# Logical Psychology

I posed my son a puzzle today. He’s a student, in senior high school, and exams are ever in his mind. I told him a story of four students who missed their exam, and gave him some information about them.

He was told the school has a rule, stating: “If you sit the replacement exam, you must have a doctor’s note.”

Of the four students, he was told:

1. A sat the replacement exam.
2. B did not sit the replacement exam.
3. C has a doctor’s note.
4. D does not have a doctor’s note.

The instruction is to find out whether the rule has been followed. He was allowed to quiz two of the students to get more information.

The puzzle: which two students should he get information on, to determine if the rule has been followed?

In a sense, this is a simple logic puzzle. There’s one correct answer. The really interesting thing about it, though, is not how people approach it logically, but psychologically.

Then, I presented the exact same options, and rule, but informed him “You are an administrator at a school, your job is to ensure students are following the school rules and regulations. Again, four students missed the exam, and he was told

1. A sat the replacement exam.
2. B did not sit the replacement exam.
3. C has a doctor’s note.
4. D does not have a doctor’s note.

Which two students should be interviewed, to determine if the rule “If you sit the replacement exam, you must have a doctor’s note” is being followed?

Before I tell you what my son said, perhaps you’d like to try. Pick one of the links below at random (or both, but not at the same time), and try to solve the puzzle. The links will open up a Google Form, and after you reply, you’ll be able to see what other people said.

There’s also a purely abstract version of the same puzzle, which you may have already seen. It goes like this:

Four cards lie on the table. Each card has a latter on one side, a number on the other. The faces you see show:

• D
• F
• 3
• 7

Suppose I claim: “If a card has D on one side, the other side is 7”. Which two cards do you flip over to test the truth of this claim?

People are bafflingly bad at this puzzle. Typically, only 25% get it right. However, the world is full of “if-then” rules, and occasions we need to know if they apply or are enforced. “If you’re buying beer, you must show a valid ID,” for example, or “if you work overtime, you get extra pay.”

If the logic puzzle is expressed in terms of a social contract, people do much better – or much worse.

Essentially, people still don’t treat it as a logic puzzle; they treat it as an opportunity to test if their allies are being cheated.

Imagine you are a student, and the school has a rule “If you sit the replacement exam, you must have a doctor’s note”. For the moment, forget about testing if the rule is being followed. Which of your classmates to you quiz to see if the school is cheating them? Let’s look at them one by one.

• A sat the replacement exam.

Great! That’s fantastic news for A. It doesn’t matter if A has a doctor’s note, your classmate, your ally, has gained a valuable thing. It doesn’t matter about the doctor’s note. In fact, it might be a very bad idea to inquire about the doctor’s note. What if they don’t have one? That would be a breach of the school rules, and seriously harm your ally.

Of course, those last three sentences of dodgy logic don’t always explicitly run through your head. You just subconsciously veer away from testing the very rule you were asked to test, lest it harm your ally’s position.

The school administrator has no such qualms. Cheating students are not their ally, and they will certainly interview A.

My son chose A in the role of administrator, and not in the role of student.

• B did not sit the replacement exam.

Why not? That’s very serious (thinks their classmate). Maybe they didn’t have a doctor’s note, but what if they did? We’d better check; if they do have one, they can then get a chance to sit the exam they missed.

However, the rule doesn’t say anything about people who don’t sit the exam. They don’t need a doctor’s note, but they are permitted to have one. The school administrator will not interview B.

My son, in the role of a student, did, in fact, choose B. When he was acting as school administrator, he did not.

• C has a doctor’s note.

Then they have a right to sit the replacement exam. Did they actually sit it? This is very important information for a student to know about their classmates. It’s not at all important for an administrator enforcing a rule. As a student, my son chose to interview C, but as an administrator he did not.

• D does not have a doctor’s note.

Poor guy. If he was lucky enough to sit the exam, great, but that would be a mercy by (their adversary) the school. If we find out he sat it, great, but if we find out he didn’t, there’s nothing we can do either way. To a student feeling compassion for an unfortunate classmate, this doesn’t feel like important information. The student will not ask for further information about D.

The administrator, by contrast, is very interested in whether D broke the rule by sitting the replacement exam with no doctor’s note.

My son chose to interview D as an administrator, but not as a student.

In short, to an administrator, the rule sounds like “If you have no doctor’s note, you have NO RIGHT to sit the exam.” To the student, the very same rule sounds like “If I have a doctor’s note, you MUST let me sit the exam.”

In this instance, the administrator’s perspective is correct, but that’s just lucky. Watch out for situations in your daily life where rules get misinterpreted to the advantage of the person hearing them.

My son, of course, didn’t appreciate me pointing out that his answers changed completely depending on the role he imagined himself filling. He gave a solid-sounding reason why he changed his answers – the fact that I asked the same puzzle again, leading him to believe his first answers were wrong.

Maybe.

However, his answers did match exactly what psychologists would have expected, based on research in this area by Leda Cosmides, John Tooby and others. And people are extremely good at inventing rationalisations for their apparently illogical behaviour.

Well, it’s nice to know he’s human!