APICS Pikes Peak Colorado Chapter

EDITORIAL

The Monty Hall Paradox: Lessons for Management

By Ira Smolowitz, Ph.D.

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Wikipedia, the free encyclopedia, indicates:

The Monty Hall problem is a puzzle involving probability loosely based on the American game show “Let’s Make a Deal.” The name comes from the show’s host, Monty Hall. A widely known, but problematic (see below) statement of the problem is from Craig F. Whitaker of Columbia, Maryland, in a letter to Marilyn vos Savant’s September 9, 1990, column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick).

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

The problem is also called the Monty Hall paradox; it is a veridical paradox in the sense that the solution is counterintuitive, although the problem does not yield a logical contradiction. 1 Marilyn vos Savant said that you should always change and pick the final door because the chances are 2 in 3 that there will be a car behind that door. But if you use your intuition you think that chance is 50-50 because you think there is an equal chance that the car is behind any door. Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things that they said:

I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error.
Robert Sachs, Ph.D., George Mason University

There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame!
Scott Smith, Ph.D., University of Florida

I am in shock that after being corrected by at least three mathematicians, you still do not see your mistake.
Kent Ford, Dickinson State University

I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for help with future columns.
W. Robert Smith, Ph.D., Georgia State University

You are utterly incorrect…How many irate mathematicians are needed to get you to change your mind?
E. Ray Bobo, Ph.D., Georgetown University

If all those Ph.D.’s were wrong, the country would be in very serious trouble.
Everett Harman, Ph.D., U.S. Army Research Institute. 2

Marilyn vos Savant is correct. The experts are wrong and intuitive reasoning is faulty in this case. I have highlighted my assessment of the lessons to be derived from the above problem. Mark Haddon nicely provides a solution to the Monty Hall Paradox. He states…you can work it out …by making a picture of all the possible outcomes like this.

So if you change, 2 times out of 3 you get a car. And, if you stick, you only get a car 1 time out of 3. And this shows that intuition can sometimes get things wrong. An intuition is what people use in life to make decisions. But logic can help you work out the right answer.3 A decision table may also be helpful because it identifies all of the possible conditions:

Note that switching your selection results in winning twice as often as staying with the original selection.4

The attention that the solution to this problem has generated has been substantial. From a management perspective, it seems to me, it calls attention to the pitfalls of relying heavily on instinct or intuition.

Consider the following:

45% of corporate executives now rely more on instinct than on facts and figures in running their businesses, according to a survey conducted in May 2002 by executive search firm Christian & Timbers.

Intuition fails when it leads to a conclusion that is erroneous. When intuition fails, it puts up quite a fight. As a demonstration, try out the “Monty Hall Problem.” This is a simple analytic exercise that yields a solution that is counter-intuitive to most people.

As I’ve presented this exercise to numerous groups, I find that more senior the audience, the more reluctant they are to embrace the solution. Many senior executives argue strenuously that they are right and the accepted solution is wrong. These executives have relied so successfully on their intuition for so long that given a choice between the correct answer and their intuition, they will choose intuition.5

Intuition is a natural mental process. Executives, in my opinion, must be particularly aware that in a complex business environment, counter-intuitive reasoning must be fully considered.

References
1. Downloaded 10/16/2006 from http://eniwikipedia.org/wikiMonty_Hall_problem, p. 1
2. Haddon, Mark “The Curious Incident of the Dog in the Night-Time.” Vintage Books, 2003, pp. 62-64
3. Ibid., pp. 64-65
4. “The Monty Hall Problem,” downloaded 10/16/2006 from http://www.coastaltech.com/monty.htm, p. 2
5. “Evolve Your Intuition,” downloaded 10/16/2006 from http://mysite.verizonnet/vze4dvjj/id18.html, pp. 1-2
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Articles printed with the permission of Dr. Ira Smolowitz, Professor of Finance and Dean, Bureau of Business Research and Program Development at American International College, Springfield, MA.
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Page updated: May 21, 2007 8:38 AM

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