Restaurant Problem
The restaurant problem asks which customers could violate a conditional drinking-age rule. Its familiar setting makes the relevant checks easier to see than in an abstract card task: check drinkers’ ages and whether underage customers are drinking.
THE IDEA
RESTAURANT PROBLEM
For this exercise, check the rule: anyone drinking must be at least twenty-one.
- Customer is fifty-plus—doesn’t matter whether customer is drinking or not.
- Isn’t drinking—doesn’t matter whether customer is at least twenty-one or not.
- Drinking—better be at least twenty-one. If not, the rule is broken.
- Under twenty-one—better not be drinking. If so, the rule is broken.
Don’t feel bad if you didn’t get the card problem right. Less than 20 percent of Oxford University students can solve the abstract version of the card problem!
Why is the card problem so much harder than the restaurant problem? At first blush this seems strange, because both problems can be solved by applying conditional logic, in fact by applying the very simplest principle of conditional logic, modus ponens:
| If P is the case, then Q is the case. | If the customer is drinking, then the customer is at least twenty-one. |
| P is in fact the case. | The customer is drinking. |
| Therefore, Q is the case. | Therefore, the customer is at least twenty-one. |
The same conditional can be checked through its contrapositive: if not Q, then not P. An instance where Q (twenty-one or over) is not the case but P (drinking) is the case contradicts the conditional rule.
Under the stated rule, P (drinking) is sufficient to require Q (being at least twenty-one). It is not necessary: someone can be old enough without drinking. The rule does not restrict the age of a customer who is not drinking.
For the biconditional, P is both necessary and sufficient in order for Q to be the case. This would include the (rather weird) rule that if you’re drinking you must be twenty-one and if you’re twenty-one you must be drinking.
Checking compliance means looking for P together with not Q: a drinker below the required age. A person who is old enough, or who is not drinking, cannot violate this rule on that information alone.
When to use it
Designing logical reasoning tests or training materials that leverage concrete examples to improve understanding.
Analyzing real-world policy compliance (e.g., age restrictions, safety rules) by identifying conditions and exceptions.
Teaching conditional logic by contrasting abstract and concrete versions of tasks.
Debugging faulty reasoning in arguments by recognizing when a rule's sufficient conditions are confused with necessary ones.
FROM THEORY TO EVERYDAY LIFE
In practice
Restaurant Problem Scenario
In this exercise, anyone drinking must be at least twenty-one. Check a drinker’s age and check whether an underage customer is drinking. Neither an older customer nor a nondrinker can violate the rule merely by being in that category.
Abstract Card Problem
The Wason selection task presents four cards showing numbers and letters (e.g., 'A', 'K', '4', '7') with a rule: 'If there is a vowel on one side, then there is an even number on the other.' Fewer than 20% of Oxford students solve this abstract version correctly, demonstrating the difficulty of abstract conditional reasoning.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-life rule that is similar to the drinking-age rule? How does contextual familiarity affect your ability to check violations?
Why do you think abstract conditional reasoning is harder than concrete reasoning? What cognitive bias might be at play?
How would the restaurant problem change if the rule were biconditional (if and only if)?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Mindware Tools for Smart Thinking (Richard E. Nisbett)