The Monty Hall problem and Cognitive Dissonance
- From: Lance <LanceGary@xxxxxxxxx>
- Date: Tue, 8 Apr 2008 02:07:03 -0700 (PDT)
NYT
April 8, 2008
Findings
And Behind Door No. 1, a Fatal Flaw
By JOHN TIERNEY
The Monty Hall Problem has struck again, and this time it’s not merely
embarrassing mathematicians. If the calculations of a Yale economist
are correct, there’s a sneaky logical fallacy in some of the most
famous experiments in psychology.
The economist, M. Keith Chen, has challenged research into cognitive
dissonance, including the 1956 experiment that first identified a
remarkable ability of people to rationalize their choices. Dr. Chen
says that choice rationalization could still turn out to be a real
phenomenon, but he maintains that there’s a fatal flaw in the classic
1956 experiment and hundreds of similar ones. He says researchers have
fallen for a version of what mathematicians call the Monty Hall
Problem, in honor of the host of the old television show, “Let’s Make
a Deal.”
Here’s how Monty’s deal works, in the math problem, anyway. (On the
real show it was a bit messier.) He shows you three closed doors, with
a car behind one and a goat behind each of the others. If you open the
one with the car, you win it. You start by picking a door, but before
it’s opened Monty will always open another door to reveal a goat. Then
he’ll let you open either remaining door.
Suppose you start by picking Door 1, and Monty opens Door 3 to reveal
a goat. Now what should you do? Stick with Door 1 or switch to Door
2?
Before I tell you the answer, I have a request. No matter how
convinced you are of my idiocy, do not immediately fire off an angry
letter. In 1991, when some mathematicians got publicly tripped up by
this problem, I investigated it by playing the game with Monty Hall
himself at his home in Beverly Hills, but even that evidence wasn’t
enough to prevent a deluge of letters demanding a correction.
Before you write, at least try a few rounds of the game, which you can
do by playing an online version of the game. Play enough rounds and
the best strategy will become clear: You should switch doors.
This answer goes against our intuition that, with two unopened doors
left, the odds are 50-50 that the car is behind one of them. But when
you stick with Door 1, you’ll win only if your original choice was
correct, which happens only 1 in 3 times on average. If you switch,
you’ll win whenever your original choice was wrong, which happens 2
out of 3 times.
Now, for anyone still reading instead of playing the Monty Hall game,
let me try to explain what this has to do with cognitive dissonance.
For half a century, experimenters have been using what’s called the
free-choice paradigm to test our tendency to rationalize decisions.
This tendency has been reported hundreds of times and detected even in
animals. Last year I wrote a column about an experiment at Yale
involving monkeys and M&Ms.
The Yale psychologists first measured monkeys’ preferences by
observing how quickly each monkey sought out different colors of M&Ms.
After identifying three colors preferred about equally by a monkey —
say, red, blue and green — the researchers gave the monkey a choice
between two of them.
If the monkey chose, say, red over blue, it was next given a choice
between blue and green. Nearly two-thirds of the time it rejected blue
in favor of green, which seemed to jibe with the theory of choice
rationalization: Once we reject something, we tell ourselves we never
liked it anyway (and thereby spare ourselves the painfully dissonant
thought that we made the wrong choice).
But Dr. Chen says that the monkey’s distaste for blue can be
completely explained with statistics alone. He says the psychologists
wrongly assumed that the monkey began by valuing all three colors
equally.
Its relative preferences might have been so slight that they were
indiscernible during the preliminary phase of the experiment, Dr. Chen
says, but there must have been some tiny differences among its tastes
for red, blue and green — some hierarchy of preferences.
If so, then the monkey’s choice of red over blue wasn’t arbitrary.
Like Monty Hall’s choice of which door to open to reveal a goat, the
monkey’s choice of red over blue discloses information that changes
the odds. If you work out the permutations (see illustration), you
find that when a monkey favors red over blue, there’s a two-thirds
chance that it also started off with a preference for green over blue
— which would explain why the monkeys chose green two-thirds of the
time in the Yale experiment, Dr. Chen says.
Does his critique make sense? Some psychologists who have seen his
working paper answer with a qualified yes. “I worked out the math
myself and was surprised to find that he was absolutely right,” says
Daniel Gilbert, a psychologist at Harvard. “He has essentially applied
the Monty Hall Problem to an experimental procedure in psychology, and
the result is both instructive and counter-intuitive.”
Dr. Gilbert, however, says that he has yet to be persuaded that this
same flaw exists in all experiments using the free-choice paradigm,
and he remains confident that the overall theory of cognitive
dissonance is solid. That view is shared by Laurie R. Santos, one of
the Yale psychologists who did the monkey experiment.
“Keith nicely points out an important problem with the baseline that
we’ve used in our first study of cognitive dissonance, but it doesn’t
apply to several new methods we’ve used that reveal the same level of
dissonance in both monkeys and children,” Dr. Santos says. “I doubt
that his critique will be all that influential for the field of
cognitive dissonance more broadly.”
Dr. Chen remains convinced it’s a broad problem. He acknowledges that
other forms of cognitive-dissonance effects have been demonstrated in
different kinds of experiments, but he says the hundreds of choice-
rationalization experiments since 1956 are flawed.
Even when the experimenters use more elaborate methods of measuring
preferences — like asking a subject to rate items on a scale before
choosing between two similarly-ranked items — Dr. Chen says the
results are still suspect because researchers haven’t recognized that
the choice during the experiment changes the odds. (For more of Dr.
Chen’s explanation, see TierneyLab.)
“I don’t know that there’s clean evidence that merely being asked to
choose between two objects will make you devalue what you didn’t
choose,” Dr. Chen says. “I wouldn’t be completely surprised if this
effect exists, but I’ve never seen it measured correctly. The whole
literature suffers from this basic problem of acting as if Monty’s
choice means nothing.”
.
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