From the "You've got to be kidding" department: Why Smart People Are Stupid
Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?Talk about a bad premise.
The vast majority of people respond quickly and confidently, insisting the ball costs ten cents. This answer is both obvious and wrong. (The correct answer is five cents for the ball and a dollar and five cents for the bat.)
For more than five decades, Daniel Kahneman, a Nobel Laureate and professor of psychology at Princeton, has been asking questions like this and analyzing our answers. His disarmingly simple experiments have profoundly changed the way we think about thinking. While philosophers, economists, and social scientists had assumed for centuries that human beings are rational agents—reason was our Promethean gift—Kahneman, the late Amos Tversky, and others, including Shane Frederick (who developed the bat-and-ball question), demonstrated that we’re not nearly as rational as we like to believe.
For starters, when economists and social scientists assume "rational actors" they are usually doing so in the context of a model, and not using it as a description of the real world. The real world is far too complex for any social scientist to incorporate every potential variable that could affect their model. As a result, things get abstracted; things like the decision making processes of people. Economists and social scientists know "rational actor" models are unrealistic, but they work well enough for what they are trying to do.
As for philosophy... anyone who would claim that for centuries philosophers, as a group, have assumed people are rational doesn't know what the hell they are talking about. Socrates and Plato certainly make no such assumption. Even a cursory reading of The Apology or Crito make it clear that while rational thinking is a human possibility it is not a universally realized one. When Criton visits Socrates under house arrest awaiting execution and urges him to flee from Athens, Socrates responds by telling Criton to not worry about what "the many" think or do. The many do not use reason, argues Socrates, therefore they do not act from knowledge but instead act randomly so worrying about it won't help. So, for Plato at least, rational thought is not the default position for human beings.
And Plato is not alone. Thinkers as diverse as Machiavelli, Nietzsche, Henri Bergson, and, especially, pragmatists like Charles Sanders Peirce and William James, make no assumptions regarding the rationality of man. The philosophy of Peirce would be especially relevant to understanding why subjects respond to these questions from Kahneman the way they do.
For Peirce the way human beings think is made up of a few mental methods, one of which is indeed the classic rational method of syllogism and deduction. However, it is much more common for us to use the process which Peirce called "abduction" in order to make educated guesses about the world. We do it all the time, Peirce argues, without even realizing it. Have you ever had a conversation with someone about another person, except you thought you were talking about Person X while your conversation partner thought you were talking about Person Y? We can go on for a little wile talking at cross purposes, even when the information doesn't exactly conform to what we knew of Person X, until something way out of whack causes us to ask "Wait. Who are we talking about?" and the problem is revealed. Now, not only do we do this all of the time, we are actually pretty good at it. Most of the time when we make these sorts of guesses we do so correctly. Only when we screw it up do we realize we have even been guessing in the first place.
Movie makers realize this fact as well. Actually, our guessing is the only thing which allows shocker surprise endings in the first place. Take the movie The Sixth Sense. The filmmakers know we will make a guess, or fill in the blanks, in a particular fashion even though we have not been given the information to make our guesses accurate. The movie only works if we continually make such guesses over the course of the film which, luckily for filmmakers, is exactly what we are prone to do.
Which brings us back to the magic questions which prove how dumb we all are. The reason they work in tripping up people is similar to the way The Sixth Sense works. They are not "simple arithmetic questions," they are riddles.
OK, lets look at these more closely:
Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?