Why Do People Get A Proposition When It's Expressed One Way, But Totally Fail To Get The Exact Same Proposition When It's Expressed Another Way?

There was once a selection task devised by psychologist Peter Wason to show that people don't naturally think well when logical symbols are required. According to statistics over 90% of you will get this wrong.

You are shown a set of four cards placed on a table, which must conform to the rule "If P then Q". That means that whenever there is a card with P on one side, the reverse side of the card must show Q. The visible faces of the cards show as follows:

CARD 1 - P

CARD 2 - not-P

CARD 3 - Q

CARD 4 - not-Q

Wason asks which card(s) must you definitely turn over in order to test the truth of the proposition that "If P then Q" holds? Have a think about it for a few seconds. 

If you're one of the 90+% you've probably reasoned that you need card 1 and card 3. You want to make sure that P has a Q on the other side, and equally you want to make sure that Q has a P on the other side.

But that's not right - the cards you need to choose are cards 1 and 4. Here's why. Because the rule is "If P then Q" you need to check card 1 (P) to ensure there's a Q on the back, but you also need to check card 4 (not-Q) to ensure there is 'no' P on the back. If there is a P on the other side of card 4, then the rule "If P then Q" has been disobeyed. Cards 2 and 3 don't need to be touched.

Now what's strange, Wason found, is that although people struggle in this task when using logical symbols, they don't when those symbols are changed to more familiar real life situations, despite the logical connection between facts being exactly the same. For example, if instead of "If P then Q" the rule used is "If you come into my pub and drink alcohol you must be 18 or over" people get that one right. The visible faces of the cards show as follows:

CARD 1 - Age 15

CARD 2 - Drinking coke

CARD 3 - Age 18

CARD 4 - Drinking vodka

When presented with the task in the social context of under age drinking, virtually nobody has any trouble choosing cards 1 and 4, even though the logical connection is exactly the same as the "If P then Q" proposition a moment ago.

Alas, such inconsistent thinking extends far into our everyday lives too - a good example being Ricardo's phenomenon of comparative advantage, which basically means that the agent that can do something with the least amount of opportunity cost should do that thing.

For example, if Gina can make 4 brownies every 10 minutes and decorate 9 cupcakes every 10 minutes, and Lisa can make 2 brownies every 10 minutes and decorate 6 cupcakes every 10 minutes, Lisa should be decorating cupcakes even though Gina can do it faster, because comparative advantage says that Lisa ought to be decorating cupcakes because she is less bad at it than making brownies.

Comparative advantage is one of the essential tenets of a free market, and it is terrific in its simplicity and efficiency, yet so many people (politicians and the general public) alike misunderstand it.

Donald Trump is currently the person most publically misunderstanding it - his daily spouting of economic nonsense concerning America and trade is one of the most disturbing exhibitions of political confusion I think I've ever seen in a Presidential candidate (and that's saying something).

Perhaps rather like the Wason selection tests people can see a proposition clearly if it's expressed one way yet miss completely exactly the same proposition when it is expressed another way.

Take imports and exports as a good example. The world is a better place when one country, say Britain, export goods in which it has the comparative advantage, and imports goods in which the importing country, say China, has the comparative advantage. The logic is simple: Brits produce more of the things we are good at producing, and other countries produce more of the things they are good at producing.

Doubtless almost everyone can understand and agree with comparative advantage when we say that it's Lisa, not Gina, who should be decorating cupcakes, but a lot of people stop understanding this very same principle when we tell them that if non-UK countries are more efficient at producing some goods than we are, we should be buying those goods from abroad not protecting our own less-efficient industries.

The mystery as to why Paul McCartney wasn't the drummer in the Beatles is no mystery at all - he may have supposedly been better at drums than Ringo, but he was also much better at playing other instruments and writing songs with them than Ringo, so it made perfect sense to have the much better songwriter writing songs on guitar and piano than the slightly better drummer playing drums.  

Once again, everyone understands why Ringo played drums, not Paul, just as everyone understands why we buy our wine from France, Spain and Italy and not Scotland, Finland and Norway - it's just a pity they cannot carry on following the logic to international trade (take note Donald Trump supporters).