The Monty Hall Problem and Monkeys

The question here is if you have a group of monkeys who like red, blue and green M&M's about equally, experiments have shown that:

1. if you give the monkey a choice of two M&M's of two colors at first

2. then give him a choice of two M&M's not the same color as he chose

3. he will reject the same color twice

For example, you give a monkey a red M&M and a blue M&M, and he picks the red one. Then you give him a blue M&M and a green one.

Two-thirds of the time, he will reject the blue M&M the second time as well.

Psychologists have made a big deal about this, claiming that having rejected the blue M&M the first time, the monkey will reject it the second time, "rationalizing" that he doesn't like blue M&M's anyway, to avoid the thought that maybe he made the wrong choice.

This is a mis-reading of statistical evidence. Even the smallest difference in the monkey's preferences will account perfectly for the statistical results found in these experiments.

To see how this works, let's take a more obvious example:

There are three items:

1. a sugar cube

2. a lettuce leaf

3. a pepper corn

Let's assume that the monkey loves sugar, will eat lettuce, and hates pepper.

We try the three possible scenarios with the monkeys countless times, and statistically we see that if he rejected something the first time, he rejected it the second time exactly 67% of the time.

Here's why. There are three possible pairs of articles offered as a first choice:

1. sugar & lettuce

2. sugar & pepper

3. pepper & lettuce

The guiding principle is that the monkey will NOT eat the pepper. For the three cases above, here are the first two choices made by the monkey:

  round 1   round 2

1. sugar / lettuce (doesn't reject the same thing twice)

2. sugar / lettuce (rejects pepper both times)

3. lettuce / sugar (rejects pepper both times)

Two-thirds of the time, the monkey will reject the same thing the second round that he rejected the first round.

Is it because he's trying to rationalize his choice? Or just that he doesn't want to burn his tongue?

It is obvious from this example that there is no deep psychological phenomenon at work. It's just simple preference for one thing over another.

In order for such an experiment to have psychological implications, it would be necessary to prove that the monkey has an absolutely equal preference for the three articles.

This would be the case if the element he chose first varied randomly.

For example, if the same monkey, when tested on separate occasions, chose the lettuce, the sugar, and the pepper with equal frequency, then we would be closer to some sort of psychological discovery.

The New York Times
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