Last time, we tested a rule.

This time, we test evidence.

Economists, doctors, investors, detectives and policymakers all face the same problem:

How much should one piece of evidence change what you believe?

Suppose you are told that a test catches 99% of cases.

That sounds reassuring.

But here is the question:

Does a positive result mean the thing is probably true?

Not always.

Today’s problem is about one of the most useful ideas in probability: Bayes’ theorem.

But do not worry if you have never seen the theorem before. The real lesson is not about memorising a formula. It is about learning to think clearly when evidence arrives.

A rare condition affects 1% of a population.

There is a test for the condition.

The test has the following properties:

A person is chosen at random from the population and takes the test.

The test result is positive.

What is the probability that the person actually has the condition?

Most people’s instinct is to say something close to:

99%

That instinct is understandable.

The test seems highly accurate.

But 99% is not the right answer.

P.S roll up your sleeves and explore the question… once you’ve grappled with it for a while, if you are still stuck…Graduated hints below — but challenge yourself first! (Answer comes in the next edition! Subscribe to receive it directly to your inbox!)

-9

This week’s marginal number is -9.

That was the UK CBI’s factory order books balance in September.

At first glance, a negative number does not sound like good news. But this is where economics gets interesting: the story is not just the level, but the movement.

The balance improved from −25 in August to −9 in September, reaching its strongest reading since July 2023. Reuters also reported that the two-month improvement was the largest in the survey’s 49-year history.

So the number is still negative, but much less negative.

That distinction matters.

A bad level can still represent improving momentum. A negative figure can still be positive news. And a single statistic only makes sense when you ask: compared with what?

That is the useful economic habit: never just read the number. Read the direction, the context, and the base you are moving from.

Last time, we looked at four cards.

Each card has a letter on one side and a number on the other.

The rule was:

If a card has a vowel on one side, then it has an even number on the other side.

The question was:

Which card or cards must you turn over to test the rule?

The answer is:

A and 7

Not A and 4 combined.

Here is why.

The rule has the logical form:

If P, then Q

where:

P = the card has a vowel

and:

Q = the card has an even number

So the rule says:

If vowel, then even number.

The only way to break the rule is to find:

vowel and not even

In this case, that means:

a vowel on one side and an odd number on the other.

So we are not looking for cards that might confirm the rule.

We are looking for cards that could falsify it.

A is a vowel.

The rule says that every vowel card must have an even number on the other side.

If A has an even number behind it, the rule survives.

If A has an odd number behind it, the rule is broken.

So we must turn over:

A

D is a consonant.

The rule says nothing about consonants.

Whether D has an even number or an odd number behind it, the rule is not broken.

So we do not need to turn over:

D

4 is an even number.

This is the tempting card.

But the rule does not say:

If even number, then vowel.

It says:

If vowel, then even number.

Those are different claims.

If the other side of 4 is a vowel, the rule is fine.

If the other side of 4 is a consonant, the rule is also fine.

So 4 cannot falsify the rule.

We do not need to turn over:

4

7 is an odd number.

This matters because the rule says that vowel cards must not have odd numbers.

If the other side of 7 is a consonant, the rule survives.

But if the other side of 7 is a vowel, the rule is broken.

So we must turn over:

7

The cards you must turn over are:

A and 7

A matters because it is a vowel, and therefore must have an even number on the other side.

7 matters because it is odd, and therefore must not have a vowel on the other side.

Many people choose:

A and 4

That is understandable. A and 4 are the two cards that seem to match the words in the rule.

The rule mentions vowels.

A is a vowel.

The rule mentions even numbers.

4 is even.

But testing a rule is not the same as looking for examples that fit it.

The real question is:

What could prove the rule false?

The card showing 4 cannot do that.

The card showing 7 can.

If there is a vowel behind 7, the rule fails.

That is why the correct answer is:

A and 7

There is a deeper philosophical point here.

The Wason Selection Task has a strong link to the philosopher of science Karl Popper.

Popper argued that science does not advance simply by collecting examples that support a theory. If we only search for confirming evidence, almost any theory can start to look convincing.

Instead, Popper argued that serious scientific theories should be falsifiable.

That means we should be able to say what kind of observation would count against them.

A good scientific attitude is not only:

What supports my claim?

but also:

What would show that my claim is wrong?

That is exactly what the card puzzle tests.

Choosing A and 4 is a confirmation-seeking approach.

Choosing A and 7 is a falsification-seeking approach.

The 7 card is crucial because it could expose the rule as false. It does not look like the obvious card, because it does not appear to match the wording of the rule. But it is the card that could break the rule.

That is the Popperian lesson:

Do not just look for confirming cases. Look for the possible falsifier.

Now compare the abstract card puzzle with a more concrete version.

The rule is:

If someone is drinking alcohol, then they must be over 18.

You see four people.

Who do you need to check?

The answer is:

the beer drinker and the 16-year-old

You need to check the beer drinker because anyone drinking alcohol must be over 18.

You need to check the 16-year-old because anyone under 18 must not be drinking alcohol.

You do not need to check the Coke drinker because the rule says nothing about people drinking Coke.

You do not need to check the 22-year-old because people over 18 are allowed to drink alcohol, but they are not required to.

The structure is the same.

In both versions, the correct choice is:

P and not Q

That means:

A and 7

or:

beer drinker and 16-year-old

Many people find the abstract version difficult but the alcohol version much easier.

Why?

One explanation is that humans are often better at reasoning when a problem is framed in terms of real-world rules, permissions, cheating and social consequences.

The abstract rule:

If vowel, then even number

feels dry and unnatural.

The social rule:

If drinking alcohol, then over 18

feels concrete.

We immediately understand what would count as breaking the rule.

So the lesson is not just about logic.

It is also about framing.

The same logical structure can become much easier when represented in the right way.

Economics is full of claims with the form:

If X, then Y.

For example:

If prices rise, quantity demanded falls.

If interest rates rise, borrowing falls.

If incentives change, behaviour changes.

If money supply growth increases, inflation rises.

If a minimum wage rises, employment falls.

But testing those claims is not just a matter of finding examples that fit them.

A good economist asks:

What would count as evidence against this claim?

That is the Wason lesson.

Do not just look for confirmation.

Look for the card that could break the rule.

The first implication is confirmation bias.

People often look for evidence that supports what they already believe.

If someone believes tax cuts increase growth, they may look for examples where tax cuts were followed by stronger growth.

If someone believes regulation damages business, they may look for examples where regulation was followed by weaker investment.

If someone believes immigration lowers wages, they may look for cases where migration rose and wages were weak.

But that may be like turning over the 4 card.

It feels relevant, but it may not be the strongest test.

The better question is:

Where would I expect my claim to fail if it were wrong?

The Wason task also matters for policy evaluation.

Suppose a government introduces a training programme and employment rises afterwards.

It is tempting to say:

The policy worked.

But that is not enough.

The real question is:

What would have happened without the policy?

This is the counterfactual.

Economists use control groups, natural experiments, randomised trials and difference-in-differences methods because they help reveal the hidden side of the card.

They help us ask not just:

Did employment rise?

but:

Did employment rise more than it would otherwise have done?

The Wason task is also a warning about causal claims.

Consider the claim:

If central banks raise interest rates, inflation falls.

You might find episodes where rates rose and inflation later fell.

But that alone does not prove the claim.

Inflation may have fallen because of lower energy prices, weaker demand, repaired supply chains, or changes in expectations.

A stronger test asks:

Are there cases where rates rose and inflation did not fall?

Or:

Are there cases where inflation fell without rate rises?

Or:

What else changed at the same time?

Economic data rarely come with only one thing changing at once. That is why causal inference is difficult.

The puzzle also reminds us that logical direction matters.

If P, then Q

does not mean:

If Q, then P

This is a common mistake in economic reasoning.

For example:

If demand rises, price rises

does not mean:

If price rises, demand must have risen.

Price might have risen because supply fell, costs increased, taxes changed, or expectations shifted.

Likewise:

If a country has strong institutions, it is more likely to be rich

does not mean:

If a country is rich, strong institutions must be the only explanation.

The direction of the claim matters.

So does the evidence needed to test it.

Finally, the Wason task belongs naturally in behavioural economics.

It shows that people are not always abstract reasoning machines.

Context matters.

Framing matters.

The same logical problem can be hard in one setting and easy in another.

That matters for how people respond to contracts, incentives, warnings, financial products, tax rules, regulation and public information.

Good policy design should take that seriously.

A rule that seems clear to the policymaker may not be clear to the person facing it.

The Wason Selection Task looks like a puzzle about cards.

But it is really a puzzle about evidence.

It teaches four important lessons.

First:

Do not just look for evidence that fits your rule.

Second:

Ask what could prove your rule false.

Third:

Pay attention to the logical direction of a claim.

Fourth:

Think like Popper: a serious claim should expose itself to possible refutation.

In economics, these lessons matter constantly.

A good economist does not simply collect examples that confirm a theory.

A good economist asks:

What would I need to observe to change my mind?

Marginal gains… Answer for today’s question is out in two days… Come back then or subscribe to get it direct to your inbox!

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