The most important item first. I promised bonus points to anyone who could tell us the author of the song “My Whole World Lies Waiting Behind Door Number 3.” If you answered Jimmy Buffet, then you are partially correct (and a Parrot Head). The complete answer is that the co-writer was Steve Goodman (no relation to John).
And now to the question: Should I switch from door number one to door number three? To recap: You were offered three doors to chose from, only one has a big prize, you pick door one, door two is revealed to show that it does not contain the big prize. Should you change from door one to door three? (You can see the details in my previous post.)
There has been a raging debate over this for a number of years. In fact, you can see many of the proofs if you Google “Monty Hall Paradox.” And, in spite of the messages your inner genius may be giving you, the correct answer is to switch doors. The reasoning is very similar to that we used for the three prisoners dilemma discussed in the previous blog
. (People seem to have an easier job accepting the conclusion of the three prisoners dilemma over that of the Monty Hall Paradox — hence, it is sometimes easier to start there.) Most people looking at the situation say that it doesn’t matter if you change — there are two doors available and that means there is a 50/50 chance that one of the doors is a winner. But, just as with the prisoners, the combined likelihood of door two and three being the winner stays at 66 percent, which means that there is a two out of three chance that door three is now the winner. Another way to think of it: If you change and you made the correct choice the first time, then one-third of the time you will change and lose. If you change and you made the wrong choice the first time, then two-thirds of the time you will change and win.
Okay, there is a chance you are still in the mental tunnel that says it is a 50/50 chance. And this usually comes from those who argue that what happened in the past has no effect on the fact that there are now two choices and an equal chance for each to hold the big prize. The assumption that the prior actions have no effect is false, and that is at the core of the mental tunnel in which people trap themselves. If you are still unconvinced, I would suggest you experiment. Try this with friends, set up your own game show, write your own computer program. (That was my personal “Aha!” moment. To prove that there was no benefit in changing, I wrote a program. And, while building the logic, I suddenly saw why you should always change.) If you actually play this through, you will see that switching provides the best opportunities.
If you would still like to plead your case, feel free to use the comments sections below. But I would also suggest you peruse the net and see some of the better articulated discussions of this issue.
And so we come to the end of our sojourn through the realms of mental tunnels. If you just joined us, you may want to go back to the beginning and work your way through some of the exercises
. If you want to explore more, I refer you to the book I previously suggested: Inevitable Illusions
by Massimo Piattelli-Palmarini. Two other very good books I have used while putting this together are Damned Lies and Statistics
by Joel Best and How to Lie With Statistics
by Darrell Huff and Irving Geiss. (The latter was first published in 1954, but the mere fact it is still in print shows just how valuable it is.)
While I was able to provide some audit examples, it was not my intent to give you specific tools to use. Rather, my purpose was to start you thinking about the assumptions you may be making. Ultimately, this is about reminding each of us to take a look at the suppositions we make, the way we come to conclusions, and the way we misuse statistics and logic.