Four cards problem (QUA-M5-02-EN)

Main objective of this activity is to learn more about belief bias and logical reasoning.

• Students
• Adolescent youth
• Educators, trainers, councillors, youth workers

Problem 1:

The facilitator prepares four cards on the table (Handout – page 1) and show them to participants with explanation that they have a letter on one side and number on the other side.

Now facilitator can give participants following rule: If a card has a vowel on one side, then it has an even number on the other side.  A D 4 7

Participants are asked: Which card(s) do you need to turn over to determine if the rule is true or false?

They are asked to write down which card(s) they would like to choose to prove if the rule is true or false.

Facilitator explains which option is correct or not (see advice for facilitators).

Problem 2:

The facilitator prepares four guests (cards) in a bar (table) (Handout – page 2) and show them to participants with explanation that they have a description on one side and number on the other side.  BEER COKE 25 17

The rule about the four guests is:  If guest is drinking a beer, then he/she must be 18 years or older.

They are asked, which card(s) do you need to turn over in order to determine if the rule is being followed?

Facilitator explains which option is correct or not (see advice for facilitators).

Pen, piece of paper.

• Self-awareness training
• Belief bias training
• Logic puzzle
• Discussion

Problem 1:

Wason selection problem has generally the following distribution of answers (Wason & Shapiro, 1971):
~ 45% pick the A card and the 4 card
~ 35% pick the A card alone
~ 7% pick the A card, 4 card, and the 7 card
~ 4% pick the A card and the 7 card [correct]
~ 9% pick other combinations of cards

Problem 1 – correct cards A4, D7

There is no logical reason to select the card with number 4, because it is not possible for it to falsify the rule - whether there is a vowel or a consonant on the other side is irrelevant as there is no restriction on an even-consonant pair. 

Problem 2 – correct cards BEER 17,  COKE 25

This problem (drinking alcohol), according to Wason's selection task, generally leads to the following distribution of responses (Griggs & Cox, 1982, Exp. 3):

~ 0% pick the BEER card and the 35 card
~ 20% pick the BEER card alone
~ 3% pick the BEER card, 35 card, and the 19 card
~ 72% pick the BEER card and the 19 card [correct]
~ 5% pick other combinations of cards

It is clear that people would understand this problem more fully. One would need to check a 17-year-old to make sure they weren’t drinking.  It’s likely that participants are familiar with the concept of alcohol laws and underaged drinking and would readily recognize that a 17-year-old could potentially violate the rule whereas a 25-year-old could not (“If you are NOT 18 years or older, then you must NOT be drinking beer”).  This is the reason why participants choose more easily the correct cards and correct answer seems much more obvious than in the abstract case.  One reason for this difference is that participants would not have personal experience with, for example, the abstract vowel-even number context from Problem 1, such that subjects would not be able to pull up a relevant memory to arrive at the normatively logical solution.

Facilitator can explain further:

Two problems are connected with belief bias of human reasoning and social conduct in the domains of abstract logic. As written in the module Ethics, bias is a state or habit of mind in which trust, or confidence is placed in some person or thing.

Because of belief bias, most participants would simply turn the cards mentioned in the rule – problem 1.

The belief bias is a cognitive bias that causes people to over-rely on preexisting beliefs and knowledge in this case, when evaluating the conclusions of an argument, instead of properly considering the argument’s content and structure.

Another example of the belief bias in a syllogism is the following:

• Premise 1: All birds can fly.
• Premise 2: Pigeons can fly.
• Conclusion: Pigeons are birds.

People might find think that this argument is logically sound, if they know that pigeons are birds. However, this argument is actually logically unsound—its conclusion doesn’t follow from its premises, since both birds and pigeons being able to fly doesn’t necessarily mean that pigeons are birds (for example, other types of animals, such as insects, can also fly). Furthermore, the first premise of this argument is wrong, since not all birds can fly (for example, ostriches, kiwis, and penguins are all flightless birds).

Discussion about belief bias and experienced belief bias also from political spectre can follow.

Nikolopoulou, Kassiani (2023). What Is Belief Bias? Definition & Examples. Retrieved from: https://www.scribbr.com/research-bias/belief-bias/

Psychology Classics: Wason Selection Task (2012) Psychology in Action. Retrieved from: https://www.psychologyinaction.org/2012-10-07-classic-psychology-experiments-wason-selection-task-part-i/

Yadav, Sourabh (2023). 12 belief bias examples. Retrieved from: https://helpfulprofessor.com/belief-bias-examples/

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