Tuesday, April 08, 2008

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Oh, Monty, Monty, Monty...

Ah, the Monty Hall Problem. It’s been done to death on the Internet, and long before — back in the pre-Internet days when networking was often by dial-up, mouse-clicking hadn’t been invented yet, and people posted pontifications by typing green text on black 80-character-wide screens. That scene at the beginning of 2001: A Space Odyssey, where the apes are going nuts? Yeah, the movie doesn’t say so, but the obelisk is one of the doors and it’s all an argument about the Monty Hall Problem.

But the Internet has a way of making things long settled resurface, resurrect, as it were, like zombies in a George Romero film. Everything you could possibly want to know about the Monty Hall Problem (well, except for the endless, endless, endless arguments about it) is summarized nicely on Wikipedia. Or you could go to Google for lots more, including this cute video that explains the problem and its solution quite well.

So what can the New York Times — or anyone else — possibly add? Well, the Times reports that Dr Keith Chen, of Yale University, has identified flaws in behavioral research going back at least 50 years... flaws rooted in the Monty Hall Problem:

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.”

The Times article then goes on to explain the flaw in an experiment involving monkeys selecting preferred colours of M&M candies. OK, look: as someone who sorts M&Ms by colour and saves the best for last (orange, of course), I find the surprise only to be that it took them 50 years to figure out that they got it wrong.

But, well, it’s not really all about M&Ms, and Dr Chen contends that they have, indeed, been misinterpreting studies involving choice for all these years:

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.”

In any case, you should check out the article, if only to play the cool simulation that they have there.

 

I chose my apparel, wore a beer barrel
And they rolled me to the very first row
I held a big sign that said “Kiss me I’m a baker,
and Monty I sure need the dough!”
Then I grabbed that sucker by the throat until he called on me
’Cause my whole world lies waiting behind door number three

—— Jimmy Buffett

1 comment:

Dr. Momentum said...

Home teams, political parties, candidates...

Polarization!