The Four-Card Puzzle That Gets Easy When Someone Might Be Cheating

Four cards lie on a table. Each has a letter on one side and a number on the other. The faces showing are E, K, 4 and 7. The rule: if a card has a vowel on one side, it has an even number on the other. Which cards do you have to turn over to find out whether anyone has broken the rule?

Most people say E, or E and 4. The answer is E and 7. K can’t break the rule whatever is behind it, and a 4 is fine with a vowel or a consonant on the back, but a 7 with a vowel behind it would sink the rule. Peter Wason set this puzzle in 1966, and in replication after replication only a minority get it right, often fewer than one in four.

DontSnooze, an alarm app where friends see whether you got up, is built on the idea that someone else is the better auditor of a promise.

What changes when the rule is about a drinking age?

In 1982 Richard Griggs and James Cox, at the University of Florida, gave people the same logical task with a different rule: if a person is drinking beer, then the person must be over 19. The cards read “drinking beer,” “drinking Coke,” “22 years of age” and “16 years of age.” Seventy-four percent chose the right pair, beer and sixteen. The logic had not changed: a rule about vowels has the same shape as a rule about beer, and one version was far easier than the other.

For a while this was filed under “familiar content helps.” Then Leda Cosmides argued that familiarity did not explain the pattern.

Is there a cheater detector in the head?

Cosmides’s 1989 paper in Cognition (“The logic of social exchange”) reported that rules framed as social contracts, where you receive a benefit only if you meet a requirement, produced correct answers roughly three times as often (about 70 to 75 percent against about 20 to 25 percent) as the same logic dressed as a description. The odd part, as she reported it, came with switched versions. When the rule was rearranged so that the logically correct cards were no longer the ones a cheater would hold, many people still turned the cheater-catching cards, even though that answer was wrong by the book.

Her reading, developed with John Tooby, was that people carry a specialized habit of looking for anyone who takes a benefit without paying the cost. It fits the argument Robert Trivers made in 1971 about reciprocal altruism: trading favors only pays if cheaters get noticed.

Is that the only explanation?

No. Patricia Cheng and Keith Holyoak proposed in 1985 that people reason well about any rule shaped like a permission or an obligation (“if you do X, you must have done Y first”), with no cheating module required. The two camps have gone back and forth for decades over cases such as safety precautions, where nobody is a cheater but people also do well. This piece takes no side. Both accounts agree that rules with a beneficiary and a cost are audited well. They disagree about why, and the promise argument below leans only on the shared part.

What does that predict about promises to yourself?

A promise made to another person has the form of a social contract: the other person gives trust, attention or help, and the promiser owes a specific action by a specific time. A private resolution to wake at 6:00 has the form of the vowel rule. It states a condition, names no beneficiary, and gives nobody the job of looking behind the 7. In the experiments, abstract rules of that kind were failed by most participants.

A promise to a friend is easier to enforce than a private resolution because it names who is owed and what is owed, which is the shape of rule that people in these experiments checked far more reliably than abstract ones. A private goal has no creditor, so no one holds the cards.

For the economics side of this, the field experiments comparing money on the table with social pressure found that the social version holds up in some settings and loses in others. For the signaling side, costly signaling theory explains why a promise is only believable when failing would hurt.

Where does the evidence stop?

Three places.

First, the detector the experiments measure looks outward. Participants judged whether other people had broken a stated rule. None of the studies above asked anyone to check their own conduct, so this piece cannot say how well anyone audits themselves. If self-audit is weaker, someone else has to hold the cards; if it is not, the case for a witness is weaker than argued here.

Second, nobody has run the selection task on wake-up promises. The step from beer and Coke to 6:00 a.m. is an inference, and a plausible one, but an inference.

Third, a witness who can be talked out of looking restores the abstract rule. If the friend’s check-in can be skipped, waved off or answered with “I’ll do it tomorrow,” the deal has no enforcer again. That is the question behind any serious attempt to keep promises to yourself: what stands behind the promise when nobody in the room is checking?

The four cards are still on the table: E and 7 for the puzzle, and for a resolution, whoever is owed the promise.