Friday, September 27, 2013

On Reasoning and Familiarity

One of the major themes of Behavioral Economics is the idea that much of human reasoning uses shortcuts known as heuristics. For example, imagine you were asked to approximate the number of marbles in a jar with reasonable speed and accuracy.  You have a number of possible strategies. You could individually count each marble, but this approach is lengthy and difficult.  You could simple take a wild guess, but that's likely not very accurate.  Alternatively, you could decide to count what seems to be a third of the marbles then multiply that result by three.  That will only take a third as much time and is likely to be reasonably accurate. This third approach is a heuristic, a mental shortcut that usually gives you an answer that is "good enough".

However, heuristics often lead to consistent and reproduceable errors in reasoning. Take this test for example. You are presented with four cards. Each card has a letter on one side and a number on the other. Which cards should you turn over to test this hypothesis: All cards with vowels on one side have an even number on the other.  The cards you're given are:

E   G   2   5

Take a moment and decide which cards you'd flip. 

Before getting into the answer let's highlight a few key things regarding the hypothesis.  All cards with vowels on one side have an even number on the other. Key words that likely jump out at you are "vowels" and "even numbers". Notably odd numbers and consonants are not mentioned. 

Here's another version of roughly the same puzzle.  See if your answers differ at all. Imagine you run a bar which serves beer and soda.  Everyone in the bar who is over 21 may have beer, but anyone below 21 must drink soda.  You only know either a patron's drink or age but not both.  Which of these patrons must you check to ensure no one under 18 has beer? (Officially our hypothesis in order to mimic the first puzzle is: if someone is drinking alcohol they must be over 21.)

Beer Drinker, Soda Drinker, 30 years old, 15 years old

This puzzle is logically the same as the first but most people will come to a rather different conclusion. Obviously you must check the age of the beer drinker. Clearly you don't need to check the age of the soda drinker or the drink of the 30 year old.  However, you must check the beverage of the 15 year old to ensure he isn't drinking beer.

Similarly most people correctly suppose that you should flip over the E card in the first puzzle.  After all, if you find an odd number on the other side you have disproven the hypothesis.  The G doesn't need flipped because our hypothesis doesn't care about numbers on consonant cards. Most people wrongly choose to flip the 2 card because the hypothesis mentions even numbers.  However, suppose you found a consonant on the other side? We just established we don't care about consonant cards so that wouldn't be helpful.  If we find a vowel it seems to lend credence to our vowel/even hypothesis but it doesn't invalidate it or prove it so we've ultimately learned nothing. Finally, most people choose not to flip the 5 card. The hypothesis doesn't mention odd numbers so it would seem unnecessary. However, if we flip the 5 card and find a vowel we have invalidated the hypothesis that vowel cards have even numbers. Thus this card must be checked along with the E card.

If you answered incorrectly to the first puzzle don't feel too bad. Over 90% of those questioned make the errors listed above.  It's entirely normal for the brain's heuristics to lead you astray in this case. 

What is interesting is that far far fewer people make mistakes on the second puzzle.  As mentioned, the drinking problem is logically the same.  Only letter/number combinations have been exchanged for soda/age combinations.  Yet seemingly due to the familiarity of the situation individuals are much more easily able to correctly solve the puzzle. 

That's it for this week. Until next week stay safe and rationale. 

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