After struggling for a day to convince myself that one should switch doors in the Monty Hall Problem, I came across this article by John TierneyAnd Behind Door No. 1, a Fatal Flaw . Excerpt:
"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.
.....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.
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."
P.S. See also the discussion here.
P.S.2. NYTimes has now a provision to play the Monty Hall Problemonline.