Do the Math

by Damon Gambuto     Department: Science & Society

Fifty years after a landmark psychological study into the human propensity to rationalize cognitive inconsistencies, an economist has revealed that the measuring procedures used were flawed.  I know you must be shocked that a social scientific study had some failings.  No?  Okay, me neither, but let's take a look at what went wrong and why doing the math is so important.

In 1957 Leon Festinger proposed the theory of 'cognitive dissonance' after performing a study on belief persistence in members of a cult.  Festinger's work ("When Prophecy Fails") was a landmark study that has been repeated in various iterations hundreds of times since.  Here's the thing.  Leon got the math wrong.

M. Keith Chen, an economist at the Yale School of Management has shown that there is a fundamental failing in Festinger's methodology (along with a lot of other social scientists' methodologies).  Festinger and subsequent researchers misunderstand the statistical impact of removing a choice in their experiments.  The experimental procedure seemed mathematically sound, but the researchers fell for a basic misstep in the understanding of what mathematicians refer to as the Monty Hall Problem.  You can read all about this in a NY Times article here.

To be fair, the Monty Hall problem is counterintuitive.  Here's the basic idea.:

Three doors.  Behind two are goats.  The third conceals. . . A NEW CAR!  (Perhaps you remember the television game show and its host Monty Hall).

Okay, so you pick one of the doors.  Before Monty let's you know if you've won, he opens one of the other two doors and reveals a goat.  Then Monty. . . well. . . offers to make you a deal (of sorts).  He says you can either remain with the door you've chosen or switch to the other unopened door.  What will it be?  

Right now you might be thinking:

What does it matter?  I have a one in two chance, switching doesn't increase my odds of winning.

Allow me to suggest a career in social psychology for you.  Turns out, switching is the right answer.  Why?  Because the reveal of the goat has changed the value of switching.  Okay, be patient with me.  I haven't taught math in years.  

When you first chose the door, you had a one in three chance of picking the one hiding the car.  Revealing the goat behind the door and then staying with your original choice doesn't change your odds of having picked correctly.  Because Monty is compelled to reveal a goat for the game to proceed, you can increase your odds of getting the car (from 33 1/3% of the time to about 68%) by switching doors.  This is because you were more likely to have selected a goat initially.  Still unclear?  I'll take the blame.  You can play the game and get an explanation here.

Now even the psychologists are coming around.  The Times article quotes the Harvard's Daniel Gilbert as saying: "I worked out the math myself and was surprised to find that he was absolutely right. He has essentially applied the Monty Hall Problem to an experimental procedure in psychology, and the result is both instructive and counter-intuitive."
The article goes on to say that Gilbert is not convinced that the same flaw is extant in other related psychological experiments.  Maybe this opinion alone is enough to convince you of the existence of cognitive dissonance. 

I only tease Daniel Gilbert because I like him.  Just an FYI: he wrote a compelling book that sounds like a self-help tome, but is actually a fun and enlightening look at psychology and neuroscience called STUMBLING ON HAPPINESS.  (I read it on a plane and almost didn't hate the experience of hurtling though the sky in an aluminum tube surrounded by swollen American air travelers.)

So I took the easy shot at Gilbert, but there was actually a point there.  That is to say, I'm not making the case that cognitive dissonance doesn't have anything to say about the human condition.  At the very least it is a wonderfully useful literary construct and (I think more likely) a real and adaptive feature of human consciousness. 

What I am trying to point out is that what is intuitive is often wrong.  Committing to getting the answer through sound reasoning and solid mathematics is the way for all science - even the kinds that aren't so science-y (I'm looking at you social sciences) - to get the right answer and reveal truths that are hidden by so many proverbial doors. 

So let's remember to do the math.  Otherwise we're just kid-ding ourselves.  (Yeah, I just used the 'kid'  pun.  Get over it.)

Tags: cognitive dissonance, Daniel Gilbert, Leon Festinger, Monty Hall Problem, psychology

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