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Analyzing risk: The Monty Hall problem


COFES (Congress on the Future of Engineering Software) is located each spring in Scottsdale, Ariz. The agenda brings many smart people together to discuss aspects of software, with some emphasis on design aids. I have been attending this conference for a decade or so and, to make it clear, I don’t get paid, but do get expenses for a nice, high-IQ vacation. I usually give a talk or a fireside chat.

This year, the food was excellent, stimulation was a plus and the speakers were entertaining. However, I had a little problem with my heart versus my head. Let me explain.

Richard Riff, a retired Ford technical fellow, gave an astounding talk on the role of risk and design, with particular attention on actions we can or should take in response to analysis. We all face risks each day, and risk is always a consideration in any decision. But how we think about risk needs to be changed, Dr. Riff says.

Now here’s the problem with my head: He presented an interesting conundrum called the Monty Hall problem — named after the host of the television game show Let’s Make a Deal. This problem was best described by American columnist Marilyn vos Savant in her “Ask Marilyn” column in Parade magazine in 1990, so I will quote her directly.

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“Suppose you’re on a game show and you are given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say, number one [but the door is not opened]. And the host, who knows what’s behind the doors, opens another door, say, number three, which has a goat. He says to you, ‘Do you want to pick door number two?’ Is it to your advantage to switch your choice?”

If you do not switch, the chances of winning is only one in three. If you change your choice, you have a two-thirds chance of success. It is not my intention here to explain why this is so. Going to the web and searching “Monty Hall problem” will list many explanations. All of them seem against common sense. My head gets it, but my heart is another story.

How do I reconcile my training and my emotions? I use my right brain. I do not, in my heart, believe that they should switch doors — but mathematics doesn’t lie, so I thought of the simulation method. There are many simulation programs on the web, and they all confirm that you should switch doors and double your odds. But humans still don’t get it. Then, I found out that pigeons do get it, outperforming humans at this problem.

How do we know this? Scientists simulated this dilemma with pigeons using an apparatus with three keys. During the experiment, the keys lit up to show that a prize was available. After the birds pecked a key, one of the keys the bird did not choose deactivated, showing it was a wrong choice, and the other two lit up again. The pigeons were rewarded with bird feed if they made the right choice. The birds quickly reached the best strategy by switching 96 percent of the time after a month of testing. Meanwhile, students almost never got it right. Twelve undergraduate volunteers failed to choose the best strategy with a similar apparatus, even after 200 trials each. Computers and pigeons all think switch! I have to buy it, but I don’t have to like it.

Are there other situations that we have difficulty accepting? Absolutely. For example, is Lean manufacturing a good thing? Intuitively, I believe that moderate Lean manufacturing is a good thing, but pushing the envelope too far increases the likelihood of a black swan event. As a hammock physicist, I have trouble with the environmentalists saying that we need to be “sustainable” in our treatment of energy. They must mean a different “sustainability” than the scientists mean.

Indeed, Riff’s talk really got me thinking. We as engineers seem to think that the only thing that counts is how we think. But the truth is that we must deal with the world the way it is, not the way we think it should be.

Who would have thought that such valuable lessons could be learned from an old game show?

This column originally appeared in the June 2012 issue of Manufacturing AUTOMATION.