see an experimenter put her hand in the box, they insist that she could have done something else.

That belief seems to persist no matter where people grow up, as experimental philosophers have discovered by querying adults in different cultures, including Hong Kong, India, Colombia and the United States. Whatever their cultural differences, people tend to reject the notion that they live in a deterministic world without free will.

They also tend to agree, across cultures, that a hypothetical person in a hypothetically deterministic world would not be responsible for his sins. This same logic explains why they they’ll excuse Mark’s tax evasion, a crime that doesn’t have an obvious victim. But that logic doesn’t hold when people are confronted with what researchers call a “high-affect” transgression, an emotionally upsetting crime like Bill’s murder of his family.

“It’s two different kinds of mechanisms in the brain,” said Alfred Mele, a philosopher at Florida State University who directs the Big Questions in Free Will project. “If you give people an abstract story and a hypothetical question, you’re priming the theory machine in their head. But their theory might be out of line with their intuitive reaction to a detailed story about someone doing something nasty. As experimenters have shown, the default assumption for people is that we do have free will.”