Tuesday, April 08, 2008
Monty Hall Strategy Shows McCain Heavily Favored
In the Science Times, John Tierney explains how the economist M. Keith Chen has challenged certain experiments in cognitive dissonance, claiming that the researchers have fallen for a version of the Monty Hall Problem. You remember the old TV show “Let’s Make a Deal” which Monty Hall hosted. One game was the one with the three closed doors, one with a car behind it and the other two with a goat behind it. The idea is to pick the door with the car, unless, of course, you have a car and need a goat.
Now the cognitive dissonance part has to do with which of three colors of M&Ms monkeys prefer. I will leave you to the Tierney article for that, as my concern here is with a problem (albeit possibly related), how people choose between the three current presidential candidates. But first I will let Mr. Tierney explain how the Monty deal works, as I still don’t believe it.
“He shows you three closed doors, … If you open the one with the car, you win it. You start by picking a door, but before it’s opened Monty will always open another door to reveal a goat. Then he’ll let you open either remaining door. Suppose you start by picking Door 1, and Monty opens Door 3 to reveal a goat. Now what should you do? Stick with Door 1 or switch to Door 2? This answer goes against our intuition that, with two unopened doors left, the odds are 50-50 that the car is behind one of them. But when you stick with Door 1, you’ll win only if your original choice was correct, which happens only 1 in 3 times on average. If you switch, you’ll win whenever your original choice was wrong, which happens 2 out of 3 times.”
We have three presidential candidates (doors) and the all important independent voter will determine which goes to the White House. Two doors have donkeys behind them (goats – both ungulates by the way) and one an elephant (car – both big). The voters will pick one door, and then one with a goat behind it will open to let either Obama or Hillary out of the race. Now the independent, most of whom are voting in the Democratic contest, must choose to stay or switch. Enough of the voters will know that the best strategy to avoid a mistake is to switch. That will be McCain, two out of three on the average.
You can prove this to yourself by playing the game on the NYT web site.