Who's behind the door? A president or a goat?

A recent article by John Tierney in the New York Times discusses the Monty Hall problem. (Featured in the old game show “Let’s Make a Deal” with host Monty Hall). This is a math problem with a psychological component, addressing probability as well as choice and decision-making.

The problem goes like this: You have three doors. Behind one is a car; behind the other two are goats. You win the car if you pick the right door.

So you pick one door (say, Door 1), but before it is opened, the game host opens one of the other doors (say, Door 3) to reveal a goat. You now get to decide whether you’ll stick with your original choice (Door 1) or switch to Door 2. Which one gives you a better chance of winning?

According to John Tierney, you may think that your chances are 50-50 no matter which of the remaining two doors you choose, but in reality you’ll be better off switching to the other door. Why? Because your chance of picking the right door out of three would be 1:3, while your chances of picking the wrong door would be 2:3. So there’s a greater chance you picked the wrong door and would be better off switching to the other door (though there is some discussion of the validity of this probability if your first choice was completely random).

Interesting concept.

Now imagine that there are three doors. Behind one is a great president and behind the other two are goats. If you pick the right door, the country will prosper, but if you pick a goat, it will go downhill from here.

You randomly pick Door 1. The game host opens Door 3 and reveals John McCain. You know that behind the other two doors are Hillary Clinton and Barack Obama. But you don’t know who’s behind which door, and you don’t know who’ll be the great president and who’ll be the goat.

What should you do?

Maybe you should ask the audience to help you. Assume that the rest of the world are sitting on the other side of the stage and can see what’s behind the doors. Sometimes the outside perspective provides an advantage.

It looks like the audience will tell you to pick the door that leads to Obama. He’s the overwhelming favorite of people in Europe and everywhere else, as this piece by Shmuel Rosner points out.

But of course Americans don’t care what the rest of the world thinks. Or they wouldn’t have reelected George W. Bush in 2004. “How can 59,054,087 people be so DUMB?” was a headline in Britain’s Daily Mirror after the 2004 election. And you’ve got to admit the Europeans were right on this one. So maybe they’ve got it right again.

OK, of course we shouldn’t pick a president based on what people in other countries think. But it doesn’t hurt to listen to some common sense.

And of course, picking a president isn’t a completely random game. We have plenty of information on which to base our decision. But when it comes down to it, we can never know for sure. We’ll just have to hope we’re picking the right door.